Springer Series in Advanced Manufacturing

Series Editor
Professor D. T. Pham Intelligent Systems Laboratory WDA Centre of Enterprise in Manufacturing Engineering University of Wales Cardiff PO Box 688 Newport Road Cardiff CF2 3ET UK

Other titles in this series
Assembly Line Design B. Rekiek and A. Delchambre Advances in Design H.A. ElMaraghy and W.H. ElMaraghy (Eds.) Effective Resource Management in Manufacturing Systems: Optimization Algorithms in Production Planning M. Caramia and P. Dell’Olmo Condition Monitoring and Control for Intelligent Manufacturing L. Wang and R.X. Gao (Eds.) Optimal Production Planning for PCB Assembly W. Ho and P. Ji Trends in Supply Chain Design and Management H. Jung, F.F. Chen and B. Jeong (Eds.) Process Planning and Scheduling for Distributed Manufacturing L. Wang and W. Shen (Eds.) Collaborative Product Design and Manufacturing Methodologies and Applications W.D. Li, S.K. Ong, A.Y.C. Nee and C. McMahon (Eds.)

R. Venkata Rao

Decision Making in the Manufacturing Environment
Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods

123

R. Venkata Rao, PhD Department of Mechanical Engineering Sardar Vallabhbhai National Institute of Technology, Surat Ichchanath Surat 395 007 Gujarat State India

British Library Cataloguing in Publication Data Rao, R. Venkata Decision making in the manufacturing environment : using graph theory and fuzzy multiple attribute decision making methods. - (Springer series in advanced manufacturing) 1. Production management - Decision making 2. Graph theory 3. Fuzzy decision making 4. Multiple criteria decision making I. Title 658.5’036 ISBN-13: 9781846288180 Library of Congress Control Number: 2007926809 Springer Series in Advanced Manufacturing ISSN 1860-5168 ISBN 978-1-84628-818-0 e-ISBN 978-1-84628-819-7 Printed on acid-free paper © Springer-Verlag London Limited 2007 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. 987654321 Springer Science+Business Media springer.com

Dedicated to my parents, Sujatha Rao (wife), and Jaya Lakshmi (daughter)

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Foreword

Manufacturing technology plays a vital role for the development of a country’s industrial growth and largely dictates the trend of the economy. Liberalization and globalization with reformed industrial trade policies have made manufacturing a key element to address global competition. In the last 20 years, strategic thinking has overtaken single-minded cost reduction and cost minimization in manufacturing. Consequently, the pursuit of cost, quality, flexibility, dependability and timeliness has replaced the singleminded cost reduction in manufacturing firms, which was the norm in manufacturing until the 1970s. Now, manufacturers find competitive advantage through better design, improved customer satisfaction, quick response, faster newproduct introduction, and other goals overshadowed in the past by the sole pursuit of cost reduction. The new engineering challenges require systematic and integrated planning and optimization approaches in the manufacturing environment. In this context, the aim of a manufacturing system is to achieve overall performance, utilizing resources in development, design, production, delivery and support of products. Decision making in the manufacturing environment is a strategic topic, especially in connection with the complexity of driving forces and factors influencing manufacturing systems dynamics. The decision-making exercise can be implemented in the manufacturing environment at different stages, if appropriate procedures are made available to the designers, manufacturing engineers, production planners, and managers. These aspects are considered in the present book using graph theory and fuzzy MADM methods. Professor R. Venkata Rao has become known as one of the leading experts in the field of decision making related to manufacturing environment. I congratulate him on his achievement, and believe that the book is highly appropriate for use by academicians, designers and practitioners, manufacturing engineers, production planners, marketing managers, applied researchers in industry, academic institutes, R&D organizations, and all decision makers in the manufacturing environment.

Surat, Gujarat, India 4th December 2006

(Prof. P. D. POREY) Director, S. V. National Institute of Technology

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Preface

The purpose of this book is to demonstrate how the graph theory and matrix approach as well as fuzzy multiple attribute decision-making methods can be effectively used for decision making in various situations of the manufacturing environment. The book is divided into two parts. In Part 1, an introduction to the decision-making situations in the manufacturing environment, graph theory and matrix approach as a decision-making method, classical MADM methods, and a logical approach to solve fuzzy MADM problems are presented. In Part 2, the applications of these methods to various real manufacturing situations are presented. The book documents the latest research works, and a significant number of these are original studies of mine published in various national and international journals and conference proceedings. As can be seen from the topics covered, the book deals with most situations in the manufacturing environment (e.g., manufacturing processes such as machining, welding, casting, forming and modern machining methods; advanced manufacturing technologies such as CAD/CAM, robotics, FMS, CIMS, and rapid prototyping; environmentally conscious design and manufacturing, environmental impact assessment; vendor selection, etc.). Both graph theory and fuzzy MADM approaches have been successfully applied to various manufacturing situations, and the results are presented. A thorough literature survey on each topic, real case studies, and computer codes have also been included. Thus, the book is expected to become essential reading for the industry and academia, as it makes decision making easier, logical, systematic, efficient, and effective. I am grateful to Anthony Doyle and Simon Rees of Springer-Verlag, London, for their support and help in producing this book. I wish to thank various researchers and the publishers of international journals for giving me the permission to reproduce certain portions of their published research works. I gratefully acknowledge Prof. P. D. Porey who has written a nice foreword. My special thanks go to my colleagues at SVNIT, Surat. While every attempt has been made to ensure that no errors (printing or otherwise) enter the book, the possibility of these creeping is always there. I would be grateful to the readers if these errors are pointed out. Suggestions for further improvement of the book will be thankfully acknowledged. (R. Venkata Rao)

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Contents

Part 1
1

Introduction to Decision Making

Introduction to Decision Making in the Manufacturing Environment ................................................................................................. 3 1.1 Introduction.......................................................................................... 3 1.2 Decision-making Methods Used .......................................................... 5 Graph Theory and Matrix Approach as a Decision-making Method...... 7 2.1 Introduction.......................................................................................... 7 2.2 Machinability Attributes Digraph ....................................................... .8 2.3 Matrix Representation of the Digraph................................................ 10 2.4 Machinability Index ........................................................................... 19 2.5 Identification and Comparison of Work Materials............................. 21 2.5.1 Identification of Work Materials ........................................... 21 2.5.2 Comparison of Work Materials ............................................. 22 2.6 Methodology of GTMA as a Decision-making Method .................... 23 References .................................................................................................... 24 Introduction to Multiple Attribute Decision-making (MADM) Methods....................................................................................................... 27 3.1 Introduction........................................................................................ 27 3.2 Multiple Attribute Decision-making Methods ................................... 28 3.2.1 Simple Additive Weighting (SAW) Method ......................... 28 3.2.2 Weighted Product Method (WPM) ........................................ 29 3.2.3 Analytic Hierarchy Process (AHP) Method........................... 29 3.2.4 Revised Analytic Hierarchy Process (RAHP) Method .......... 32 3.2.5 Multiplicative Analytic Hierarchy Process (MAHP) Method................................................................................... 32 3.2.6 TOPSIS Method..................................................................... 32 3.2.6.1 Entropy Method........................................................ 34 3.2.6.2 Standard Deviation Method...................................... 35 3.2.6.3 AHP Method ............................................................ 35

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3.2.7 Modified TOPSIS Method..................................................... 35 3.2.8 Compromise Ranking Method (VIKOR)............................... 36 3.3 Sensitivity Analysis............................................................................ 37 3.4 Group Decision Making (GDM) ........................................................ 38 References .................................................................................................... 39 4 A Logical Approach to Fuzzy MADM Problems..................................... 43 4.1 Introduction........................................................................................ 43 4.2 Method Proposed by Chen and Hwang (1992.................................... 44 4.2.1 Converting Linguistic Terms to Fuzzy Numbers................... 44 4.2.2 Converting Fuzzy Numbers to Crisp Scores.......................... 44 4.3 Demonstration of the Method ............................................................ 45 References .................................................................................................... 49

Part 2
5

Applications of GTMA and Fuzzy MADM Methods in the Manufacturing Environment

Material Selection for a Given Engineering Application ........................ 53 5.1 Introduction........................................................................................ 53 5.2 Examples............................................................................................ 55 5.2.1 Example 1 .............................................................................. 56 5.2.1.1 Application of GTMA .............................................. 56 5.2.1.2 SAW Method............................................................ 58 5.2.1.3 WPM ........................................................................ 59 5.2.1.4 AHP and its Versions ............................................... 59 5.2.1.5 TOPSIS Method ....................................................... 61 5.2.1.6 Modified TOPSIS Method ....................................... 62 5.2.1.7 VIKOR ..................................................................... 63 5.2.2 Example 2 .............................................................................. 64 5.2.2.1 Application of GTMA .............................................. 64 5.2.2.2 SAW Method............................................................ 65 5.2.2.3 WPM ........................................................................ 66 5.2.2.4 AHP and its Versions……… .......... ……………….66 5.2.2.5 TOPSIS Method ....................................................... 67 5.2.2.6 Modified TOPSIS Method ....................................... 67 References .................................................................................................... 68 Evaluation of Product Designs .................................................................. 71 6.1 Introduction........................................................................................ 71 6.2 Example ............................................................................................. 74 6.2.1 GTMA ................................................................................... 74 6.2.2 AHP Method.......................................................................... 76 6.2.3 TOPSIS Method..................................................................... 77 6.2.4 Modified TOPSIS Method..................................................... 79 References .................................................................................................... 79

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7

Machinability Evaluation of Work Materials.......................................... 81 7.1 Introduction........................................................................................ 81 7.2 Examples............................................................................................ 84 7.2.1 Example 1 .............................................................................. 84 7.2.1.1 Application of GTMA .............................................. 85 7.2.1.2 SAW Method............................................................ 87 7.2.1.3 WPM ........................................................................ 87 7.2.1.4 AHP and its Versions ............................................... 88 7.2.1.5 TOPSIS Method ....................................................... 88 7.2.1.6 Modified TOPSIS Method ....................................... 89 7.2.2 Example 2 .............................................................................. 90 7.2.2.1 Application of SAW Method ................................... 90 7.2.2.2 WPM ........................................................................ 91 7.2.2.3 AHP and its Versions ............................................... 91 7.2.2.4 TOPSIS Method ....................................................... 92 7.2.2.5 Modified TOPSIS Method ....................................... 93 References .................................................................................................... 93 Cutting Fluid Selection for a Given Machining Application .................. 97 8.1 Introduction........................................................................................ 97 8.2 Examples.......................................................................................... 103 8.2.1 Example 1 ............................................................................ 103 8.2.1.1 Application of GTMA ............................................ 104 8.2.1.2 SAW Method.......................................................... 105 8.2.1.3 WPM ...................................................................... 106 8.2.1.4 AHP and its Versions ............................................. 106 8.2.1.5 TOPSIS Method ..................................................... 107 8.2.1.6 Modified TOPSIS Method ..................................... 108 8.2.2 Example 2 ............................................................................ 109 8.2.2.1 GTMA .................................................................... 109 8.2.2.2 SAW Method.......................................................... 110 8.2.2.3 WPM ...................................................................... 111 8.2.2.4 AHP and its Versions ............................................. 111 8.2.2.5 TOPSIS Method ..................................................... 111 8.2.2.6 Modified TOPSIS Method ..................................... 112 References .................................................................................................. 112 Evaluation and Selection of Modern Machining Methods.................... 115 9.1 Introduction...................................................................................... 115 9.2 Examples.......................................................................................... 117 9.2.1 Example 1 ............................................................................ 117 9.2.1.1 GTMA .................................................................... 117 9.2.1.2 SAW Method.......................................................... 119 9.2.1.3 WPM ...................................................................... 120 9.2.1.4 AHP and its Versions ............................................. 120 9.2.1.5 TOPSIS Method ..................................................... 121 9.2.1.6 Modified TOPSIS Method ..................................... 121

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Example 2 ............................................................................ 121 9.2.2.1 GTMA .................................................................... 122 9.2.2.2 TOPSIS Method ..................................................... 123 9.2.2.3 Modified TOPSIS Method ..................................... 124 References .................................................................................................. 124 10 Evaluation of Flexible Manufacturing Systems..................................... 125 10.1 Introduction...................................................................................... 125 10.2 Examples.......................................................................................... 127 10.2.1 Example 1 ............................................................................ 127 10.2.1.1 Application of GTMA ............................................ 128 10.2.1.2 AHP and its Versions ............................................. 130 10.2.2 Example 2 ............................................................................ 131 10.2.2.1 Application of GTMA ............................................ 132 10.2.2.2 AHP and its Versions ............................................. 133 10.2.2.3 TOPSIS & Modified TOPSIS Methods ................. 134 10.2.2.4 Compromise Ranking Method (VIKOR) ............... 134 References .................................................................................................. 135 Machine Selection in a Flexible Manufacturing Cell ............................ 139 11.1 Introduction...................................................................................... 139 11.2 Example ........................................................................................... 141 11.2.1 Application of GTMA ......................................................... 142 11.2.2 SAW Method ....................................................................... 144 11.2.3 WPM.................................................................................... 145 11.2.4 AHP and its Versions........................................................... 145 11.2.5 TOPSIS Method................................................................... 146 11.2.6 Modified TOPSIS Method................................................... 146 References .................................................................................................. 147 Failure Cause Analysis of Machine Tools .............................................. 149 12.1 Introduction...................................................................................... 149 12.2 Identifying Contributing Events of a Failure Cause......................... 154 12.3 MTFCD and its Matrix Representation............................................ 156 12.4 General Machine Tool Failure Causality Function .......................... 158 12.5 Machine Tool Failure Cause Evaluation .......................................... 160 12.6 Machine Tool Failure Cause Analysis ............................................. 162 12.7 Methodology .................................................................................... 163 12.8 Summary .......................................................................................... 164 References……………………………………………………................... 165 Robot Selection for a Given Industrial Application .............................. 169 13.1 Introduction...................................................................................... 169 13.2 Examples.......................................................................................... 171 13.2.1 Example 1 ............................................................................ 172 13.2.1.1 Application of GTMA ............................................ 172 13.2.1.2 SAW Method.......................................................... 173

9.2.2

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13.2.1.3 WPM ...................................................................... 173 13.2.1.4 AHP and its Versions ............................................. 174 13.2.1.5 TOPSIS Method ..................................................... 174 13.2.1.6 Modified TOPSIS Method ..................................... 175 13.2.2 Example 2 ............................................................................ 176 13.2.2.1 Application of GTMA ............................................ 176 13.2.2.2 AHP and its Versions ............................................. 177 References .................................................................................................. 178 14 Selection of Automated Inspection Systems ........................................... 181 14.1 Introduction...................................................................................... 181 14.2 Example ........................................................................................... 182 14.2.1 Application of GTMA ......................................................... 182 14.2.2 AHP and its Versions........................................................... 185 14.2.3 TOPSIS Method................................................................... 186 14.2.4 Modified TOPSIS Method................................................... 186 References .................................................................................................. 186 Selection of Material Handling Equipment............................................ 187 15.1 Introduction...................................................................................... 187 15.2 Example ........................................................................................... 191 15.2.1 Application of GTMA ......................................................... 191 15.2.2 SAW Method ....................................................................... 192 15.2.3 WPM.................................................................................... 193 15.2.4 AHP and its Versions........................................................... 193 15.2.5 TOPSIS Method................................................................... 193 15.2.6 Modified TOPSIS Method................................................... 194 References .................................................................................................. 194 Selection of Rapid Prototyping Process in Rapid Product Development ............................................................................................. 197 16.1 Introduction...................................................................................... 197 16.2 Example ........................................................................................... 200 16.2.1 Application of GTMA ......................................................... 201 16.2.2 SAW Method ....................................................................... 203 16.2.3 WPM.................................................................................... 204 16.2.4 AHP and its Versions........................................................... 204 16.2.5 TOPSIS Method................................................................... 205 16.2.6 Modified TOPSIS Method................................................... 205 16.2.7 VIKOR................................................................................. 206 References .................................................................................................. 206 Selection of Software in Manufacturing Industries............................... 209 17.1 Introduction...................................................................................... 209 17.2 Example ........................................................................................... 211 17.3 General Remarks.............................................................................. 213 References .................................................................................................. 213

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Welding Process Selection for a Given Application .............................. 215 18.1 Introduction...................................................................................... 215 18.2 Example ........................................................................................... 216 18.2.1 GTMA ................................................................................. 216 18.2.2 SAW Method ....................................................................... 218 18.2.3 WPM.................................................................................... 218 18.2.4 AHP and its Versions........................................................... 218 18.2.5 TOPSIS Method................................................................... 219 References .................................................................................................. 219 Geometric Moldability Analysis of Parts ............................................... 221 19.1 Introduction...................................................................................... 221 19.2 Example ........................................................................................... 224 19.2.1 GTMA ................................................................................. 225 19.2.2 SAW Method ....................................................................... 226 19.2.3 AHP Method........................................................................ 226 19.2.4 TOPSIS Method................................................................... 227 19.2.5 Modified TOPSIS Method................................................... 228 19.3 General Remarks.............................................................................. 228 References .................................................................................................. 228 Evaluation of Metal Stamping Layouts .................................................. 231 20.1 Introduction...................................................................................... 231 20.2 Example ........................................................................................... 233 20.2.1 Application of GTMA ......................................................... 234 20.2.2 SAW Method ....................................................................... 236 20.2.3 WPM.................................................................................... 236 20.2.4 AHP and its Versions........................................................... 237 20.2.5 TOPSIS Method................................................................... 238 20.2.6 Modified TOPSIS Method................................................... 238 References .................................................................................................. 239 Selection of Forging Conditions for Forging a Given Component....... 243 21.1 Introduction...................................................................................... 243 21.2 Example ........................................................................................... 248 21.2.1 GTMA ................................................................................. 248 21.2.2 SAW Method ....................................................................... 249 21.2.3 WPM.................................................................................... 250 21.2.4 AHP Method........................................................................ 250 21.2.5 TOPSIS Method................................................................... 250 21.2.6 Modified TOPSIS Method................................................... 251 References .................................................................................................. 251 Evaluation of Environmentally Conscious Manufacturing Programs................................................................................................... 255 22.1 Introduction...................................................................................... 255 22.2 Example ........................................................................................... 257

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22.2.1 GTMA ................................................................................. 258 22.2.2 SAW Method ....................................................................... 259 22.2.3 AHP and its Versions........................................................... 260 22.2.4 TOPSIS Method................................................................... 260 22.2.5 Modified TOPSIS Method................................................... 261 References .................................................................................................. 262 23 Environmental Impact Assessment of Manufacturing Processes ........ 265 23.1 Introduction...................................................................................... 265 23.2 Example ........................................................................................... 268 23.2.1 GTMA ................................................................................. 270 23.2.2 AHP Method........................................................................ 271 23.2.3 TOPSIS Method................................................................... 272 23.2.4 Modified TOPSIS Method................................................... 274 References .................................................................................................. 274 Evaluation of Aggregate Risk in Green Manufacturing ....................... 277 24.1 Introduction...................................................................................... 277 24.2 Example ........................................................................................... 280 24.2.1 GTMA ................................................................................. 280 24.2.2 AHP Method........................................................................ 281 24.2.3 TOPSIS Method................................................................... 282 24.2.4 Modified TOPSIS Method................................................... 282 References .................................................................................................. 283 Selection of Best Product End-of-Life Scenario..................................... 285 25.1 Introduction...................................................................................... 285 25.2 Example ........................................................................................... 288 25.2.1 GTMA ................................................................................. 289 25.2.2 SAW Method ........................................................................ 290 25.2.3 WPM.................................................................................... 290 25.2.4 TOPSIS Method................................................................... 291 25.2.5 Modified TOPSIS Method................................................... 291 25.2.6 Compromise Ranking Method (VIKOR)............................. 292 References .................................................................................................. 292 Integrated Project Evaluation and Selection ......................................... 295 26.1 Introduction...................................................................................... 295 26.2 Example ........................................................................................... 299 26.2.1 WPM.................................................................................... 301 26.2.2 TOPSIS Method................................................................... 301 26.2.3 Modified TOPSIS Method................................................... 302 References .................................................................................................. 303 Facility Location Selection....................................................................... 305 27.1 Introduction...................................................................................... 305 27.2 Examples.......................................................................................... 306

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Contents

27.2.1 Example 1 ............................................................................ 306 27.2.1.1 GTMA .................................................................... 306 27.2.1.2 SAW Method.......................................................... 308 27.2.1.3 WPM ...................................................................... 308 27.2.1.4 AHP and its Versions ............................................. 309 27.2.1.5 TOPSIS Method ..................................................... 309 27.2.1.6 Modified TOPSIS Method ..................................... 310 27.2.2 Example 2 ............................................................................ 310 27.2.2.1 GTMA .................................................................... 311 27.2.2.2 AHP and its Versions ............................................. 312 References .................................................................................................. 312 28 Operational Performance Evaluation of Competing Companies......... 315 28.1 Introduction...................................................................................... 315 28.2 Example ........................................................................................... 316 28.2.1 Application of GTMA ......................................................... 317 28.2.2 SAW Method ....................................................................... 318 28.2.3 WPM.................................................................................... 318 28.2.4 AHP and its Versions........................................................... 318 28.2.5 TOPSIS Method................................................................... 319 28.2.6 Modified TOPSIS Method................................................... 319 References .................................................................................................. 319 Vendor Selection in a Supply Chain Environment................................ 321 29.1 Introduction...................................................................................... 321 29.2 Example 1 ........................................................................................ 323 29.2.1 GTMA ................................................................................. 324 29.2.2 TOPSIS Method................................................................... 326 29.3 Genetic Algorithms .......................................................................... 329 29.4 Proposed Methodology .................................................................... 330 29.5 Example 2 ........................................................................................ 331 29.6 General Remarks.............................................................................. 336 References .................................................................................................. 337 Group Decision Making in the Manufacturing Environment .............. 341 30.1 Introduction...................................................................................... 341 30.2 Example ........................................................................................... 342 30.2.1 Application of GTMA ......................................................... 343 30.2.2 SAW Method ....................................................................... 344 30.2.3 WPM.................................................................................... 344 30.2.4 TOPSIS Method................................................................... 345 30.2.5 Modified TOPSIS Method................................................... 345 30.3 General Remarks.............................................................................. 345 References .................................................................................................. 346

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Appendix Computer Codes ............................................................................... 347 Index .................................................................................................................... 371

Part 1
Introduction to Decision Making

1
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Introduction to Decision Making in the Manufacturing Environment

1.1 Introduction
Manufacturing is the backbone of any industrialized nation. Its importance is emphasized by the fact that, as an economic activity, it comprises approximately 20 to 30% of the value of all goods and services produced. A country’s level of manufacturing activity is directly related to its economic health. In general, the higher the level of manufacturing activity in a country, the higher the standard of living of its people. Manufacturing can be defined as the application of mechanical, physical, and chemical processes to modify the geometry, properties and/or appearance of a given starting material in the making of new, finished parts or products. This effort includes all intermediate processes required for the production and integration of a product’s components. The ability to produce this conversion efficiently determines the success of the company. The type of manufacturing performed by a company depends on the kinds of products it makes. Manufacturing is an important commercial activity carried out by companies that sell products to customers. In the modern sense, manufacturing involves interrelated activities that include product design and documentation, material selection, process planning, production, quality assurance, management, and marketing of products. These activities should be integrated to yield viable and competitive products. Manufacturing technologies have continually gone through gradual but revolutionary changes. These advancements in manufacturing technologies have brought about a metamorphism in the world industrial scene. They include CNC, CAD/CAM, FMS, robotics, rapid prototyping, environmentally sustainable technologies, etc., which have become an integral part of manufacturing. Parallel to this are rapid strides in the development of new products, and the emergence of an open economy leading to global competition. Manufacturing industries are compelled to move away from traditional setups to more responsive and dynamic ones. Many new concepts have emerged from these changes, sustained by strategies aimed at meeting the challenges arising from global markets. Product

4

Decision Making in the Manufacturing Environment

attributes like quality, reliability, cost, life-cycle prediction, and the organizational ability to meet market pressures like delivery and service, have come into focus. A long array of emerging technologies have opened up the potential for a variety of new products. Fast-changing technologies on the product front cautioned the need for an equally fast response from the manufacturing industries. The old, traditional model of ‘unfocused, short-term views and non-holistic vision’ is becoming replaced by the enlightened approach of ‘focused, holistic and strategic vision’. To meet the challenges, manufacturing industries have to select appropriate manufacturing strategies, product designs, manufacturing processes, work piece and tool materials, machinery and equipment, etc. The selection decisions are complex, as decision making is more challenging today. Necessary conditions for achieving efficient decision making consist in understanding the current and upcoming events and factors influencing the whole manufacturing environment, in exploring the nature of decision-making processes and the reach of different typologies of methods and techniques, and finally in structuring appropriately the decision-making approach based on a wide range of issues related to manufacturing systems design, planning, and management. Decision makers in the manufacturing sector frequently face the problem of assessing a wide range of alternative options, and selecting one based on a set of conflicting criteria. Some of the important decision-making situations in the manufacturing environment are listed below: Material selection for a given engineering application Evaluation of alternative product designs Machinability evaluation of work materials Cutting fluid selection for a given machining application Evaluation and selection of modern machining methods Evaluation and selection of flexible manufacturing systems Machine group selection in a flexible manufacturing cell Failure cause analysis of machine tools Robot selection for a given industrial application Selection of automated inspection systems Selection of material handling equipment Selection of a rapid prototyping process in rapid product development Selection of software for design and manufacturing applications Selection of the most appropriate welding process for a given job Mouldability analysis of parts Evaluation of metal stamping layouts Selection of forging conditions for a given component Evaluation of environmentally conscious manufacturing programs Environmental impact assessment of manufacturing processes Evaluation of aggregate risk in green manufacturing Selection of best product end-of-life scenario Integrated project evaluation and selection Facility location selection

Introduction

5

Operational performance evaluation of competing companies Vendor selection in a supply chain environment It must be noted that in choosing the right alternative, there is not always a single definite criterion of selection, and decision makers have to take into account a large number of criteria including technological, economic, ethical, political, legal, and social factors. There is a need for simple, systematic, and logical methods or mathematical tools to guide decision makers in considering a number of selection criteria and their interrelations. The objective of any selection procedure is to identify appropriate selection criteria, and obtain the most appropriate combination of criteria in conjunction with the real requirement. Thus, efforts need to be extended to identify those criteria that influence an alternative selection for a given problem, using simple and logical methods, to eliminate unsuitable alternatives, and to select the most appropriate alternative to strengthen existing selection procedures. This book presents such simple, systematic and logical methods.

1.2 Decision- making Methods Used
The methods included in this book for decision making in the manufacturing environment are: (i) Graph theory and matrix approach (ii) Fuzzy multiple attribute decision-making methods. Graph theory is a logical and systematic approach. The advanced theory of graphs, and its applications are very well documented. Graph/digraph model representations have proved to be useful for modeling and analyzing various kinds of systems and problems in numerous fields of science and technology. If the graph/digraph is complex, it becomes difficult to analyze it visually. This can be done by computer through the use of the matrix method. An equivalent matrix of the graph/digraph model can be defined. Graph theory and the matrix approach help in identifying attributes, and offer a better visual appraisal of the attributes and their interrelations. This approach is capable of handling the inherent errors, and can deal with any number of qualitative and quantitative attributes simultaneously. The method has axiomatic foundation, involves less computation, provides great emphasis on decision-making methodology, and offers a more objective, simple and consistent decision-making approach. In addition, identification and comparison of alternatives in terms of their similarity/ dissimilarity can be carried out. The application of graph theory and the matrix approach as a decision-making tool in manufacturing situations is relatively new, and this approach has not been used by previous researchers. In addition to graph theory and the matrix approach, some other important methods, known as multiple attribute decision-making (MADM) methods, are also used in this book for decision making in the manufacturing environment. These methods fall under the category of multiple criteria decision making (MCDM), i.e., decision making in the presence of multiple, generally conflicting criteria. Depending on the domain of alternatives, MCDM problems are usually subdivided

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Decision Making in the Manufacturing Environment

into continuous and discrete types. MCDM problems have two classifications: multiple objective decision making (MODM), and multiple attribute decision making (MADM). MODM methods have decision variable values that are determined in a continuous or integer domain with either an infinitive or a large number of alternative choices, the best of which should satisfy the decision maker’s constraints and preference priorities. MADM methods, on the other hand, are generally discrete, with a limited number of pre-specified alternatives. These methods require both intra- and inter-attribute comparisons, and involve explicit tradeoffs that are appropriate for the problem considered. Each decision matrix in MADM methods has four main parts, namely: (a) alternatives, (b) attributes, (c) weight or relative importance of each attribute (i.e., weight), and (d) measures of performance of alternatives with respect to the attributes. Of the many MADM methods, five methods are commonly used: the weighted sum method (WSM), weighted product method (WPM), four modes of the analytic hierarchy process (AHP), Revised AHP, and technique for order preference by similarity to ideal solution (TOPSIS). A compromise ranking method (VIKOR) is also included in this book as an MADM method. However, one of the most crucial problems in many decision-making methods is the precise evaluation of pertinent data. Often, the data are imprecise and fuzzy. It is desirable to develop decision-making methods to deal with this aspect. Classical MADM methods can not effectively handle problems with such imprecise information. To resolve this difficulty, fuzzy MADM methods are used. The purpose of this book is to demonstrate how graph theory and the matrix approach as well as fuzzy multiple attribute decision-making methods can be effectively used for decision making in various situations of the manufacturing environment. Some of the situations have been mentioned above. Further, the book presents the concept of group decision making, the process of making a judgment based upon the opinion of different individuals. Such decision-making is a key component to the functioning of an organization, because organizational performance involves more than just one individual’s action. Moving from a single decision maker to a multiple decision maker setting introduces a great deal of complexity into the analysis. However, this book suggests simple and efficient methods to make the analysis less complex. The book documents the latest research works related to each of the manufacturing situations listed. Further, it presents the real case studies under most of the topics, as well as results of application of the proposed methods and the comparisons. The methods described in this book will be very useful to the decision makers in the manufacturing sector, as these methods make decision making easier, logical, systematic, efficient, and effective. The next chapter describes the graph theory and matrix approach as a decisionmaking method in the manufacturing environment.

2
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Graph Theory and Matrix Approach as a Decision- making Method

2.1 Introduction
A graph G = (V, E) consists of a set of objects V = {v1, v2, ….} called vertices or nodes, and another set E = {e1, e2, ….}, of which the elements are called edges, such that each edge ek is identified with a pair of vertices. The vertices vi and vj associated with edge ek are called the end vertices of ek. The most common representation of a graph is by means of a diagram, in which the vertices are represented by small points or circles, and each edge as a line segment joining its end vertices. The application of graph theory was known centuries ago, when the longstanding problem of the Konigsberg bridge was solved by Leonhard Euler in 1736 by means of a graph. Since then, graph theory has proved its mettle in various fields of science and technology such as physics, chemistry, mathematics, communication science, computer technology, electrical engineering, sociology, economics, operations research, linguistics, internet, etc. Graph theory has served an important purpose in the modeling of systems, network analysis, functional representation, conceptual modeling, diagnosis, etc. Graph theory is not only effective in dealing with the structure (physical or abstract) of the system, explicitly or implicitly, but also useful in handling problems of structural relationship. The theory is intimately related to many branches of mathematics including group theory, matrix theory, numerical analysis, probability, topology, and combinatorics. The advanced theory of graphs and their applications are well documented (Harary, 1985; Wilson and Watkins, 1990; Chen, 1997; Deo, 2000; Jense and Gutin, 2000; Liu and Lai, 2001; Tutte, 2001; Pemmaraju and Skiena, 2003; Gross and Yellen, 2005; Biswal, 2005). This chapter presents the details of graph theory and the matrix approach as a decision-making method in the manufacturing environment. To demonstrate the approach, an example of machinability evaluation of work materials for a given machining operation is considered. Machinability is a measure of ease with which a work material can satisfactorily be machined. The machinability aspect is of considerable importance for the manufacturing engineer to know in advance, so

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Decision Making in the Manufacturing Environment

that the processing can be planned in an efficient manner. The study can also be a basis for cutting tool and cutting fluid performance evaluation, and machining parameter optimization. In the process of product design, material selection is important for realizing the design objective, and for reducing the production cost. The machinability of engineering materials, owing to the marked influence on the production cost, needs to be taken into account in the product design, although it will not always be a criterion considered top priority in the process of material selection. If there is a finite number of work materials from among which the best material is to be chosen, and if each work material satisfies the required design and functionality of the product, then the main criterion to choose the work material is its operational performance during machining, i.e., machinability. Machinability evaluation is based on the evaluation of certain economic and technical objectives (e.g., higher production rate, low operational cost, good product quality, etc.), which are the consequences of the machining operation on a given work material. Machining process output variables (e.g., cutting tool life, cutting tool wear, cutting forces, power consumption, processed surface finish, processed dimensional accuracy, etc.) are nothing but the behavioral properties of the work materials during machining operations in terms of economic and technical consequences and are directly related to machining operations, and hence to machinability. Thus, the machining process output variables are the pertinent and most commonly accepted measures of machinability, and are also called pertinent machinability attributes.

2.2 Machinability Attributes Digraph
A directed graph (or a digraph) is nothing but a graph with directed edges. A machinability attributes digraph models the machinability attributes and their interrelationship for a given machining operation. This digraph consists of nodes and edges. A node {Vi} represents presence or measure of an i-th machinability attribute. The number of nodes considered is equal to the number of machinability attributes considered for a given machining operation. The directed edge represents the relative importance among the attributes. If node ‘i’ has a relative importance over another anode ‘j’ in the machinability evaluation of work materials for the given machining operation, then a directed edge or arrow is drawn from node i to node j (i.e., eij). If j has relative importance over i, then the directed edge or arrow is drawn from node j to node i (i.e., eji). To demonstrate a machinability attributes digraph, an example of machinability evaluation of work materials in cylindrical grinding operation is considered. Grinding is a machining process of material removal in the form of small chips by the mechanical action of abrasive particles bonded together in a grinding wheel. In this operation, wheel wear is most important, so as to reduce the cost of production. The wheel wear is measured in terms of a ratio known as ‘grinding ratio’, which is defined as the ratio of amount of work material removed to the amount of wheel wear. Higher values of grinding ratio are desired for economic reasons. Two components of the cutting force, namely, normal force and tangential force, significantly affect the grinding process. Higher values of normal

Graph Theory and Matrix Approach

9

force increase the roughness of the processed surfaces, and the geometric and dimensional inaccuracy of the processed parts. Tangential force affects the rating of the motors driving the wheel and the work piece, and higher values of tangential force mean increased power consumption. The grinding process imparts high-grade surface finish and good dimensional accuracy to the job. However, the temperature encountered in the grinding process is very high, and adversely affects the process. So, every care is to be taken to reduce the grinding temperature. All these variables described are the machining process output variables and are the pertinent machinability attributes and these attributes refer to the performance of work material during machining operations in terms of technical and economic consequences, and can be used for objective comparison. A work material is said to possess good machinability in cylindrical grinding operation if it offers higher grinding ratio, and lower values of normal force, tangential force, surface roughness, dimensional inaccuracy, and grinding temperature. Based on the above discussion, the machinability attributes considered for the cylindrical grinding operation are: grinding ratio (GR), normal force (NF), tangential force (TF), surface finish (SF), dimensional accuracy of the produced job (DA), and grinding temperature (GT). A machinability attributes digraph for the cylindrical grinding operation is shown in Figure 2.1. As six machinability attributes are considered here, there are six nodes in the machinability attributes digraph with nodes 1, 2, 3, 4, 5, and 6 representing the machinability attributes GR, NF, TF, SF, DA, and GT, respectively. The attribute GR is more important than the other machinability attributes in cylindrical grinding. Every effort should be made to increase the grinding ratio, as it greatly affects the cost of production. So, directed edges are drawn for the attribute GR (i.e., node 1) to the other attributes (i.e., nodes 2, 3, 4, 5, and 6). NF is more important than the attributes TF, SF, DA, and GT in cylindrical grinding operation, as it affects the surface roughness, and the geometric and dimensional accuracy of the processed parts. So, directed edges are drawn from node 2, representing NF, to the nodes 3, 4, 5, and 6. SF is more important than TF, so a directed edge is drawn from node 4 to node 3. DA is more important than TF, so a directed edge is drawn from node 5 to node 3. GT is more important than TF, SF, and DA in cylindrical grinding operation, so directed edges are drawn from node 6 to the nodes 3, 4, and 5 representing TF, SF, and DA, respectively. A machinability attributes digraph gives a graphical representation of the attributes and their relative importance for quick visual appraisal. As the number of nodes and their interrelations increase, the digraph becomes more complex. In such a case, the visual analysis of the digraph is expected to be difficult and complex. To overcome this constraint, the digraph is represented in a matrix form.

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Decision Making in the Manufacturing Environment

Figure 2.1. Machinability attributes digraph for the cylindrical grinding operation (attributes: 1. grinding ratio, 2. normal force, 3. tangential force, 4. surface finish, 5. dimensional accuracy, and 6. grinding temperature)

2.3 Matrix Representation of the Digraph
Matrix representation of the machinability attributes digraph gives one-to-one representation. A matrix called the machinability attributes relative importance matrix is defined. This is represented by a binary matrix (aij), where aij represents the relative importance between attributes i and j such that, aij = 1, if the i-th machinability attribute is more important than the j-th machinability attribute for a given machining operation = 0, otherwise. It is noted that aii = 0 for all i, as an attribute can not have relative importance over itself. The machinability attributes relative importance matrix (RIM) for the machinability attributes digraph shown in Figure 2.1 is written as: Attributes GR NF B= TF SF DA GT GR 0 0 0 0 0 0 NF 1 0 0 0 0 0 TF 1 1 0 1 1 1 SF 1 1 0 0 0 1 DA 1 1 0 0 0 1 GT 1 1 0 0 0 0 (2.1)

Graph Theory and Matrix Approach

11

The machinability attributes relative importance matrix (RIM) is analogous to the adjacency matrix in graph theory. It is noted from the RIM that all diagonal elements have value 0 and all off-diagonal elements have value either 0 or 1. This means that in this matrix only relative importance among the machinability attributes is considered, and the measures of the machinability attributes is not considered. To incorporate this, another matrix, called ‘characteristic machinability attributes presence and relative importance matrix (CPRIM)’, is defined and this, for the machinability attributes digraph of Figure 2.1, is written as C given by: Attributes GR NF C = [AI-B] = TF SF DA GT GR A 0 0 0 0 0 NF -1 A 0 0 0 0 TF -1 -1 A -1 -1 -1 SF -1 -1 0 A 0 -1 DA -1 -1 0 0 A -1 GT -1 -1 0 0 0 A (2.2) where I is an identity matrix, and A is a variable representing the measure of the machinability attribute. Matrix C is analogous to the characteristic matrix in graph theory. Referring to the matrix in Equation 2.2, it is noted that the value of all diagonal elements is identical, i.e., the presence or measure of each machinability attribute is taken to be the same. In practice, this is not true. Also, the relative importance of one machinability attribute over the other machinability attribute, i.e., aij, may take any value other than the extreme value 0 or 1. Thus, there is a need for considering a general attribute value representing attribute presence or measure as well as relative importance value to develop a matrix equation leading to a broad-based machinability evaluation. To consider these aspects, another matrix, D, called ‘variable characteristic machinability attributes presence and relative importance matrix (VCPRIM)’, is developed. Attributes GR NF D = [E-F] = TF SF DA GT GR A1 0 0 0 0 0 NF -a12 A2 0 0 0 0 TF -a13 -a23 A3 -a43 -a53 -a63 SF -a14 -a24 0 A4 0 -a64 DA -a15 -a25 0 0 A5 -a65 GT -a16 -a26 0 0 0 A6 (2.3) where E is a diagonal matrix with diagonal element Ai representing a variable of presence or measure of the i-th machinablity attribute. If a machinability attribute is excellent, then it is assigned a maximum value. If a machinability attribute is not very significant, then it is assigned a minimum value. In general, most of the machinability attributes are assigned intermediate values of the interval scale, as attributes may be moderately present. These judgments are to be made based on an appropriate test of the machinability attribute. In the absence of this

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Decision Making in the Manufacturing Environment

test, a subjective value based on experience is assigned. F is a matrix of which the off-diagonal elements are represented as aij, instead of 1, wherever the i-th machinability attribute has more relative importance than the j-th machinability attribute. It may be noted that the matrix VCPRIM considers the presence or measures of the machinability attributes, and their relative importance for the given machining operation. The characteristic multinomial of the matrix VCPRIM is nothing but the determinant of the matrix VCPRIM, and may be written as: det (D) = A1 A2 A3 A4 A5 A6 (2.4)

Equation 2.4 contains only one term, i.e., A1 A2 A3 A4 A5 A6, which is a set of six machinability attributes measures. It is evident that the relative importance among the machinability attributes is not represented by this characteristic multinomial. It is therefore necessary to look into the aspect of relative importance representation in the machinability attributes digraph and its matrix to identify the reasons. If the i-th machinablity attribute is more important than the j-th machinability attribute, then a directed edge is drawn from i to j to represent this relative importance. Similarly, if the j-th machinability attribute is more important than the i-th machinability attribute, then a directed edge is drawn from j to i to represent their relative importance. But if the i-th machinability attribute is less important than the j-th machinability attribute, then no directed edge is drawn from i to j, and vice versa. In that case, aij (or aji) becomes 0 in the matrix representation of the digraph. This 0 causes many terms of the characteristic multinomial to become 0 (as there are no relative importance loops in the corresponding machinability attributes digraph), thus leading to the loss of a fair amount of information useful during the machinability evaluation. Hence, the relative importance between i, j and j, i is distributed on a scale 0 to L and is defined as: aji = L - aij (2.5)

It means that a scale is adapted from 0 to L on which the relative importance values are compared. If aij represents the relative importance of the i-th machinability attribute over the j-th machinability attribute, then the relative importance of the j-th machinability attribute over the i-th machinability attribute is evaluated using Equation 2.5. The modified machinability attributes digraph showing the presence or measures of the machinabilty attributes, and all the possible relative importance among these is shown in Figure 2.2.

Graph Theory and Matrix Approach

13

Figure 2.2. Modified machinability attributes digraph for the cylindrical grinding operation (attributes: 1. grinding ratio, 2. normal force, 3. tangential force, 4. surface finish, 5. dimensional accuracy, and 6. grinding temperature)

The modified VCPRIM for this digraph for the cylindrical grinding operation is represented as: Attributes GR NF G= TF SF DA GT GR A1 -a21 -a31 -a41 -a51 -a61 NF -a12 A2 -a32 -a42 -a52 -a62 TF -a13 -a23 A3 -a43 -a53 -a63 SF -a14 -a24 -a34 A4 -a54 -a64 DA -a15 -a25 -a35 -a45 A5 -a65 GT -a16 -a26 -a36 -a46 -a56 A6 (2.6) where Ai is the measure of the i-th machinability attribute represented by node vi, and aij the relative importance of the i-th machinability attribute over the j-th, represented by the edge eij. The characteristic multinomial of this matrix G is defined as ‘variable characteristic machinability function (VCF)’, and is written as Equation 2.6.
6 5 6 3 4 5 6

det (G) = i =1

Ai i=1 j=i+1 k=1 l=k+1 m=l+1 n=m+1 k,l,m,n 4 5 6 4 5 6

(aijaji )AkAlAmAn pus i=1 j=i+1 k=j+1 l=1 m=l+1 n=m+1

(aijajkaki + aikakjaji)AlAmAn k,l,m,n pus

14

Decision Making in the Manufacturing Environment

3

6

5

6

5

6

+[ i=1 j=i+1 k=i+1 l=i+2 m=1

(aijaji) (aklalk )AmAn n=m+1 k,l,m,n pus

3

5

6

6

5

6

i=1 j=i+1

(aijajkaklali + ailalkakjaji)AmAn] k=i+1 l=j+1 m=1 n=m+1 k,l,m,n 4 5 6 5 6 6 pus

+[ i=1 j=i+1 k=j+1 l=1 m=l+1 n=1

(aijajkaki + aikakjaji) (almaml)An k,l,m,n pus

2

5

6

6

6

6

i=1 j=i+1 k=i+1 l=i+1 m=j+1 n=1

(aijajkaklalmami+ aimamlalkakjaji)An] k,l,m,n 3 5 6 6 5 6 pus

+[ i=1 j=i+1

(aijajkaklali + ailalkakjaji) (amnanm) k=i+1 l=j+1 m=1 n=m+1 k,l,m,n pus

1

5

6

4

5

6

+ i=1 j=i+1 k=j+1

(aijajkaki + aikakjaji)(almamnanl + alnanmaml) l=1 m=l+1 n=m+1 k,l,m,n 1 6 3 6 5 6 pus

i=1 j=i+1 k=i+1

(aijaji) (aklalk ) (amnanm ) l=i+2 m=k+1 n=k+2 k,l,m,n 1 5 6 6 6 6 pus

-

(aijajkaklalmamnani + ainanmamlalkakjaji)] i=1 j=i+1 k=i+1 l=i+1 m=i+1 n=j+1 k,l,m,n pus

(2.7) ‘pus’ stands for ‘previously used subscripts’, i.e., in Equation 2.7, k, l, m and n take those subscripts that are other than previously used subscripts. The multinomial Equation 2.7 in symbolic form is a complete expression for the considered cylindrical grinding operation, as it considers measures of the attributes and all possible relative importance among the attributes. Mathematically, each term is a product of six different matrix elements. If this function is interpreted from a combinatorial point of view, it is found that different terms are the sets of distinct diagonal elements (Ai) and loops of off-diagonal elements of different sizes (i.e., aijaji, aijajkaki, etc.). The variable characteristic machinability function (VCF) contains terms arranged in (6 + 1) groupings and these groupings represent the measures of attributes and the relative importance loops. The first grouping represents the measures of the machinability attributes. The second grouping is absent, as there is no self-loop in the digraph. The third grouping contains 2-attribute relative

Graph Theory and Matrix Approach

15

importance loops and measures of four attributes. Each term of the fourth grouping represents a set of a 3-attribute relative importance loop, or its pair, and measures of three attributes. The fifth grouping contains two sub-groupings. Each term of the first sub-grouping is a set of two 2-attribute relative importance loops and the measures of two attributes. Each term of the second sub-grouping is a set of a 4attribute relative importance loop, or its pair, and the measures of two attributes. The sixth grouping contains two sub-groupings. Each term of the first subgrouping is a set of a 3-attribute relative importance loop, or its pair, and a 2attribute relative importance loop and the measure of one attribute. Each term of the second sub-grouping is a set of 5-attribute relative importance loop, or its pair, and the measure of one attribute. The seventh grouping contains four subgroupings. Each term of the first sub-grouping is a set of a 4-attribute relative importance loop, or its pair, and a 2-attribute relative importance loop. Each term of the second sub-grouping is a set of a 3-attribute relative importance loop, or its pair, and another 3-attribute relative importance loop, or its pair. Each term of the third sub-grouping is a set of three 2-attribute relative importance loops. Each term of the fourth sub-grouping is a set of a 6-attribute relative importance loop, or its pair. After identifying these combinatorial terms, and by associating a proper physical meaning with these, a new mathematical meaning of the multinomial is obtained. The variable characteristic machinability function is the characteristic of the work material, and a powerful tool for machinability evaluation. However, a close look at the multinomial reveals that its various characteristic coefficients carry both positive and negative signs. The variable characteristic machinability function may not be able to provide the total objective value, when the numerical values for Ai and aij are substituted in the multinomial, because some of the information is lost by subtraction and addition operations in the determinant function. Considering these factors, the ‘variable permanent machinability function (VPF)’ is defined. This function is derived from a new matrix called the ‘machinability permanent matrix’. The machinability permanent matrix, H, for the machinability attributes digraph (Figure 2.2) is written as Equation 2.8. Attributes GR NF H= TF SF DA GT GR A1 a21 a31 a41 a51 a61 NF a12 A2 a32 a42 a52 a62 TF a13 a23 A3 a43 a53 a63 SF a14 a24 a34 A4 a54 a64 DA a15 a25 a35 a45 A5 a65 GT a16 a26 a36 a46 a56 A6 (2.8) The permanent of H may be called the ‘variable permanent machinability function (VPF)’.
6 5 6 3 4 5 6

per (H) = i =1

Ai + i=1 j=i+1 k=1 l=k+1 m=l+1 n=m+1 k,l,m,n

(aijaji )AkAlAmAn pus 16

Decision Making in the Manufacturing Environment

4

5

6

4

5

6

+ i=1 j=i+1 k=j+1 l=1 m=l+1 n=m+1

(aijajkaki + aikakjaji)AlAmAn k,l,m,n 3 6 5 6 5 6 pus

+[ i=1 j=i+1 k=i+1 l=i+2 m=1

(aijaji) (aklalk)AmAn n=m+1 k,l,m,n pus

3

5

6

6

5

6

+ i=1 j=i+1

(aijajkaklali + ailalkakjaji)AmAn] k=i+1 l=j+1 m=1 n=m+1 k,l,m,n 4 5 6 5 6 6 pus

+[ i=1 j=i+1 k=j+1 l=1 m=l+1 n=1

(aijajkaki + aikakjaji) (almaml)An k,l,m,n pus

2

5

6

6

6

6

+ i=1 j=i+1 k=i+1 l=i+1 m=j+1 n=1

(aijajkaklalmami+ aimamlalkakjaji)An] k,l,m,n 3 5 6 6 5 6 pus

+[ i=1 j=i+1

(aijajkaklali + ailalkakjaji) (amnanm) k=i+1 l=j+1 m=1 n=m+1 k,l,m,n pus

1

5

6

4

5

6

+ i=1 j=i+1 k=j+1

(aijajkaki + aikakjaji)(almamnanl + alnanmaml) l=1 m=l+1 n=m+1 k,l,m,n 1 6 3 6 5 6 pus

+ i=1 j=i+1 k=i+1

(aijaji) (aklalk) (amnanm) l=i+2 m=k+1 n=k+2 k,l,m,n 1 5 6 6 6 6 pus

+

(aijajkaklalmamnani + ainanmamlalkakjaji)] k,l,m,n pus

i=1 j=i+1 k=i+1 l=i+1 m=i+1 n=j+1

(2.9) It may be noted that the only difference between the VPF, i.e., per (H), and the determinant polynomial det (G), i.e., VCF, is that the former does not carry negative signs with its terms, while both positive and negative signs appear in the latter. Comparing Equations 2.8 and 2.9, it is noted that each term of the grouping/ sub-grouping is the same in both cases, the only difference being in the signs of the coefficients. Both the functions are basically the same, and have the same physical meaning, except for the difference in signs. It may be mentioned that the

Graph Theory and Matrix Approach

17

permanent is a standard matrix function, and is used in combinatorial mathematics (Marcus and Minc, 1965; Jurkat and Ryser, 1966; Nijenhuis and Wilf, 1975). Use of the permanent concept in machinability evaluation will help in representing machinability attributes of work materials as obtained from combinatorial consideration. Application of the permanent concept will lead to a better appreciation of machinability attributes of the work materials. Moreover, using this, no negative sign will appear in the equation, and hence no information will be lost. The adjacency matrix, incidence matrix, characteristic matrix, etc., could also be used for machinability evaluation, but these matrices have their own drawbacks. The adjacency matrix makes no provision for parallel-directed edges in both directions (i.e., relative importance in both directions), and the elements of the matrix are either 0 or 1. On expanding the adjacency matrix, only some numbers can be obtained that do not reveal much physical information associated with the machinability attributes and their relative importance. The incidence matrix contains the elements either 0 or 1, and it requires more computer storage than needed for an adjacency matrix, as the number of edges is usually greater than the number of nodes. Moreover, as the incidence matrix is a non-square matrix, its further use for machinability evaluation is not possible. The characteristic matrix is not an invariant of the system, as a new matrix can be obtained by changing the labeling, but one matrix can be obtained from the other by proper permutations of rows and columns. The characteristic multinomial or characteristic function, which is nothing but the determinant of the characteristic matrix, contains both positive and negative signs, and may not be able to provide the total objective value when the numerical values for Ai and aij are substituted in the multinomial, because some of the information is lost by subtraction and addition operations in the determinant function, as explained above. Due to these reasons, researchers have used the permanent function of a matrix, which does not contain any negative terms, and thus provides the complete information without any loss (Gandhi et al., 1991; Gandhi and Agrawal, 1992, 1994; Venkatasamy and Agrawal, 1996, 1997; Rao and Gandhi, 2001, 2002a, 2002b; Rao, 2004, 2006a, 2006b, 2006c, 2006d; Grover et al., 2004; Rao and Padmanabhan, 2006). In general, if there is M number of machinability attributes, and the relative importance exists among all the machinability attributes, then the machinability attributes matrix, J, for the considered machinability attributes digraph is written as Equation 2.10. Attributes 1 2 J= 3 M 1 A1 a21 a31 aM1 2 a12 A2 a32 aM2 3 a13 a23 A3 aM3 M a1M a2M a3M AM

(2.10) The VPF for this matrix J contains factorial M (M!) number of terms. In sigma form, it is written as Equation 2.11.

18

Decision Making in the Manufacturing Environment

M

M-1

M

M

per (J) =

Ai + i =1 i=1 j=i+1

………
M=t+1

(aijaji)AkAlAmAnAo …..AtAM
... , M pus

M-2

M-1

M

M

+ i=1 j=i+1 k=j+1

.......... l=1 (aijajkaki + aikakjaji)AlAmAnAo …..AtAM k, … , M pus

M=t+1

M- 3

M

M-1

M

M

+[ i=1 ……… j=i+1 k=i+1 l=i+2

(aijaji) (aklalk )AmAnAo …..AtAM k,l, … , M pus

M=t+1

M-3

M-1

M

M

M

+ i=1 j=i+1

……… (aijajkaklali + ailalkakjaji)AmAnAo …..AtAM] k=i+1 l=j+1 M=t+1 k,l, ... , M M-2 M-1 M M-1 M M pus

+[ i=1 j=i+1

……… (aijajkaki + aikakjaji)(almaml)AnAo …..AtAM k=j+1 l=1 m=l+1 M=t+1 k,l,m, ... , M pus

M-4 M-1

M

M

M

M

+ i=1 .......... (aijajkaklalmami + aimamlalkakjaji)AnAo…..AtAM] j=i+1 k=i+1 l=i+1 m=j+1 M=t+1 k,l,m, ... , M M-3 M-1 M M M-1 M M pus

+[(

……… (aijajkaklali + ailalkakjaji)(amnanm)Ao…..AtAM
M=t+1 k,l,m,n, ... , M pus

i=1 j=i+1 k=i+1 l=j+1 m=1 n=m+1

M-5 M-1 M M-2 M-1 M

M

+

….… (aijajkaki + aikakjaji)(almamnanl + alnanmaml)Ao..AtAM k,l,m,n, ... , M pus

i=1 j=i+1 k=j+1 l=1 m=l+1 n=m+1 M=t+1

M-5 M

M- 3 M

M-1

M

M

+ i=1 j=i+1 k=i+1

......... (aijaji) (aklalk) (amnanm) Ao …..AtAM l=i+2 m=k+1 n=k+2 M=t+1 pus k,l,m,n, ... , M

M-5 M-1 M M

M

M

M

+

... (aijajkaklalmamnani + ainanmamlalkakjaji)Ao…..AtAM)] k,l,m,n, ... , M pus

i=1 j=i+1 k=i+1 l=i+1 m=i+1 n=j+1 M=t+1

+ ----------

(2.11)

‘pus’ stands for ‘previously used subscripts’, i.e., in the Equation 2.11, k, l, m, n, … , M take those subscripts that are other than previously used subscripts. The VPF contains terms arranged in (M + 1) groups, and these groups represent the measures of attributes and the relative importance loops. The first group represents

Graph Theory and Matrix Approach

19

the measures of M attributes. The second group is absent as there is no self-loop in the digraph. The third group contains 2-attribute relative importance loops and measures of (M-2) attributes. Each term of the fourth group represents a set of a 3attribute relative importance loop, or its pair, and measures of (M-3) attributes. The fifth group contains two sub-groups. The terms of the first sub-group is a set of two 2-attribute relative importance loops and the measures of (M-4) attributes. Each term of second sub-group is a set of a 4-attribute relative importance loop, or its pair, and the measures of (M-4) attributes. The sixth group contains two subgroups. The terms of the first sub-group is a set of a 3-attribute relative importance loop, or its pair, and 2-attribute relative importance loop and the measures of (M-5) attributes. Each term of the second sub-group is a set of a 5-attribute relative importance loop, or its pair, and the measures of (M-5) attributes. Similarly other terms of the equation are defined. Thus, the VPF fully characterizes the considered machinability evaluation problem, as it contains all possible structural components of the attributes and their relative importance. It may be mentioned that this equation is nothing but the determinant of an M * M matrix but considering all the terms as positive. The computer program written in C++ language to calculate the permanent function of a square matrix of M * M size is given in Appendix A.

2.4 Machinability Index
The machinability index is a measure of the ease with which a work material can satisfactorily be machined in a given machining operation. The machinability function defined above, i.e., Equation 2.11, contains measures of attributes and their relative importance, and is hence appropriate, and can be used for evaluation of the machinability index. As the machinability function contains only positive terms, higher values of Ai and aij will result in increased value of the machinability index. To calculate this index, the required information is the values of Ai and aij. The value of Ai should preferably be obtained from a standard or specific test. If such objective value is not available, then a ranked value judgment on a scale, e.g., 0 to 1, is adapted. Table 2.1 represents the machinability attribute on a subjective scale. It holds for a given machining operation, some of the Ai will be subjective, and the others objective. Moreover, these objective values will have different units. It is therefore desirable to convert, or normalize, the objective values of Ai on the same scale as the subjective values, i.e., 0 to 1. If Ai has range Ail and Aiu, the value 0 is assigned to the lowest range value Ail and 1 is assigned to the highest range value Aiu. The other, intermediate value Aii of the machinability attribute is assigned a value in between 0 and 1, as per the following: Ai = (Aii - Ail) / (Aiu - Ail) (2.12)

Equation 2.12 is applicable for general beneficial attributes only. A beneficial attribute (e.g., grinding ratio) is one of which higher attribute value is more desirable for the given machining operation. A non-beneficial attribute (e.g., normal force) is one of which the lower attribute value is desirable. Therefore, in

20

Decision Making in the Manufacturing Environment

the case of non-beneficial machinability attributes, the attribute value 0, on scale 0 to 1, is assigned to the highest range value Aiu, and the value 1 is assigned to the lower range value Ail. The other intermediate value Aii of the machinability attribute is assigned a value in between 0 and 1, as per the following: Ai = (Aiu - Aii) / (Aiu - Ail) (2.13)

Alternatively, the normalized value Ai can be calculated by Aii /Aiu in the case of the beneficial attribute, and by Ail /Aii in the case of the non-beneficial attribute. This alternative method is better than the method described by Equations 2.12 and 2.13 as it does not contain ‘0’ as the normalized attribute value, and hence no information will be lost subsequently in machinability index calculation. The relative importance between two attributes (i.e., aij) for a given machining operation is also assigned value on the scale 0 to 1, and is arranged into six classes. The relative importance implies that an attribute ‘i’ is compared with another attribute ‘j’ in terms of relative importance for the given machining operation. The relative importance between i, j and j, i is distributed on the scale 0 to 1, and is defined similarly to Equation 2.5 in which L is taken as 1. If aij represents the relative importance of the i-th attribute over the j-th attribute, then the relative importance of the j-th attribute over the i-th attribute is evaluated using Equation 2.5. For example, if the i-th attribute is slightly more important than the j-th attribute, then aij = 6 and aji = 4. Table 2.2 aids in assigning aij values based on the above. The relative importance is expressed in six classes, which lead to minimization of subjectivity while deciding the relative importance between machinability attributes.
Table 2.1. Value of attribute ________________________________________________________________ Subjective measure of attribute Assigned value ________________________________________________________________ Exceptionally low 0.0 Extremely low 0.1 Very low 0.2 Low 0.3 0.4 Below average Average 0.5 Above average 0.6 High 0.7 0.8 Very high Extremely high 0.9 Exceptionally high 1.0 ________________________________________________________________

Graph Theory and Matrix Approach

21

Table 2.2. Relative importance of attributes ______________________________________________________________________ Class description Relative importance aji = 1 - aij aij ______________________________________________________________________ Two attributes are equally important 0.5 0.5 One attribute is slightly more important over the other 0.6 0.4 One attribute is strongly more important over the other 0.7 0.3 One attribute is very strongly important over the other 0.8 0.2 One attribute is extremely important over the other 0.9 0.1 One attribute is exceptionally more important over the other 1.0 0.0 ______________________________________________________________________

It may be mentioned that one may choose any scale, e.g., 0 to 1, 0 to 5, 1 to 5, 0 to 10, 1 to 10, 1 to 11, 0 to 50, 0 to 100, 1 to 100, 1 to 110, 0 to 1000, 1 to 1000, or any other scale for Ai and aij. But the final ranking will not change, as these are relative values. It is, however, desirable to choose a lower scale for Ai and aij to obtain a manageable value of machinability index. It may be further mentioned that the scales adapted for Ai and aij can be independent of each other. Whenever the machinability index is calculated for a work material, only the diagonal elements will change, i.e., (Ai), and the off-diagonal elements (aij) remain the same. The machinability index for each material is evaluated using Equation 2.11, and substituting the value of Ai and aij. The work materials are arranged in the descending or ascending order of the machinability index to rank these for a given machining operation. These are called the machinability ranking values of the work materials for the given machining operation. The work material, for which the value of machinability index is highest, is the best choice for the machining operation considered. However, the final decision depends on factors such as cost, availability, environmental constraints, economical constraints, political constraints, etc. Compromise, however, should be made to select the work material having the highest value of machinability index. The next section describes the identification and comparison of work materials.

2.5 Identification and Comparison of Work Materials
2.5.1 Identification of Work Materials The variable permanent machinability function, i.e., Equation 2.11, is useful for the identification and comparison of work materials for a given machining operation. The number of terms in each grouping of the machinability function for all the work materials for a given machining operation will be the same. However, their values will be different. This aspect is used for the purpose. Let Tij represent the total value of terms of the j-th sub-grouping of i-th grouping of the machinability function. In case there is no sub-grouping, then Tij = Ti, i.e., total value of terms of the i-th grouping. The identification set for a work material for the given machining operation is:

22

Decision Making in the Manufacturing Environment

/ T1 / T2 / T3 / T4 / T51 + T52 / T61 + T62 / ……… Two work materials can be compared using Equation 2.14. 2.5.2 Comparison of Work Materials

(2.14)

In general, two work materials are never identical from the performance (i.e., machinability) point of view. If two work materials are similar, then they must be similar in performance, and vice versa. Comparison of two work materials is also carried out by evaluating the coefficient of similarity/dissimilarity based on the numerical value of the terms of the machinability function in its grouping/subgrouping. The coefficient of similarity/dissimilarity lies in the range 0 – 1. If two work materials are of similar performance, then the coefficient of similarity is 1 and coefficient of dissimilarity is 0. In the same manner, if two work materials are of dissimilar performance, then the coefficient of dissimilarity is 1 and coefficient of similarity is 0. Based on performance dissimilarity, the coefficient of dissimilarity for two work materials is proposed as Equation 2.15.
M-1 M j=i+1 ij)

Cd = (1/Q) (

(2.15)
M-1 M M-1 i=1 M j=i+1

i=1

where, Q = maximum of i=1 j=i+1

Tij and

T’ij

Tij and T’ij denote the values of the terms for the machinability function of the two work materials under comparison, and ij = Tij - T’ij . It may be noted that the absolute difference between the values of the terms for the machinability function of the two work materials is considered for proposing Cd. The coefficient of similarity is proposed as: Cs = 1 - Cd (2.16)

Equations 2.15 and 2.16 are useful for comparing two work materials, based upon their performance in a given machining operation. The coefficients of similarity and dissimilarity, and the identification sets are also useful for work materials documentation, and for easy storage and retrieval of the work materials data for various machining operations. Thus, graph theory and the matrix approach can be used as a decision-making method for choosing an appropriate alternative work material from amongst the given alternatives, based on machinability. The proposed method offers a general procedure that can be used for any type of decision-making problem involving any number of selection attributes and alternatives. The next section describes the general methodology of graph theory and matrix approach as a decision-making method.

Graph Theory and Matrix Approach

23

2.6 Methodology of GTMA as a Decision- making Method
The main steps are given below: Step 1: Identify the pertinent attributes and the alternatives involved in the decision-making problem under consideration. Obtain the values of the attributes (Ai) and their relative importance (aij). An objective or subjective value, or its range, may be assigned to each identified attribute as a limiting value or threshold value for its acceptance for the considered decision-making problem. An alternative with each of its selection attributes, meeting the acceptance value, may be short-listed. After short-listing the alternatives, the main task in choosing the alternative is to see how it serves the considered attributes. Step 2: 1. Develop the attributes digraph considering the identified pertinent attributes and their relative importance. The number of nodes shall be equal to the number of attributes considered in Step 1 above. The edges and their directions will be decided upon based on the interrelations among the attributes (aij). Refer to Section 2.2 for details. 2. Develop the attributes matrix for the attributes digraph. This will be the M*M matrix with diagonal elements as Ai and off-diagonal elements as aij. Refer to Section 2.3 for details. 3. Obtain the permanent function for the attributes matrix, on the lines of Equation 2.11. 4. Substitute the values of Ai and aij, obtained in step 1, in Equation 2.11 above to evaluate the index for the short-listed alternatives. 5. Arrange the alternatives in the descending order of the index. The alternative having the highest value of index is the best choice for the decision-making problem under consideration. 6. Obtain the identification set for each alternative, using Equation 2.14. Refer to Section 2.5 for details. 7. Evaluate the coefficients of dissimilarity and similarity using Equations 2.15 and 2.16. List also the values of the coefficients for all possible combinations. 8. Document the results for future analysis/reference. Step 3: Take a final decision, keeping practical considerations in mind. All possible constraints likely to be experienced by the user are looked into during this stage. These include constraints such as: availability or assured supply, management constraints, political constraints, economic constraints, environmental constraints, etc. However, compromise may be made in favor of an alternative with a higher index. From the above, it is clear that the graph theory and matrix approach as a decision-making method is relatively new, and offers a generic, simple, easy, and convenient decision-making method that involves less computation. The method lays emphasis on decision-making methodology, gives much attention to the issues of identifying the attributes, and to associating the alternatives with the attributes, etc. The method enables a more critical analysis and any number of objective and subjective attributes can be considered. In the permanent procedure, even a small variation in attributes leads to a significant difference in the selection index, and

24

Decision Making in the Manufacturing Environment

hence it is easy to rank the alternatives in the descending order, with clear-cut difference in the selection index. Further, the proposed procedure not only provides the analysis of alternatives, but also enables the visualization of various attributes present and their interrelations, using graphical representation. The measures of the attributes and their relative importance are used together to rank the alternatives, and hence provides a better evaluation of the alternatives. The permanent concept fully characterizes the considered selection problem, as it contains all possible structural components of the attributes and their relative importance. The decision-making capability of graph theory and the matrix approach can be utilized for making decisions in the manufacturing environment, and Chapters 5-30 of this book present those details. The next chapter gives an introduction to the multiple attribute decisionmaking methods.

References
Biswal PC (2005) Discrete mathematics and graph theory. Prentice Hall India, New Delhi Chen WK (1997) Graph theory and its engineering applications. Advanced Series in Electrical and Computer Engineering, University of Illinois, Chicago Deo N (2000) Graph theory with applications to engineering and computer science. Prentice Hall India, New Delhi Gandhi OP, Agrawal VP (1992) FMEA - A digraph and matrix approach. Reliability Engineering and System Safety 35:147–158 Gandhi OP, Agrawal VP (1994) A digraph approach to system wear evaluation and analysis. Journal of Tribology 116:268–274 Gandhi OP, Agrawal VP, Shishodia KS (1991) Reliability analysis and evaluation of systems. Reliability Engineering and System Safety 32:283–305 Gross J, Yellen J (2005) Graph theory and its applications. CRC Press, Florida Grover S, Agrawal VP, Khan IA (2004) A digraph approach to TQM evaluation of an industry. International Journal of Production Research 42:4031–4053 Harary F (1985) Graphs and applications. Wiley, New York Jense JB, Gutin G (2000) Digraph theory, algorithms, and applications. Springer, London Jurkat WB, Ryser HJ (1966) Matrix factorisation of determinants and permanents. Journal of Algebra 3:1–11 Liu LB, Lai LHJ (2001) Matrices in combinatorics and graph theory. Kluwer Academic Publishers, Dordrecht Marcus M, Minc H (1965) Permanents. American Mathematics Monthly 72:571– 591 Nijenhuis A, Wilf HS (1975) Combinatorial algorithms. Academic Press, New York Pemmaraju S, Skiena S (2003) Computational discrete mathematics: combinatorics and graph theory with mathematica. Cambridge University Press, UK

Graph Theory and Matrix Approach

25

Rao RV (2004) Digraph and matrix methods for evaluating environmentally conscious manufacturing programs. International Journal of Environmentally Conscious Design and Manufacturing 12:23–33 Rao RV (2006a) A decision making framework model for evaluating flexible manufacturing systems using digraph and matrix methods. International Journal of Advanced Manufacturing Technology 30:1101–1110 Rao RV (2006b) A material selection model using graph theory and matrix approach. Materials Science and Engineering A 431:248–255 Rao RV (2006c) Machine group selection in a flexible manufacturing cell using digraph and matrix methods. International Journal of Industrial and Systems Engineering 1:502–518 Rao RV (2006d) Plant location selection using fuzzy digraph and matrix methods. International Journal of Industrial Engineering 13:357–362 Rao RV, Gandhi OP (2001) Digraph and matrix method for selection, identification and comparison of metal cutting fluids. Proc. IME, Journal of Engineering Tribology 212:307–318 Rao RV, Gandhi OP (2002a) Digraph and matrix methods for machinability evaluation of work materials. International Journal of Machine Tools and Manufacture 42:321–330 Rao RV, Gandhi OP (2002b) Failure cause analysis of machine tools using digraph and matrix methods. International Journal of Machine Tools & Manufacture 42:521–528 Rao RV, Padmanabhan KK (2006) Selection, identification and comparison of industrial robots using digraph and matrix methods Robotics and Computer Integrated Manufacturing 22:373–383 Tutte WT (2001) Graph theory. Cambridge University Press, UK Venkatasamy R, Agrawal VP (1996) Selection of automobile vehicle by evaluation through graph theoretical methodology. International Journal of Vehicle Design 17:449–470 Venkatasamy R, Agrawal VP (1997) A digraph approach to quality evaluation of an automotive vehicle. Quality Engineering 9:405–417 Wilson RJ, Watkins JJ (1990) Graphs, an introductory approach. Wiley, New York

3
__________________________________________________________________

Introduction to Multiple Attribute Decision- m aking (MADM) Methods

3.1 Introduction
Multiple criterion decision making (MCDM) refers to making decisions in the presence of multiple, usually conflicting criteria. The problems of MCDM can be broadly classified into two categories: multiple attribute decision making (MADM) and multiple objective decision making (MODM), depending on whether the problem is a selection problem or a design problem. MODM methods have decision variable values that are determined in a continuous or integer domain, with either an infinitive or a large number of choices, the best of which should satisfy the decision maker’s constraints and preference priorities. MADM methods, on the other hand, are generally discrete, with a limited number of predetermined alternatives. MADM is an approach employed to solve problems involving selection from among a finite number of alternatives. An MADM method specifies how attribute information is to be processed in order to arrive at a choice. MADM methods require both inter- and intra-attribute comparisons, and involve appropriate explicit tradeoffs. Each decision table (also called decision matrix) in MADM methods has four main parts, namely: (a) alternatives, (b) attributes, (c) weight or relative importance of each attribute, and (d) measures of performance of alternatives with respect to the attributes. The decision table is shown in Table 3.1. The decision table shows alternatives, Ai (for i = 1, 2, ….. , N), attributes, Bj (for j = 1, 2, ….. , M), weights of attributes, wj (for j=1, 2, ….., M) and the measures of performance of alternatives, mij (for i= 1, 2, ….., N; j=1, 2, ….., M). Given the decision table information and a decision-making method, the task of the decision maker is to find the best alternative and/or to rank the entire set of alternatives. It may be added here that all the elements in the decision table must be normalized to the same units, so that all possible attributes in the decision problem can be considered.

28

Decision Making in the Manufacturing Environment

Table 3.1. Decision table in MADM methods ________________________________________________________________ Alternatives Attributes B2 B3 BM B1 (w1) (w2) (w3) (-) (-) (wM) ________________________________________________________________ A1 m11 m12 m13 m1M A2 m21 m22 m23 m2M A3 m31 m32 m33 m3M mN1 mN2 mN3 mNM AN ________________________________________________________________

Of the many MADM methods reported in the literature (Saaty, 1980, 2000; Hwang and Yoon, 1981, Chen and Hwang, 1992; Yoon and Hwang 1995; Olson, 1996; Triantaphyllou and Sanchez, 1997; Zanakis et al., 1998; Gal et al., 1999; Triantaphyllou, 2000; Figueira et al., 2004), few important methods that have a higher potential to solve decision-making problems in the manufacturing environment are presented in this chapter.

3.2 Multiple Attribute Decision- making Methods
3.2.1 Simple Additive Weighting (SAW) Method This is also called the weighted sum method (Fishburn, 1967) and is the simplest, and still the widest used MADM method. Here, each attribute is given a weight, and the sum of all weights must be 1. Each alternative is assessed with regard to every attribute. The overall or composite performance score of an alternative is given by Equation 3.1.
M

Pi =

j=1

wj mij

(3.1)

Previously, it was argued that SAW should be used only when the decision attributes can be expressed in identical units of measure (e.g., only dollars, only pounds, only seconds, etc.). However, if all the elements of the decision table are normalized, then SAW can be used for any type and any number of attributes. In that case, Equation 3.1 will take the following form:
M

Pi =

j=1

wj (mij)normal

(3.2)

where (mij)normal represents the normalized value of mij, and Pi is the overall or composite score of the alternative Ai. The alternative with the highest value of Pi is considered as the best alternative. The attributes can be beneficial or non-beneficial. When objective values of the attribute are available, normalized values are calculated by (mij)K/(mij)L, where (mij)K is the measure of the attribute for the K-th alternative, and (mij)L is the measure of the attribute for the L-th alternative that has the highest measure of the

MADM Methods

29

attribute out of all alternatives considered. This ratio is valid for beneficial attributes only. A beneficial attribute (e.g., profit) means its higher measures are more desirable for the given decision-making problem. By contrast, non-beneficial attribute (e.g., cost) is that for which the lower measures are desirable, and the normalized values are calculated by (mij)L/(mij)K. If the restriction that the sum of all weights is to be equal to 1 is relaxed, then Equation 3.3 can be used and this method is called simple multiple attribute rating technique (SMART).
M M

Pi = [

j=1

wj (mij)normal ] /

j=1

wj

(3.3)

Edwards et al. (1982) proposed a simple method to assess weights for each attribute to reflect its relative importance to the decision. For a start, the attributes are ranked in order of importance and 10 points are assigned to the least important attribute. Then, the next-least important attribute is chosen, more points are assigned to it, and so on, to reflect their relative importance. The final weights are obtained by normalizing the sum of the points to one. 3.2.2 Weighted Product Method (WPM) This method is similar to SAW. The main difference is that, instead of addition in the model, there is multiplication (Miller and Starr, 1969). The overall or composite performance score of an alternative is given by Equation 3.4.
M

Pi =

j=1

[(mij)normal]wj

(3.4)

The normalized values are calculated as explained under the SAW method. Each normalized value of an alternative with respect to an attribute, i.e., (mij)normal, is raised to the power of the relative weight of the corresponding attribute. The alternative with the highest Pi value is considered the best alternative. 3.2.3 Analytic Hierarchy Process (AHP) Method One of the most popular analytical techniques for complex decision-making problems is the analytic hierarchy process (AHP). Saaty (1980, 2000) developed AHP, which decomposes a decision-making problem into a system of hierarchies of objectives, attributes (or criteria), and alternatives. An AHP hierarchy can have as many levels as needed to fully characterize a particular decision situation. A number of functional characteristics make AHP a useful methodology. These include the ability to handle decision situations involving subjective judgements, multiple decision makers, and the ability to provide measures of consistency of preference (Triantaphyllou, 2000). Designed to reflect the way people actually think, AHP continues to be the most highly regarded and widely used decision-making method. AHP can efficiently deal with tangible (i.e., objective) as well as non-tangible (i.e., subjective) attributes, especially where the subjective judgements of different individuals constitute an

30

Decision Making in the Manufacturing Environment

important part of the decision process. The main procedure of AHP using the radical root method (also called the geometric mean method) is as follows: Step 1: Determine the objective and the evaluation attributes. Develop a hierarchical structure with a goal or objective at the top level, the attributes at the second level and the alternatives at the third level. Step 2: Determine the relative importance of different attributes with respect to the goal or objective. Construct a pair-wise comparison matrix using a scale of relative importance. The judgements are entered using the fundamental scale of the analytic hierarchy process (Saaty 1980, 2000). An attribute compared with itself is always assigned the value 1, so the main diagonal entries of the pair-wise comparison matrix are all 1. The numbers 3, 5, 7, and 9 correspond to the verbal judgements ‘moderate importance’, ‘strong importance’, ‘very strong importance’, and ‘absolute importance’ (with 2, 4, 6, and 8 for compromise between these values). Assuming M attributes, the pair-wise comparison of attribute i with attribute j yields a square matrix BM x M where aij denotes the comparative importance of attribute i with respect to attribute j. In the matrix, bij = 1 when i = j and bji = 1/bij. Attributes B1 B2 BMxM = B3 BM B1 1 b21 b31 bM1 B2 b12 1 b32 bM2 B3 b13 b23 1 bM3 BM b1M b2M b3M 1 (3.5) Find the relative normalized weight (wj) of each attribute by (i) calculating the geometric mean of the i-th row, and (ii) normalizing the geometric means of rows in the comparison matrix. This can be represented as:
M

GMj = [

j=1

bij ]1/M and
M

(3.6)

wj = GMj /

j=1

GMj

(3.7)

The geometric mean method of AHP is commonly used to determine the relative normalized weights of the attributes, because of its simplicity, easy determination of the maximum Eigen value, and reduction in inconsistency of judgements. Calculate matrices A3 and A4 such that A3 = A1 * A2 and A4 = A3 / A2, where A2 = [w1, w2, ….. , wj]T. Determine the maximum Eigen value max that is the average of matrix A4.

MADM Methods

31

Calculate the consistency index CI = ( max - M) / (M - 1). The smaller the value of CI, the smaller is the deviation from the consistency. Obtain the random index (RI) for the number of attributes used in decision making. Refer to Table 3.2 for details. Calculate the consistency ratio CR = CI/RI. Usually, a CR of 0.1 or less is considered as acceptable, and it reflects an informed judgement attributable to the knowledge of the analyst regarding the problem under study. Step 3: The next step is to compare the alternatives pair-wise with respect to how much better (i.e., more dominant) they are in satisfying each of the attributes, i.e., to ascertain how well each alternative serves each attribute. If there is N number of alternatives, then there will be M number of N x N matrices of judgements, since there are M attributes. Construct pair-wise comparison matrices using a scale of relative importance. The judgements are entered using the fundamental scale of the AHP method (Saaty, 1980, 2000). The steps are the same as those suggested under main step 2.
Table 3.2. Random index (RI) values __________________________________________________________________________ Attributes 3 4 5 6 7 8 9 10 RI 0.52 0.89 1.11 1.25 1.35 1.4 1.45 1.49 __________________________________________________________________________

In the AHP model, both the relative and absolute modes of comparison can be performed. The relative mode can be used when decision makers have prior knowledge of the attributes for different alternatives to be used, or when objective data of the attributes for different alternatives to be evaluated are not available. The absolute mode is used when data of the attributes for different alternatives to be evaluated are readily available. In the absolute mode, CI is always equal to 0, and complete consistency in judgements exists, since the exact values are used in the comparison matrices. Step 4: The next step is to obtain the overall or composite performance scores for the alternatives by multiplying the relative normalized weight (wj) of each attribute (obtained in step 2) with its corresponding normalized weight value for each alternative (obtained in step 3), and summing over the attributes for each alternative. This step is similar to the SAW method. Kwiesielewicz and Uden (2004) stated that even if the pair-wise comparison matrix BMxM is of acceptable consistency, the matrix may still be contradictory. If a matrix is contradictory, then it is difficult to derive weights that satisfy all the judgements expressed in BMxM. Hence, it is imperative to remove any such contradictory matrix from the decision-making process. For example, if bij = 1 and bik = 1, then bjk must be equal to 1. If any judgement is made such that bjk > 1, then contradiction is present in the matrix, and needs to be removed. Kwiesielewicz and Uden (2004) formulated an algorithm to check for the presence of any contradiction in BMxM.

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Decision Making in the Manufacturing Environment

It may be added here that the AHP method can also be used for assigning the values of relative importance (aij) to the attributes in graph theory and the matrix approach (GTMA). Refer to Sections 2.3 and 2.4. 3.2.4 Revised Analytic Hierarchy Process (RAHP) Method The revised AHP (RAHP) method was suggested by Belton and Gear (1983). They observed that sometimes it is possible for AHP to yield unjustifiable ranking reversals. The problem is that if a new alternative, identical to a non-optimal alternative, is introduced, then the ranking of the existing alternatives changes. Belton and Gear (1983) argued that the reason for this ranking inconsistency was that the relative performance measures of all alternatives in terms of each attribute (obtained in step 3 of Section 3.2.3) summed to one. Instead of having the relative performance values sum up to one, dividing each relative performance value by the maximum value in the corresponding vector of relative values was suggested. This avoids the rank reversals when a new non-optimal alternative is introduced. This method is also called ‘ideal mode AHP’. Saaty, the author of the original AHP, had accepted this revised version. 3.2.5 Multiplicative Analytic Hierarchy Process (MAHP) Method Barzilai and Lootsma (1994) and Lootsma (1999) proposed a multiplicative version of the AHP. In this MAHP method, the normalized weight value for each alternative (obtained in step 3 of Section 2.2.3) is raised to the power of the relative normalized weight (wj) of each attribute (obtained in step 2 of Section 3.2.3), with multiplication over all the attributes for each alternative. This step is similar to WPM. 3.2.6 Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) Method The TOPSIS method was developed by Hwang and Yoon (1981). This method is based on the concept that the chosen alternative should have the shortest Euclidean distance from the ideal solution, and the farthest from the negative ideal solution. The ideal solution is a hypothetical solution for which all attribute values correspond to the maximum attribute values in the database comprising the satisfying solutions; the negative ideal solution is the hypothetical solution for which all attribute values correspond to the minimum attribute values in the database. TOPSIS thus gives a solution that is not only closest to the hypothetically best, that is also the farthest from the hypothetically worst. The main procedure of the TOPSIS method for the selection of the best alternative from among those available is described below: Step 1: The first step is to determine the objective, and to identify the pertinent evaluation attributes. Step 2: This step represents a matrix based on all the information available on attributes. This matrix is nothing but the decision table shown in Table 3.1. Each row of this matrix is allocated to one alternative, and each column to one attribute.

MADM Methods

33

Therefore, an element mij of the decision table ‘D’ gives the value of the j-th attribute in original real values, that is, non-normalized form and units, for the i-th alternative. In the case of a subjective attribute (i.e., objective value is not available), a ranked value judgement on a scale is adopted. Table 2.1, as explained in Chapter 2, may be used for this purpose. Once a subjective attribute is represented on a scale, then the normalized values of the attribute assigned for different alternatives are calculated in the same manner as that for objective attributes. Step 3: Obtain the normalized decision matrix, Rij. This can be represented as Rij = mij / [ m2ij ]1/2 j=1 M

(3.8)

Step 4: Decide on the relative importance (i.e., weights) of different attributes with respect to the objective. A set of weights wj (for j=1, 2, ….. , M) such that wj =1 may be decided upon. Step 5: Obtain the weighted normalized matrix Vij. This is done by the multiplication of each element of the column of the matrix Rij with its associated weight wj. Hence, the elements of the weighted normalized matrix Vij are expressed as: Vij = wj Rij (3.9)

Step 6: Obtain the ideal (best) and negative ideal (worst) solutions in this step. The ideal (best) and negative ideal (worst) solutions can be expressed as: max min V+ = {( Vij / j J), ( Vij / j J’) / i = 1,2, …, N}, i i ={V1+, V2+, V3+, ……, VM+} min max V- = {( Vij / j J), ( Vij / j J’) / i = 1,2, …, N}, i i = {V1-, V2-, V3-, ……, VM-} where J = (j = 1, 2, …, M) /j is associated with beneficial attributes, and J’ = (j = 1, 2, …, M) /j is associated with non-beneficial attributes.

(3.10)

(3.11)

Vj+ indicates the ideal (best) value of the considered attribute among the values of the attribute for different alternatives. In the case of beneficial attributes (i.e., those of which higher values are desirable for the given application), Vj+ indicates the higher value of the attribute. In the case of non-beneficial attributes (i.e., those of which lower values are desired for the given application), Vj+ indicates the lower value of the attribute. Vj- indicates the negative ideal (worst) value of the considered attribute among the values of the attribute for different alternatives. In the case of beneficial attributes (i.e., those of which higher values are desirable for the given

34

Decision Making in the Manufacturing Environment

application), Vj- indicates the lower value of the attribute. In the case of nonbeneficial attributes (i.e., those of which lower values are desired for the given application), Vj- indicates the higher value of the attribute. Step 7: Obtain the separation measures. The separation of each alternative from the ideal one is given by the Euclidean distance in the following equations.
M

Si+ = { (Vij - Vj+ )2 }0.5 ,
J=1 M

i = 1, 2, …., N

(3.12)

Si- = { (Vij - Vj- )2 }0.5 ,
J=1

i = 1, 2, …., N

(3.13)

Step 8: The relative closeness of a particular alternative to the ideal solution, Pi, can be expressed in this step as follows. Pi = Si- / (Si+ + Si-) (3.14)

Step 9: A set of alternatives is generated in the descending order in this step, according to the value of Pi indicating the most preferred and least preferred feasible solutions. Pi may also be called the overall or composite performance score of alternative Ai. It may be added here that in step 4 of the TOPSIS method, even though the weights of different attributes with respect to the objective, wj (for j=1, 2, ….. , M), are decided by the decision maker rather arbitrarily, only few systematic methods can be used. The systematic methods of deciding the weights of attributes are explained below. 3.2.6.1 Entropy Method Shannon and Weaver (1947) proposed the entropy concept and this concept has been highlighted by Zeleny (1982) for deciding the objective weights of attributes. Entropy is a measure of uncertainty in the information formulated using probability theory. It indicates that a broad distribution represents more uncertainty than does a sharply peaked one. To determine weights by the entropy measure, the normalized decision matrix Rij, given by Equation 3.8, is considered. The amount of decision information contained in Equation 3.8 and associated with each attribute can be measured by the entropy value ej as:
N

ej = -k

i=1

Rij ln Rij

(3.15)

where k = 1/ln N is a constant that guarantees 0 ej 1. The degree of divergence (dj) of the average information contained by each attribute can be calculated as: dj = 1 - ej (3.16) The more divergent the performance ratings Rij (for i = 1, 2, ….., N) for the attribute Bj, the higher its corresponding dj, and the more important the attribute Bj for the decision-making problem under consideration (Zeleny, 1982).

MADM Methods

35

The objective weight for each attribute Bj (for j = 1, 2, ….., M) is thus given by:
M

w j = dj / d k k=1 (3.17)

3.2.6.2 Standard Deviation Method The standard deviation (SD) method calculates objective weights of the attributes by Equation 3.18.
M

wj =

j

/ k=1 k

(3.18)

where j is the standard deviation of the normalized vector Rj = (R1j, R2j, R3j, ….. , RNj) in Equation 3.8. Both the entropy method and standard deviation method calculate the objective weights of the attributes without giving any consideration to the preferences of the decision maker. 3.2.6.3 AHP Method Step 2 of the AHP method, described in Section 3.2.3, can be used for deciding the weights of attributes. In this case, the weights obtained are not objective but subjective, giving consideration to the preferences of the decision maker. 3.2.7 Modified TOPSIS Method In the TOPSIS method, the normalized decision matrix Rij is weighted by multiplying each column of the matrix by its associated attribute weight. The overall performance of an alternative is then determined by its Euclidean distance to Vj+ and Vj-. However, this distance is interrelated with the attribute weights, and should be incorporated in the distance measurement. This is because all alternatives are compared with Vj+ and Vj-, rather than directly among themselves. Deng et al. (2000) presented the weighted Euclidean distances, rather than creating a weighted decision matrix. In this process, the positive ideal solution (R+) and the negative ideal solution (R-), which are not dependent on the weighted decision matrix, are defined as: max min R+ = {( Rij / j J), ( Rij / j J’) / i = 1,2, …, N}, i i ={R1+, R2+, R3+, ……, RM+} min max R- = {( Rij / j J), ( Rij / j J’) / i = 1,2, …, N}, i i = {R1-, R2-, R3-, ……, RM-} where J = (j = 1, 2, …, M) /j is associated with beneficial attributes, and J’ = (j = 1, 2, …, M) /j is associated with non-beneficial attributes. The weighted Euclidean distances are calculated as

(3.19)

(3.20)

36

Decision Making in the Manufacturing Environment

M

Di+ = { wj(Rij - Rj+ )2 }0.5 ,
J=1

i = 1, 2, …., N

(3.21)

M

Di- = { wj (Rij - Rj- )2 }0.5 ,
J=1

i = 1, 2, …., N

(3.22)

The relative closeness of a particular alternative to the ideal solution, Pi-mod, can be expressed in this step as follows. Pi-mod = Di- / (Di+ + Di-) (3.23)

A set of alternatives is made in the descending order, according to the value of Pi-mod indicating the most preferred and least preferred feasible solutions. It may be mentioned here that instead of using vector normalization in the TOPSIS (or modified TOPSIS) method, linear normalization may be used (Lai et al., 1994). In that case, normalization is carried out as per Equation 3.24. Rij = mij / [(mij)max - (mij)min] (3.24)

where (mij)max is the best value and (mij)min the worst value of an attribute corresponding to the considered alternatives. 3.2.8 Compromise Ranking Method (VIKOR) The foundation for compromise solution was established by Yu (1973) and Zeleny (1982) and later advocated by Opricovic and Tzeng (2002, 2003, 2004, 2007) and Tzeng et al. (2002a, 2002b, 2005). The compromise solution is a feasible solution that is the closest to the ideal solution, and a compromise means an agreement established by mutual concession. The compromise solution method, also known as the VIKOR (VIšekriterijumsko KOmpromisno Rangiranje) method, was introduced as one applicable technique to implement within MADM. The multiple attribute merit for compromise ranking was developed from the Lp-metric used in the compromise programing method (Zeleny, 1982).
M

Lp,i = { 1 p

j=1

(wj [(mij)max - (mij )] / [(mij)max - (mij)min])p}1/p

(3.25)

; i = 1, 2, ….. , N

Within the VIKOR method L1,i (as Ei in Equation 3.26) and L ,i (as Fi in Equation 3.27) are used to formulate the ranking measure. The main procedure of the VIKOR method is described below: Step 1: The first step is to determine the objective, and to identify the pertinent evaluation attributes. Also determine the best, i.e., (mij)max, and the worst, i.e., (mij)min, values of all attributes. Step 2: Calculate the values of Ei and Fi:

MADM Methods

37

M

Ei =

j=1

wj [(mij)max - (mij )] / [(mij)max - (mij)min]

(3.26)

Fi = Maxm of {wj [(mij)max - (mij )] / [(mij)max - (mij)min] | j = 1, 2, ….., M} Step 3: Calculate the values of Pi: Pi = v ((Ei - Ei-min) / (Ei-max - Ei-min)) + (1 - v) ((Fi - Fi-min) / (Fi-max - Fi-min))

(3.27)

(3.28)

where Ei-max is the maximum value of Ei, and Ei-min the minimum value of Ei; Fi-max is the maximum value of Fi, and Fi-min is the minimum value of Fi.. v is introduced as weight of the strategy of ‘the majority of attributes’. Usually, the value of v is taken as 0.5. However, v can take any value from 0 to 1. Step 4: Arrange the alternatives in the ascending order, according to the values of Pi. Similarly, arrange the alternatives according to the values of Ei and Fi separately. Thus, three ranking lists can be obtained. The compromise ranking list for a given v is obtained by ranking with Pi measures. The best alternative, ranked by Pi, is the one with the minimum value of Pi. Step 5: For given attribute weights, propose a compromise solution, alternative Ak, which is the best ranked by the measure P, if the following two conditions are satisfied (Tzeng et al., 2005): (1/(N-1)). Al is the Condition 1: ‘Acceptable advantage’ P(Ak) - P(Al) second-best alternative in the ranking by P. Condition 2: ‘Acceptable stability in decision making’ aternative Ak must also be the best ranked by E and/or F. This compromise solution is stable within a decision-making process, which could be: ‘voting by majority rule’ (when v > 0.5 is needed) or ‘by consensus’ (when v 0.5) or ‘with veto’ (when v > 0.5). If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of: Alternatives Ak and Al if only condition 2 is not satisfied Alternatives Ak, Al, ….. , Ap if condition 1 is not satisfied; Ap is determined by the relation P(Ap) - P(Al) (1/(N-1)). VIKOR is a helpful tool in MADM, particularly in a situation where the decision maker is not able, or does not know how to express preference at the beginning of system design. The obtained compromise solution could be accepted by the decision makers because it provides a maximum ‘group utility’ (represented by Ei-min) of the ‘majority’, and a minimum of individual regret (represented by Fimin) of the ‘opponent’ (Opricovic and Tzeng, 2002, 2003, 2004, 2007). The compromise solutions could be the basis for negotiations, involving the decision makers’ preference by attribute weights.

3.3 Sensitivity Analysis
In sensitivity analysis, the ranking reversal of the alternatives is checked by changing the weights of relative importance of the attributes. The decision maker

38

Decision Making in the Manufacturing Environment

can check the ranking reversals by changing the weights (of relative importance) of the attributes by a percentage. However, it is obvious that if the assigned weights are changed, then the chances for rank reversals of the alternatives increase. Once the decision maker is clear about the relative importance of the attributes and assigns accordingly, then there is no need to check the ranking reversals simply by changing the weights. Hence, this is not developed further in this book. If the decision maker wishes to conduct sensitivity analysis, then he or she can do so.

3.4 Group Decision Making (GDM)
Group decision making is the process of making a judgement based upon the opinion of different individuals. Such decision making is a key component to the functioning of an organization, because organizational performance involves more than only one individual’s action. Moving from a single decision maker to a multiple decision-maker setting introduces a great deal of complexity into the analysis. Various methods of group decision making are used on a wide set of attributes ranging from the strictly technical, to the psychophysical and social, and finally to the logical and scientifically valid. The group decision-making concept can be applied to the MADM techniques described in Section 3.2. There are different ways in which GDM can be carried out (Yu, 1973; Chen and Hwang, 1992; Dyer and Forman, 1992; Csáki et al., 1995; Forman and Penewati, 1998; Chen, 2000; Lai et al., 2002; Jaganathan et al., 2006). Two ways were described by Forman and Peniwati (1998) and Jaganathan et al. (2006) for achieving group consensus in AHP. The two ways are: 1. Aggregation of individual judgements (AIJ), and 2. Aggregation of individual priorities (AIP). In the first case, it is assumed that several individuals act as one individual and their judgements, i.e., the opinions expressed regarding the relative importance (or weights) of the attributes, are aggregated using the weighted geometric mean to form a single composite attribute weight representing the total view of the group. In the second case, the group members act individually, and their final priorities are aggregated using the weighted arithmetic mean or weighted geometric mean. If there are n decision makers (g(k), k = 1, 2, ….. , n), then mathematically n bij (AIJ) = Pi (AIP) =

k=1 n k=1

(bij g(k))lg(k) (Pi g(k))lg(k) or n k=1

(3.29)

lg(k) Pi g(k)

(3.30)

where lg(k) is the importance of the decision maker in the group, and lg(k)= 1. Pi is the performance score of alternative Ai. The same approaches can be extended to other MADM methods, where group consensus is required. Csáki et al. (1995) presented a group decision support system. In this system, the method of calculating the group utility (group composite performance score) of alternative Ai (for i = 1, 2, ….., N) is as follows.

MADM Methods

39

For each attribute Bj (for j = 1, 2, ….., M), the individual weights of importance of the attributes are aggregated into the group weights wj (for j = 1, 2, ….. , M): n n

wj = [

k=1

lg(k) wj /

k=1

lg(k)

j = 1, 2, ….., M

(3.31)

The group qualification Qij of alternative Ai against attribute Bj is: n n

Qij = [

k=1

lg(k) mij /

k=1

lg(k) j = 1, 2, ….., M; i = 1, 2, ….., N

(3.32)

lg(k) need not be equal to 1 in Equations 3.31 and 3.32. The group utility Pi of alternative Ai is determined as the weighted algebraic mean of the aggregated qualification values with the aggregated weights:
M M

Pi = [

j=1

wj Qij /

j=1

wj

i = 1, 2, ….., N

(3.33)

In addition to the weighted algebraic means used in the above aggregations, weighted geometric means can be used. The best alternative of group decision is the one associated with the highest value of Pi. The MADM methods described in this chapter can efficiently deal with objective attributes. But most of the real-world MADM problems involve objective (i.e., crisp) as well as subjective (i.e., fuzzy and/or linguistic) attributes. Hence fuzzy MADM methods have been proposed by different researchers that can deal with fuzzy as well as crisp data of the attributes. However, Table 2.1, as explained in Chapter 2, may be used for the purpose of assigning a crisp value to the subjective attribute. Once a subjective attribute is represented by a crisp value, then the decision table contains only crisp data, and any MADM method can be applied. The next chapter presents a logical approach to solve fuzzy MADM problems.

References
Barzilai J, Lootsma FA (1994) Power relations and group aggregation in the multiplicative AHP and SMART. In: Proc. of the 3rd International Symposium on the AHP, George Washington University, Washington Belton V, Gear T (1983) On a short-coming of Saaty’s method of analytic hierarchies. Omega 11:228–230 Chen CT (2000) Extension of the TOPSIS for group decision making under fuzzy environment. Fuzzy Sets and Systems 114:1–9 Chen SJ, Hwang CL (1992) Fuzzy multiple attribute decision making-methods and applications. Lecture Notes in Economics and Mathematical Systems, Springer, New York Csáki P, Rapcsák T, Turchányi P, Vermes M (1995) Research and development for group decision aid in Hungary by WINGDSS, a Microsoft Windows based group decision support system. Decision Support Systems 14:205–221

40

Decision Making in the Manufacturing Environment

Deng H, Yeh CH, Willis RJ (2000) Inter-company comparison using modified TOPSIS with objective weights. Computers & Operations Research 27: 963– 973 Dyer RF, Forman EH (1992) Group decision support with the analytic hierarchy process. Decision Support Systems 8:99–124 Edwards W, Newman JR, Snapper K, Seaver D (1982) Multiattribute Evaluation. SAGE Publications, Newbury Park, California Figueira J, Greco S, Ehrgott M (2004) Multiple criteria decision analysis: state of the art surveys. Springer, New York Fishburn PC (1967) Additive utilities with incomplete product set: applications to priorities and assignments. Operations Research Society of America, Baltimore Forman E, Penewati K (1998) Aggregating individual judgements and priorities with the analytic hierarchy process. European Journal of Operational Research 108:165–169 Gal T (1999) Multicriteria decision making:advances in MCDM models algorithms, theory and applications. Kluwer Academic Publishers, Dordrecht Hwang CL, Yoon KP (1981) Multiple attribute decision making: methods and applications. Springer, New York Jaganathan S, Erinjeri JJ, Ker JI (2006) Fuzzy analytic hierarchy process based group decision support system to select and evaluate new manufacturing technologies. International Journal of Advanced Manufacturing Technology doi:10.1007/s00170-006-0446-1 Kwiesielewicz M, Uden EV (2004) Inconsistent and contradictory judgements in pairwise comparison method in the AHP. Computers & Operations Research 31:713–719 Lai VS, Bo KW, Cheung W (2002) Group decision making in a multiple criteria environment: a case using the AHP in software selection. European Journal of Operational Research 137:134–144 Lai YJ, Liu TY, Hwang CL (1994) TOPSIS for MODM. European Journal of Operational Research 76:486–500 Lootsma FA (1999) Multi-criteria decision analysis via ratio and difference judgement. Applied Optimization Series, Kluwer Academic Publishers, Dordrecht Miller DW, Starr MK (1969) Executive decisions with operations research. Prentice Hall, Englewood Cliffs, New Jersey Olson DL (1996) Decision aids for selection problems. Springer, New York Opricovic S, Tzeng GH (2002) Multicriteria planning of post-earthquake sustainable reconstruction. Computer-Aided Civil and Infrastructure Engineering 17:211–220 Opricovic S, Tzeng GH (2003) Fuzzy multicriteria model for post-earthquake landuse planning. Natural Hazards Review 4:59–64 Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research 156:445–455 Opricovic S, Tzeng GH (2007) Extended VIKOR method in comparison with outranking methods. European Journal of Operational Research 178:514–529

MADM Methods

41

Saaty TL (1980) The analytic hierarchy process. McGraw Hill, New York Saaty TL (2000) Fundamentals of decision making and priority theory with the AHP. RWS Publications, Pittsburg Shannon CE, Weaver W (1947) The mathematical theory of communication. The University of Illinois Press, Urbana Triantaphyllou E (2000) Multi-criteria decision making methods: a comparative study. Kluwer Academic Publishers, Dordrecht Triantaphyllou E and Sanchez (1997) A sensitivity analysis approach for some deterministic multi-criteria decision-making methods. Decision Sciences 28:151–194 Tzeng GH, Tsaur SH, Laiw YD, Opricovic S (2002) Multicriteria analysis of environmental quality in Taipei:public preferences and improvement strategies. Journal of Environmental Management 65:109–120 Tzeng GH, Teng MH, Chen JJ, Opricovic S (2002) Multicriteria selection for a restaurant location in Taipei. International Journal of Hospitality Management 21:171–187 Tzeng GH, Lin CW, Opricovic S (2005) Multi-criteria analysis of alternative-fuel buses for public transportation. Energy Policy 33:1373–1383 Yoon KP, Hwang CL (1995) Multiple attribute decision making. SAGE Publications, Beverly Hills, CA Yu PL (1973) A class of solutions for group decision problems. Management Science 19:936–946 Zanakis S, Solomon A, Wishart N, Dublish S (1998) Multi-attribute decision making: a comparison of select methods. European Journal of Operational Research, 107:507–529 Zeleny M (1982) Multiple criteria decision making. McGraw Hill, New York

4
__________________________________________________________________

A Logical Approach to Fuzzy MADM Problems

4.1 Introduction
The classical MADM methods assume all measures of performance of alternatives (mij) and weights of attributes (wj) values are crisp numbers. The alternatives with higher overall or composite performance scores are considered to be preferred by the decision maker. Since the final scores are real numbers, the preferred alternatives are those with higher overall or composite performance scores. In reality, measure of performance (mij) can be crisp, fuzzy and/or linguistic. For example, let a material be chosen for making an engineering component and the attributes considered are: cost of material, tensile strength, hardness, density, and corrosion resistance. The last attribute, corrosion resistance, is not quantifiable; rather, it is represented by linguistic terms such as ‘low’, ‘average’, ‘high’, etc. The other attributes can be crisp numbers. This MADM problem contains a mixture of fuzzy and crisp data. Most of the real-world MADM problems are of this type. Fuzzy MADM methods are proposed to solve problems that involve fuzzy data. Bellman and Zadeh (1970) were the first to relate fuzzy set theory to decision-making problems. Yager and Basson (1975) proposed fuzzy sets for decision making. Bass and Kwakernaak (1977) proposed a fuzzy MADM method that is widely regarded as the classic work of fuzzy MADM methods. During the last three decades, several fuzzy MADM methods have been proposed and reviewed (Chen and Hwang, 1992; Triantaphyllou and Lin, 1996; Triantaphyllou, 2000; Figueira et al., 2004). After a systematic and critical study of the existing fuzzy MADM methods, it has been found that the majority of the approaches require cumbersome computations. As a result, none of them are suitable for solving problems with more than 10 alternatives associated with more than 10 attributes. That drawback certainly limits their applicability to real-world problems. Further, most approaches require that the elements in the decision matrix be presented in a fuzzy format, though they are crisp in nature. Such an assumption violates the original intent of fuzzy set theory. If the data is precisely known, there is no subjectivity involved in the decision problem. Such data should never be represented in any fuzzy format. The conversion of crisp data into fuzzy format will increase the computational requirements. This, in turn, makes these fuzzy

44

Decision Making in the Manufacturing Environment

methods cumbersome to use, and incapable of solving problems that contain more than 10 alternatives and 10 attributes. Chen and Hwang (1992) proposed an approach to avoid the abovementioned difficulties, so that MADM problems can be meaningfully and efficiently solved in a fuzzy environment. The approach is composed of two phases. The first phase converts fuzzy data into crisp scores. The result of the first phase is a decision matrix that contains only crisp data. In the second phase, MADM methods, described in Chapter 3, can be utilized to determine the ranking order of alternatives. The easy-to-use and easy-to-understand characteristics of this approach make it valuable to management and system analysts.

4.2 Method Proposed by Chen and Hwang (1992)
The method proposed by Chen and Hwang (1992) first converts linguistic terms into fuzzy numbers and then the fuzzy numbers into crisp scores. The method is described below. 4.2.1 Converting Linguistic Terms to Fuzzy Numbers This method systematically converts linguistic terms into their corresponding fuzzy numbers. It contains eight conversion scales. The conversion scales were proposed by synthesizing and modifying the works of Wenstop (1976), Bass and Kwakernaak (1977), Efstathiou and Rajkovic (1979), Bonissone (1982), Efstathiou and Tong (1982), Kerre (1982), and Chen (1988), To demonstrate the method, a 5-point scale having the linguistic terms low, fairly low, medium, fairly high, and high, as shown in Figure 4.1 (Chen and Hwang, 1992), is considered. These linguistic terms can be equated to other terms like low, below average, average, above average, and high. 4.2.2 Converting Fuzzy Numbers to Crisp Scores The method uses a fuzzy scoring approach that is a modification of the fuzzy ranking approaches proposed by Jain (1976, 1977), and Chen (1985). The crisp score of fuzzy number ‘M’ is obtained as follows: max (x)

=

x, 0 x 1 0, otherwise 1 - x, 0 x 1 0, otherwise

(4.1)

min

(x) =

(4.2)

The fuzzy max and fuzzy min of fuzzy numbers are defined in a manner such that absolute locations of fuzzy numbers can be automatically incorporated in the comparison cases. The left score of each fuzzy number ‘Mi’ is defined as (4.3) L(Mi) = Sup[ min(x) ^ Mi(x)] x A Logical Approach

45

Figure 4.1. Linguistic terms to fuzzy numbers conversion (5-point scale) (from Chen and Hwang 1992; with kind permission of Springer Science and Business Media)

The L(Mi) score is a unique, crisp, real number in (0, 1). It is the maximum membership value of the intersection of fuzzy number Mi and the fuzzy min. The right score may be obtained in a similar manner: (4.4) R (Mi) = Sup[ max(x) ^ Mi(x)] x Again, R (Mi) is a crisp number [0,1]. Given the left and right scores, the total score of a fuzzy number Mi is defined as: (4.5) T (Mi) = [ R(Mi) + 1 - L(Mi)] / 2

4.3 Demonstration of the Method
Now, the 5-point scale is considered to demonstrate the conversion of fuzzy numbers into crisp scores (Figure 4.1). Linguistic term Fuzzy number Low M1 Below average M2 Average M3 Above average M4 High M5 The maximizing and minimizing sets are defined as Equations 4.1 and 4.2. From Figure 4.1, membership functions of M1, M2, M3, M4, and M5 are written as:

46

Decision Making in the Manufacturing Environment

M1(x)

=

1, x = 0 (0.3-x) / (0.3), 0

x

0.3

M2(x)

=

(x-0)/ (0.25), 0 x 0.3 (0.5-x) / (0.25), 0.25 x 0.5 (x-0.3)/ (0.2), 0.3 (0.7-x)/ (0.2), 0.5 x x 0.5 0.7

M3(x)

=

M4(x)

=

(x-0.5)/ (0.25), 0.5 x 0.75 (1.0-x)/ (0.25), 0.75 x 1.0 (x-0.7)/ (0.3), 0.7 1, x = 1 x 1.0

M5(x)

=

The right, left, and total scores are computed as follows for M1:
R

(M1) = Sup [ x max (x) ^ min (x) ^

M1(x)] M1(x)]

= 0.23

L(M1)

= Sup [ x = 1.0

T

(M1) = [

R (M1) + 1 -

L(M1)]

/ 2 = 0.115

Similarly, the right, left, and total scores are computed for M2, M3, M4, and M5 and are tabulated as follows: i 1 2 3 4 5
R (Mi) 0.23 0.39 0.58 0.79 1.0 L (Mi) 1.0 0.8 0.59 0.4 0.23 T (Mi) 0.115 0.295 0.495 0.695 0.895

Hence, the linguistic terms with their corresponding crisp scores are given in Table 4.1. Instead of assigning arbitrary values for various attributes, this fuzzy method reflects the exact linguistic descriptions in terms of crisp scores. Hence, it gives better approximation of linguistic descriptions that are widely used. It may be added here that this method can be used not only for assigning values to the attributes, but also for deciding the relative importance between the attributes. For example, using the same 5-point scale, the relative importance between two attributes can be described as given in Table 4.2.

A Logical Approach

47

Table 4.1. Conversion of linguistic terms into fuzzy scores (5-point scale) __________________________________________________________ Linguistic term Fuzzy number Crisp score __________________________________________________________ 0.115 Low M1 Below average M2 0.295 0.495 Average M3 Above average M4 0.695 High M5 0.895 __________________________________________________________

Table 4.2. Conversion of linguistic terms into fuzzy scores (relative importance value on a 5-point scale) ________________________________________________________________________ Linguistic term Fuzzy number Crisp score ________________________________________________________________________ One attribute is very less important than the other M1 0.115 0.295 One attribute is less important than the other M2 Two attributes are equally important M3 0.495 One attribute is more important than the other M4 0.695 One attribute is much more important than the other M5 0.895 ________________________________________________________________________

The decision makers can appropriately make use of any of the eight scales suggested by Chen and Hwang (1992). For example, an 11-point scale is shown in Figure 4.2, and the corresponding crisp scores of the fuzzy numbers are given in Table 4.3.
Table 4.3. Conversion of linguistic terms into fuzzy scores (11-point scale) __________________________________________________________ Linguistic term Fuzzy number Crisp score __________________________________________________________ Exceptionally low M1 0.045 0.135 Extremely low M2 Very low M3 0.255 0.335 M4 Low Below average M5 0.410 0.500 Average M6 Above average M7 0.590 0.665 High M8 Very high M9 0.745 0.865 Extremely high M10 0.955 Exceptionally high M11 __________________________________________________________

48

Decision Making in the Manufacturing Environment

Figure 4.2. Linguistic terms to fuzzy numbers conversion (11-point scale) (from Chen and Hwang 1992; with kind permission of Springer Science and Business Media)

Using the same 11-point scale, the relative importance between two attributes can be described as given in Table 4.4.
Table 4.4. Conversion of linguistic terms into fuzzy scores (relative importance value on an 11-point scale) __________________________________________________________________________ Fuzzy number Crisp score Linguistic term __________________________________________________________________________ 0.045 One attribute is exceptionally less important than the other M1 0.135 One attribute is extremely less important than the other M2 One attribute is very less important than the other M3 0.255 0.335 One attribute is less important than the other M4 One attribute is slightly less important than the other M5 0.410 0.500 Two attributes are equally important than the other M6 One attribute is slightly more important than the other M7 0.590 0.665 One attribute is more important than the other M8 One attribute is much more important than the other M9 0.745 0.865 One attribute is extremely more important than the other M10 One attribute is exceptionally more important than the other M11 0.955 __________________________________________________________________________

It may be remembered that Tables 2.1 and 2.2 are suggested in Chapter 2 for assigning the objective values to the subjective attributes, and for assigning the relative importance between the attributes, respectively. Now, Tables 4.1 (or 4.3) and 4.2 (or 4.4) may be used for the same purpose, as these give better

A Logical Approach

49

approximation of the linguistic terms. The case studies presented in Chapters 5–30 of this book utilize Tables 4.3 and 4.4.

References
Bass SJ, Kwakernaak H (1977) Rating and ranking of multi-aspects alternatives using fuzzy sets. Automatica 13:47–58 Bellman RE, Zadeh LE (1970) Decision-making in a fuzzy environment. Management Science 17:212–223 Bonissone PP (1982) A fuzzy sets based linguistic approach: theory and applications. In: Gupta MM, Sanchez E (eds) Approximate reasoning in decision analysis. North Holland, pp 329–339 Chen SH (1985) Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems 17:113–129 Chen SM (1988) A new approach to handling fuzzy decision-making problems. In: Proc. 18th International Symposium on Multiple-Valued Logic, Computer Society Press, Palma de Mallorca, Spain Chen SJ, Hwang CL (1992) Fuzzy multiple attribute decision making-methods and applications. Lecture Notes in Economics and Mathematical Systems, Springer, New York Efstathiou J, Rajkovic V (1979) Multiattribute decision making using a fuzzy hewristic approach. IEEE Transactions on Systems, Man, Cybernetics, SMC9:326–333 Efstathiou J, Tong R (1980) Ranking fuzzy sets using linguistic preference relations. In: Proc. 10th International Symposium on Multiple-Valued Logic, Northwestern University, Evanston Figueira J, Greco S, Ehrgott M (2004) Multiple criteria decision analysis: state of the art surveys. Springer, New York Jain R (1976) Decision making in the presence of fuzzy variables. IEEE Transactions on Systems, Man and Cybernetics, SMC 6:698–703 Jain R (1977) A procedure for multi-aspect decision making using fuzzy sets. International Journal of System Science 8:1–7 Kerre EE (1982) The use of fuzzy set theory in electrocardiological diagnostics. In: Gupta MM, Sanchez E (eds) Approximate reasoning in decision analysis. North Holland, pp 277–282 Triantaphyllou E (2000) Multi-criteria decision making methods: a comparative study. Kluwer Academic Publishers, Dordrecht Triantaphyllou E, Lin CT (1996) Development and evaluation of five fuzzy multiattribute decision making methods. International Journal of Approximate Reasoning 14:281–310 Wenstop F (1976) Fuzzy set simulation models in a systems dynamic perspective. Kybernetes 6:209–218 Yager RR, Basson D (1975) Decision-making with fuzzy sets. Decision Sciences 6:590–600

Part 2
Applications of GTMA and Fuzzy MADM Methods in the Manufacturing Environment

5
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Material Selection for a Given Engineering Application

5.1 Introduction
An ever increasing variety of materials is available today, each having its own characteristics, applications, advantages, and limitations. When selecting materials for engineering designs, a clear understanding of the functional requirements for each individual component is required, and various important criteria or attributes need to be considered. Material selection attribute is defined as a factor that influences the selection of a material for a given application. These attributes include: physical properties, electrical properties, magnetic properties, mechanical properties, chemical properties, manufacturing properties (machinability, formability, weldability, castability, heat treatability, etc.), material cost, product shape, material impact on environment, performance characteristics, availability, fashion, market trends, cultural aspects, esthetics, recycling, target group, etc. The selection of an optimal material for an engineering design from among two or more alternative materials on the basis of two or more attributes is a multiple attribute decision-making problem. Various approaches have been proposed in the past to help address the issue of material selection. Liao (1996) presented a fuzzy multicriteria decision-making method for material selection. However, the method is complicated and requires much more computation. Farag (1997) proposed a simple mathematics-based weighted properties method that can be used when several properties should be taken into consideration. Giachetti (1998) described a prototype material and manufacturing process selection system that integrates a formal multiple attribute decision model with a relational database. The decision model enables the representation of the designer's preferences over the decision attributes. A compatibility rating between the product profile requirements and the alternatives stored in the database for each decision attribute was generated using possibility theory. The vectors of compatibility ratings were aggregated into a single rating of that alternative's compatibility. A ranked set of compatible material and manufacturing process alternatives was the output by the system. Ashby (2000) proposed multi-objective optimization in materials design and selection, using ‘utility’ functions. Ashby et al. (2004) provided a comprehensive

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review of the strategies or methods for materials selection, from which three types of materials selection methodology were identified: (i) free searching based on quantitative analysis, (ii) checklist/questionnaire based on expertise capture, and (iii) inductive reasoning and analog procedure. All of these methods use materials data in either a non-computerized or computerized form. For the free-searching method, there are already a number of well-documented methods, the best known being the graphical engineering selection method or the ranking method (Ashby, 1992; Ashby and Johnson, 2002). A checklist/questionnaire method has been proposed by a number of researchers, the most recent described by Edwards (2005), where the author developed a structured set of questions to improve the likelihood of achieving an optimal design solution. The inductive reasoning and analog procedure resulted from the rapid development of information technology tools, and the application of artificial intelligence. Some of representative examples include a knowledge-based system for materials management that involves materials selection (Trethewey et al., 1998), a knowledge-based system for materials selection (Sapuan, 2001), integrated information technology approach (Jalham, 2006), fuzzy knowledge-based decision support system for selection of manufacturing processes and materials (Zha, 2005) and a case-based reasoning method (Amen and Vomacka, 2001). However, these systems and methods are complex and necessitate knowledge extensive. A framework to represent and deal with the relationships between design variables of both materials parameters and system-level parameters was proposed by Raj (2000) and Raj et al. (2000). The idea of an integrated approach for materials selection and structural design had been advocated by Edwards (2002). The materials parameters could be material properties, or they could be parameters describing the micro/nanostructure of the materials. Ermolaeva et al. (2002) studied materials selection combined with structural optimization. However, the elaborate materials selection method proposed by these authors was limited to selecting from a limited number of specific materials. Lin and Lin (2003) discussed state-of-art research on environmentally conscious material selection methodologies. Ljungberg (2005) presented guidelines for sustainable product development with special regard to materials, design and ecology. Giudice et al. (2005) proposed a method to integrate mechanical and environmental performances for materials selection in the life-cycle design process. Kuo et al. (2006) presented an innovative method, namely, green fuzzy design analysis (GFDA), which involves simple and efficient procedures to evaluate product design alternatives based on environmental consideration using fuzzy logic. The hierarchical structure of environmentally conscious design indices was constructed using the analytical hierarchy process (AHP), which includes five aspects: (1) energy, (2) recycling, (3) toxicity, (4) cost, and (5) material. After weighting factors for the environmental attributes are determined, the most desirable design alternative can be selected using a fuzzy MADM method. Edwards and Deng (2006) discussed the aspects of supporting design decision making when applying materials in combination. Deng and Edwards (2007) presented an overview of recent research in materials identification and materials selection. Shanian and Savadogo (2006a) had presented a material selection model using an MADM method known as ELECTRE. However, the ELECTRE method

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uses the concept of outranking relationship, and the procedure is rather lengthy. Only a partial prioritization of alternative materials is computed in ELECTRE models. As the number of alternatives increases, the amount of calculations rises quite rapidly, and the computational procedures are elaborate. In their other works (Shanian and Savadogo, 2006b, 2006c), the authors had proposed ELECTRE IV and TOPSIS methods for material selection of metallic bipolar plates for polymer electrolyte fuel cell. Matos and Simplicio (2006) presented a practical example concerning the selection of materials to substitute polyvinyl chloride in automobile interiors. Bovea and Gallardo (2006) tested five life-cycle impact assessment methods, and applied to different polymer materials used for packaging purposes. The aim of the study was to demonstrate the need to perform a sensitivity analysis when a single environmental score is applied during the process of selecting materials, in order to enhance the environmental performance of products. Chan and Tong (2006) proposed a multicriteria weighted average method using gray relational analysis to rank the materials. Rao (2006) presented a material selection model using graph theory and the matrix approach. A ‘material suitability index’ was proposed that evaluates and ranks the materials for a given engineering component. Kumar and Singh (2006) presented an intelligent system for selection of materials for progressive die components. Cheng et al. (2006) used the fuzzy AHP method for selection of technological forecasting methods for predictuion of new materials development. Manshadi et al. (2007) proposed a numerical method for materials selection combining non-linear normalization with a modified digital logic method. Guisbiers and Wautelet (2007) presented the details of materials selection for thin films for radio frequency micro-electromechanical systems (MEMS). Rao and Davim (2007) used the TOPSIS method for selection of materials for a given application. A good amount of research work has been carried out in the past on materials selection. However, there is a need for a simple, systematic, and logical scientific method or mathematical tool to guide user organizations in taking a proper material selection decision. The objective of a material selection procedure is to identify the material selection attributes, and obtain the most appropriate combination of material selection attributes in conjunction with the real requirement. Thus, efforts need to be extended to determine attributes that influence material selection, using a simple logical approach, to eliminate unsuitable materials and to select a proper material to strengthen the existing material selection procedure. This is considered in this chapter using graph theory and the matrix approach (GTMA) and fuzzy MADM methods described in Chapters 2–4 of the book.

5.2 Examples
To demonstrate and validate the application of decision-making methods, two examples are considered. In both, GTMA is applied first, and subsequently a few MADM methods are applied to rank and select the materials for the given applications.

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5.2.1 Example 1 Manshadi et al. (2007) proposed a numerical method for materials selection combining nonlinear normalization with a modified digital logic method. This example problem is related with selection of a suitable material for a cryogenic storage tank for transportation of liquid nitrogen. The material selection problem considers seven alternative materials and seven attributes, and the data are given in Table 5.1.
Table 5.1. Objective data of the attributes of example 5.2.1(from Manshadi et al., 2007; reprinted with permission from Elsevier) _______________________________________________________________ Material Material selection attributes TI YS YM D TE TC SH _______________________________________________________________ 1 75.5 420 74.2 2.8 21.4 0.37 0.16 2 95 91 70 2.68 22.1 0.33 0.16 3 770 1,365 189 7.9 16.9 0.04 0.08 4 187 1,120 210 7.9 14.4 0.03 0.08 5 179 875 112 4.43 9.4 0.016 0.09 6 239 1,190 217 8.51 11.5 0.31 0.07 7 273 200 112 8.53 19.9 0.29 0.06 _______________________________________________________________ TI = Toughness index (based on UTS, yield strength YS, and ductility e at -196°C) = (UTS + YS)e/2; YS = Yield strength (MPa); YM = Young’s modulus (GPa); D= Density (g/cm3); TE = Thermal expansion (given in 106 /°C); TC = Thermal conductivity (cal/cm2/cm/°C/s); SH = Specific heat (cal/g/°C) Material 1:Al 2024-T6; Material 2:Al 5052-O; Material 3:SS 301-FH; Material 4:SS310-3AH; Material 5:Ti-6Al-4V; Material 6:Inconel 718; Material 7:70Cu-30Zn

5.2.1.1 Application of Graph Theory and Matrix Approach (GTMA) Various steps of the methodology, proposed in Section 2.6, are carried out: Step 1: In the present work, the attributes considered are the same as those of Manshadi et al. (2007) and these are: toughness index (TI), yield strength (YS), Young’s modulus (YM), density (D), thermal expansion (TE), thermal conductivity (TC) and specific heat (SH). The quantitative values of the material selection attributes, which are given in Table 5.1, are normalized. TI, YS, and YM are considered as beneficial attributes, and the remaining attributes as nonbeneficial. Values of these seven attributes are normalized, as explained in Section 2.4, and are given in Table 5.2 in the respective columns.

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Table 5.2. Normalized data of the attributes of example 5.2.1 __________________________________________________________ Material Normalized values of material selection attributes TI YS YM D TE TC SH __________________________________________________________ 1 0.0981 0.3077 0.3419 0.9571 0.4393 0.0432 0.375 2 0.1234 0.0667 0.3226 1 0.4253 0.0485 0.375 3 1 1 0.8709 0.3392 0.5562 0.4 0.75 4 0.2429 0.8205 0.9677 0.3392 0.6528 0.5333 0.75 5 0.2325 0.6410 0.5161 0.6049 1 1 0.6667 6 0.3104 0.8718 1 0.3149 0.8174 0.0516 0.8571 7 0.3546 0.1465 0.5161 0.3142 0.4724 0.0552 1 __________________________________________________________

Relative importance of attributes (aij) is also assigned the values, as explained in Section 2.4, using Table 4.4. Let the decision maker (i.e., designer) select the following assignments: TI 0.255 0.135 0.410 0.335 0.135 0.135 YS 0.745 0.335 0.665 0.665 0.335 0.335 YM 0.865 0.665 0.255 0.745 0.500 0.500 D 0.590 0.335 0.745 0.410 0.255 0.255 TE 0.665 0.335 0.255 0.590 0.335 0.335 TC 0.865 0.665 0.500 0.745 0.665 0.500 SH 0.865 0.665 0.500 0.745 0.665 0.500 (5.1) However, it may be added that, in actual practice, the designer can judiciously decide these values of relative importance depending on the requirements. The assigned values are for demonstration purpose only. Step 2: 1. The material selection attributes graph, showing the presence as well as relative importance of the above attributes, is similar to Figure 2.2 but with seven attributes is drawn. It is not shown here for obvious reasons. 2. The material selection attributes matrix of this graph can be written based on Equation 2.10. It is similar to matrix Equation 5.1 but also with the presence of diagonal elements Ai. 3. The material selection attributes function is written. However, it may be added that as a computer program is developed for calculating the permanent function value of a matrix, this step can be skipped. 4 & 5. The material selection index is calculated using the values of Ai and aij for each alternative material. The material selection index values of different materials are given below in descending order: Material 3: SS 301-FH 39.1123 Material 5: Ti-6Al-4V 34.0554 Material 4: SS 310-3AH 30.6316 Material 6: Inconel 718 29.0377

TI YS YM A17x7 = D TE TC SH

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Material 7: 70Cu-30Zn 20.0377 Material 1: Al 2024-T6 17.2897 Material 2: Al 5052-O 16.2634 From the above values of the material selection index, it is understood that the material designated as 3, i.e., SS 301-FH, is the right choice for the given problem of selection of a suitable material for a cryogenic storage tank for transportation of liquid nitrogen. The second choice is Ti-6Al-4V, and the last choice is Al 5052-O. These results match those suggested by Manshadi et al. (2007) using nonlinear normalization and a modified digital logic method. However, it may be mentioned that the ranking depends upon the judgements of relative importance made by the designer. The ranking presented may change if the designer assigns different relative importance values to the attributes. The same is true for the approach proposed by Manshadi et al. (2007). However, the GTMA method is superior to the method used by Manshadi et al. (2007) in that it enables a more critical analysis than the digital logic method, since any number of quantitative and qualitative attributes can be considered. Also, the proposed method can deal with material selection attributes on a qualitative scale using fuzzy logic. Such a provision is missing in the method suggested by Manshadi et al. (2007). Further, the proposed method assigns the values of relative importance based on a fuzzy scale, whereas the weights assigned to various attributes by Manshadi et al. (2007) were rather arbitrary and too simplistic. The use of permanent concept helps in better appreciation of the attributes, and it characterizes the considered material selection problem, as it contains all possible structural components of the attributes and their relative importance (from a combinatorial point of view). The coefficients of similarity are calculated and are given in Table 5.3.
Table 5.3. Values of coefficient of similarity for the alternative materials of example 5.2.1 ___________________________________________________________________ Material 2 3 4 5 6 7 ___________________________________________________________________ 1 0.94 0.442 0.564 0.508 0.595 0.863 2 0.416 0.531 0.531 0.56 0.812 3 0.783 0.871 0.742 0.512 4 0.899 0.948 0.654 0.853 0.588 5 6 0.69 ___________________________________________________________________

5.2.1.2 SAW Method Using the same weights of the attributes as those of Manshadi et al. (2007), the overall performance score (i.e., material selection index, in this example) for each material is calculated using the normalized data of the attributes given in Table 5.2, and Equation 3.2. For example, the value of Pi for the material designated as 1 is calculated as: 0.28x0.0981 + 0.14x0.3077 + 0.05x0.3419 + 0.24x0.9571 + 0.19x0.4393 + 0.05x0.0432 + 0.05x0.0432 = 0.421722. The values of Pi are arranged in descending order as given below:

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Material 3: SS 301-FH 0.4217 Material 5: Ti-6Al-4V 0.5991 Material 6: Inconel 718 0.5352 Material 4: SS 310-3AH 0.5008 Material 1: Al 2024-T6 0.4217 Material 2: Al 5052-O 0.4020 Material 7: 70Cu-30Zn 0.3635 The SAW method also suggests the material designated as 3, i.e., SS 301-FH, as the right choice for the given problem of selection of a suitable material for a cryogenic storage tank for transportation of liquid nitrogen. The second choice is Ti-6Al-4V, and the last choice is the material designated as 7, i.e., 70Cu-30Zn. However, comparing the attribute data of the materials of the last two choices, i.e., materials 2 and 7, it may not be logical to propose 7 as the last choice. 5.2.1.3 WPM The overall performance score (i.e., material selection index, in this example) for each material is calculated using the normalized data of the attributes given in Table 5.2 for the given weights of the attributes, and Equation 3.4. For example, the value of Pi for the material designated as 1 is calculated as: 0.09810.28 + 0.30770.14 + 0.34190.05 + 0.95710.24 + 0.43930.19 + 0.04320.05 + 0.04320.05 = 0.2889. The values of Pi are arranged in the descending order as given below: Material 3: SS 301-FH 0.6843 Material 5: Ti-6Al-4V 0.5248 Material 4: SS 310-3AH 0.4440 Material 6: Inconel 718 0.4412 Material 1: Al 2024-T6 0.2889 Material 2: Al 5052-O 0.2505 Material 7: 70Cu-30Zn 0.1809 WPM also suggests the material designated as 3, i.e., SS 301-FH, as the right choice for the given material selection problem. The second choice is Ti-6Al-4V, and the last choice is material designated as 7, i.e., 70Cu-30Zn. 5.2.1.4 AHP and its Versions As the weights of the attributes are already available, the alternatives are compared pair-wise with respect to how much better they are in satisfying each of the attributes. This means ascertaining how well each alternative serves each attribute. In this example, as there are seven alternatives and seven attributes, there will be seven numbers of 7 x 7 matrices of judgements. The absolute mode is used, as data of the attributes for different alternatives to be evaluated are readily available. Comparison of alternative materials is shown in Table 5.4 with respect to TI (a beneficial attribute), and D (a non-beneficial attribute) only for demonstration purpose. Similar comparisons can be shown with respect to the other five attributes. Since the exact values are used in these comparison matrices, CI is always equal to 0, as there is complete consistency in judgements.

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Table 5.4. Pair-wise comparison matrices for the alternative materials of example 5.2.1 __________________________________________________________________________ 1 2 3 4 5 6 7 R I __________________________________________________________________________ TI 1 1 0.7947 0.098 0.4037 0.4218 0.316 0.2765 0.0415 0.0981 2 1.258 1 0.123 0.508 0.531 0.397 0.348 0.0522 0.1234 3 10.2 8.13 1 4.12 4.3 3.22 2.82 0.4235 1 4 2.477 1.97 0.243 1 1.045 0.782 0.685 0.1028 0.2429 5 2.37 1.883 0.233 0.957 1 0.75 0.656 0.0984 0.2325 6 3.1645 2.52 0.31 1.28 1.33 1 0.875 0.1314 0.3104 7 3.62 2.87 0.355 1.46 1.524 1.143 1 0.1501 0.3546 D 1 2 3 4 5 6 7

1 1.045 0.355 0.355 0.633 0.329 0.329

0.957 1 0.339 0.339 0.605 0.315 0.315

2.82 2.95 1 1 1.78 0.929 0.929

2.82 2.95 1 1 1.78 0.929 0.929

1.58 1.653 0.561 0.561 1 0.521 0.521

3.04 3.17 1.077 1.077 1.92 1 1

0.046 3.18 1.079 1.079 1.926 1.002 1.002

0.2473 0.2584 0.0877 0.0877 0.1563 0.0815 0.0812

0.9571 1 0.3392 0.3392 0.6049 0.3149 0.3142

__________________________________________________________________
R: Relative weight I: Ideal weight

In the above table, both relative (R) and idealized (I) weight vectors of the seven alternatives are given. The idealized vector is obtained by dividing each element of the relative weight vector by its largest element. The advantage of using idealized weights is that the ranking of the existing alternatives does not change even if a new alternative, identical to a non-optimal alternative, is introduced. It may be observed that the idealized weights of the alternatives obtained for the attributes in Table 5.4 are nothing but the normalized data given in Table 5.2. This means that whenever quantitative data of the attributes are available, the data can be normalized directly as explained in Section 3.2.1. The overall or composite performance scores (i.e., material selection indexes, in this example) for the alternatives are obtained by multiplying the relative normalized weight (wj) of each attribute with its corresponding normalized weight value (relative weight or ideal weight) for each alternative, and summing over all the attributes for each alternative. This step is similar to the SAW method. The alternative materials are arranged in the descending order of the material selection index. The results of the revised AHP and relative AHP are shown below: Material Ideal mode Relative mode Material 3: SS 301-FH 0.4217 0.2246 Material 5: Ti-6Al-4V 0.5991 0.1691 Material 6: Inconel 718 0.5352 0.1449 Material 4: SS 310-3AH 0.5008 0.1397 Material 1: Al 2024-T6 0.4217 0.1105 Material 2: Al 5052-O 0.4020 0.1062 Material 7: 70Cu-30Zn 0.3635 0.1049

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Both the AHP and revised AHP methods give the same material rankings in this example. The application of the multiplicative AHP method gives the ranking of materials in the sequence of 3-5-4-6-1-2-7 for the given weights of the attributes. This ranking is the same as that obtained using WPM. 5.2.1.5 TOPSIS Method Step 1: The objective is to evaluate the seven alternative materials, and the attributes are: toughness index (TI), yield strength (YS), Young’s modulus (YM), density (D), thermal expansion (TE), thermal conductivity (TC), and specific heat (SH). For this particular material selection problem, TI, YS, and YM are considered as beneficial attributes, and remaining attributes as non-beneficial. Step 2: The next step is to represent all the information available for the attributes in the form of a decision matrix. The data given in Table 5.1 are represented as matrix D7x7. However, the matrix is not shown here, as it is simply the repetition of data given in Table 5.1 but represented in a matrix form. Step 3: The quantitative values of the material selection attributes, which are given in Table 5.1, are normalized as explained in Section 3.2.6 and the normalized matrix R7x7 is shown below: 0.0843 0.1058 0.8575 0.2083 0.1994 0.2662 0.3040 0.1787 0.0387 0.5808 0.4765 0.3723 0.5064 0.0851 0.1842 0.1738 0.4690 0.5212 0.2780 0.5384 0.2780 0.1604 0.1535 0.4526 0.4526 0.2538 0.4875 0.4888 0.4719 0.4873 0.3727 0.3176 0.2073 0.2537 0.4389 0.5660 0.5040 0.0610 0.0458 0.0244 0.4734 0.4430 0.5640 0.5640 0.2820 0.2820 0.3170 0.2466 0.2114

Step 4: Relative importance of attributes (aij) can be assigned the values as explained in Section 3.2.6. However, to make a comparison of the proposed method with that of Manshadi et al. (2007), the same weights considered by those authors are assigned in the present work. These are: WTI = 0.28, WYS = 0.14, WYM = 0.05, WD = 0.24, WTE = 0.19, WTC = 0.05, and WSH = 0.05. Step 5: The weighted normalized matrix, V7x7, is calculated. 0.0236 0.0296 0.2401 0.0583 0.0558 0.0745 0.0851 0.0250 0.0054 0.0813 0.0667 0.0521 0.0708 0.0119 0.0092 0.0087 0.0234 0.0260 0.0139 0.0269 0.0139 0.0385 0.0368 0.1086 0.1086 0.0609 0.1170 0.1173 0.0896 0.0926 0.0708 0.0603 0.0393 0.0482 0.0834 0.0283 0.0252 0.00305 0.0022 0.0012 0.0236 0.0221 0.0282 0.0282 0.0141 0.0141 0.0158 0.0123 0.0105

Step 6: The next step is to obtain the ideal (best) and negative ideal (worst) solution. These are calculated as: VTI+ = 0.24011 VTI= 0.02362 + VYS = 0.08131 VYS= 0.00542

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= 0.00869 0.02692 VYMVYM+ = + VD = 0.03685 V D= 0.11730 = 0.09260 = 0.03938 VTEVTE+ = 0.02830 = 0.00122 VTCVTC+ VSH+ = 0.01057 VSH= 0.02820 Step 7: The next step is to obtain the separation measures, and these are calculated as: S 1+ = 0.23222 S 1= 0.08126 + = 0.08073 = 0.23263 S 2S2 = 0.23287 S 3= 0.07854 S 3+ S 4+ = 0.19715 S 4= 0.08516 = 0.10071 = 0.18865 S 5S 5+ = 0.09724 S 6= 0.18583 S 6+ S 7+ = 0.19456 S 7= 0.06547 Step 8: The relative closeness of a particular alternative to the ideal solution is calculated and these are: P1 = 0.25922 P2 = 0.25763 P3 = 0.74779 P4 = 0.30165 P5 = 0.34804 P6 = 0.34352 P7 = 0.25178 This relative closeness to ideal solution can be considered as the ‘material selection index ’. Step 9: The alternative materials are arranged in descending order of their material selection index. This can be arranged as: 3-5-6-4-1-2-7. From these values of index, it is understood that the material designated as 3 is the first right choice, material 5 the second choice, and material 7 the last choice for the given application under the given conditions. These results match with those suggested by Manshadi et al. (2007) regarding the first five choices. Manshadi et al. (2007) proposed a preference order of 3-5-6-4-1-7-2 for the same weights assigned to the attributes. A close look at the data presented in Table 5.1 suggests that material 7 is better than 2 with respect to six attributes (it may be remembered that the total number of attributes is seven). Thus, it is not logical to propose material 7 as the last choice in the TOPSIS method. Rather, proposing material 2 as the last choice is the right decision. Thus, the proposal of material 2 as the last choice by Manshadi et al. (2007) is logical. 5.2.1.6 Modified TOPSIS Method In this process, the positive ideal solution (R+) and the negative ideal solution (R-), which are not dependent on the weighted decision matrix, are given by using Equations 3.19 and 3.20. RTI+ RYS+ RYM+ RD+ RTE+ RTC+ RSH+ = = = = = = = 0.8575 0.5808 0.5384 0.1535 0.2073 0.0244 0.2114 RTIRYSRYMR DRTERTCRSH= = = = = = = 0.0843 0.0387 0.1738 0.4888 0.4873 0.5660 0.5640

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D1+ D2+ D3+ D4+ D5+ D6+ D7+

The weighted Euclidean distances are calculated as = 0.4801 D1= 0.1693 = 0.1652 = 0.4885 D2= 0.4821 = 0.1650 D3= 0.3789 D4= 0.2459 = 0.2563 = 0.3657 D5= 0.2497 = 0.3688 D6= 0.4117 D7= 0.1476 The relative closeness of a particular alternative to the ideal solution is calculated (i.e., material selection index) and these are: P1-mod = 0.26067 P2-mod = 0.25268 P3-mod = 0.74505 P4-mod = 0.39345 P5-mod = 0.41196 P6-mod = 0.40376 P7-mod = 0.26392 The alternative materials are arranged in descending order of their material selection index. This can be arranged as: 3-5-6-4-7-1-2. It can be observed that material 2 can be proposed as the last choice. Thus, the modified TOPSIS method has provided a more logical selection procedure, compared to the simple TOPSIS method. 5.2.1.7 Compromise Ranking Method (VIKOR) Step 1: The objective is to evaluate the seven alternative materials, and the attributes are: toughness index (TI), yield strength (YS), Young’s modulus (YM), density (D), thermal expansion (TE), thermal conductivity (TC), and specific heat (SH). For this particular material selection problem, TI, YS, and YM are considered as beneficial attributes, and remaining attributes as non-beneficial. The best, i.e., (mij)max, and the worst, i.e., (mij)min values of all attributes are also determined. Step 2: The values of Ei and Fi are calculated using Equations 3.26 and 3.27, and are given below. The same weights as those considered by Manshadi et al. (2007) are assigned in the present work. The weights are: wTI = 0.28, wYS = 0.14, wYM = 0.05, wD = 0.24, wTE = 0.19, wTC = 0.05, and wSH = 0.05. E1 = 0.28 + 0.1039 + 0.0486 + 0.0049 + 0.1795 + 0.05 + 0.05 = 0.7169 E2 = 0.2721 + 0.14 + 0.05 + 0 + 0.19 + 0.0443 + 0.05 = 0.7464 E3 = 0 + 0 + 0.0095 + 0.2142 + 0.1122 + 0.0034 + 0.001 = 0.3403 E4 = 0.2351 + 0.0269 + 0.0024 + 0.2142 + 0.0748 + 0.00198 + 0.001 = 0.5564 E5 = 0.2383 + 0.0538 + 0.0357 + 0.0718 + 0 + 0 + 0.015 = 0.4146 E6 = 0.2141 + 0.0192 + 0 + 0.2392 + 0.0314 + 0.0415 + 0.005 = 0.5504 E7 = 0.2004 + 0.1280 + 0.0357 + 0.24 + 0.1571 + 0.0387 + 0 = 0.7999 Ei-min = 0.3403 Ei-max = 0.7999 R1 = 0.28 R2 = 0.2721 R3 = 0.2142 R4 = 0.2351 R5= 0.2383 R6 = 0.2392 R7 = 0.24 Fi-min = 0.2142 Fi-max = 0.28 Step 3: The values of Pi are calculated using Equation 3.28 and for v = 0.5. P1 = 0.9095 P2 = 0.8817 P3 = 0 P4 = 0.3938 P5 = 0.2639 P6 = 0.4185 P7 = 0.696

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Step 4: The alternatives are arranged in ascending order, according to the values of Pi. Similarly, the alternatives are arranged according to the values of Ei and Fi separately. Thus, three ranking lists are obtained. The best alternative, ranked by Pi, is the one with the minimum value of Pi. P3 = 0 E3 = 0.3403 F3 = 0.2142 P5 = 0.2639 E5 = 0.4146 F4 = 0.2351 E6 = 0.5504 F5 = 0.2383 P4 = 0.3938 P6 = 0.4185 E4 = 0.5564 F6 = 0.2392 P7 = 0.696 E1 = 0.7169 F7 = 0.24 E2 = 0.7464 F2 = 0.2721 P2 = 0.8817 P1 = 0.9095 E7 = 0.7999 F1 = 0.28 Step 5: For the given attribute weights, the compromise solution, alternative material 3, which is the best ranked by the measure P is suggested, as it satisfies both conditions discussed in Section 3.2.7. It may be noted here that for the same weights of importance of the attributes, all decision-making methods described in the example suggest material 3 as the first right choice. The choice may change when different weights are used. 5.2.2 Example 2 Now, another example is considered to demonstrate the application of the GTMA and fuzzy MADM methods. This example problem is related with selection of a suitable work material for a product that needs to be designed for operating in a high-temperature oxygen-rich environment. This selection problem considers six alternative materials and four attributes and the data are shown in Table 5.5.
Table 5.5. Quantitative data of the attributes of example 5.2.2 __________________________________________________________________________ Material Material selection attributes Hardness (HB) MR (%) Cost ($/lb) Corrosion resistance __________________________________________________________________________ 1 420 25 5 Extremely high (0.865) 2 350 40 3 High (0.665) 3 390 30 3 Very high (0.745) 4 250 35 1.3 High (0.665) 5 600 30 2.2 High (0.665) 6 230 55 4 Average (0.5) __________________________________________________________________________ MR: Machinability rating is based upon machining AISI 1112 steel with a rating of 100%

5.2.2.1 Application of Graph Theory and Matrix Approach (GTMA) Step 1: In this example, the attributes considered are: hardness (H), machinability rating of work material based on cutting speed (MR), cost of the material (C), and corrosion resistance (CR). The quantitative values of the material selection attributes, which are given in Table 5.5, are to be normalized. For the given material selection problem, H, M, and CR are considered as beneficial attributes and C as a non-beneficial attribute. Cost is not considered that important in the present example. Corrosion resistance (CR) is expressed qualitatively, and hence

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ranked value judgements on fuzzy conversion scale, as shown in Table 2.3, are made and given in parentheses in Table 5.5. Values of the four attributes are normalized, and are given in Table 5.6 in the respective columns.
Table 5.6. Normalized data of example 5.2.2 ___________________________________________________________________ Material Normalized values of material selection attributes H M C R ___________________________________________________________________ 1 0.7 0.4545 0.26 1 2 0.5833 0.7273 0.4333 0.7688 3 0.65 0.5454 0.4333 0.8613 4 0.4167 0.6364 1 0.7688 5 1 0.5454 0.5909 0.7688 6 0.3833 1 0.325 0.578 ___________________________________________________________________

Step 2: The relative importance of attributes (aij) is also assigned. Let the decision maker (i.e., designer) select the following assignments: H 0.665 0.335 0.335 M 0.335 0.255 0.255 C 0.665 0.745 0.335 CR 0.665 0.745 0.335 -

H M A24x4 = C CR

It may be added once again that the assigned values in this example are for demonstration purpose only. Following the remaining steps given in the methodology, the material selection index is calculated using the values of Ai and aij for each alternative material. The material selection index values of different materials are given below in descending order: Material 5: 1.635251 Material 4: 1.616897 Material 2: 1.335821 Material 3: 1.316612 Material 1: 1.201707 Material 6: 1.125037 From the above values of the material selection index, it is understood that the material designated as 5 is the right choice for the given material selection problem. The second choice is material 4, and the last choice is material 6. 5.2.2.2 SAW Method The procedure suggested by Edwards et al. (1982) to assess weights for each of the attributes to reflect its relative importance in the material selection decision is followed here. First, the attributes are ranked in order of importance and 10 points are assigned to the least important attribute CR. Cost C is also considered least important, and equal to CR in this example. Then, the next-least important attribute H is chosen, 20 points are assigned to it, and the attribute M is given 30 points to

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reflect the relative importance. The final weights are obtained by normalizing the sum of the points to one. For example, the weight for attribute M is calculated by 30/(30+20+10+10) = 0.4286. The weights of H, C, and CR are calculated as 0.2857, 0.1428, and 0.1428 respectively. Using these weights and the normalized data of the attributes for different alternative materials, the material selection index values are calculated, and are arranged in descending order of the index. Material 5: 0.7786 Material 2: 0.6295 Material 3: 0.6193 Material 4: 0.6130 Material 1: 0.6098 Material 6: 0.5789 This method also suggests material 5 as the first choice. 5.2.2.3 WPM The weights used in the SAW method are used in this method and the values of Pi are calculated. The values of Pi are arranged in descending order as given below: Material 5: 0.7514 Material 2: 0.6194 Material 3: 0.6074 Material 4: 0.5817 Material 1: 0.5652 Material 6: 0.5222 The ranking suggested by both the SAW method and WPM is the same for this example. 5.2.2.4 AHP and its Versions The AHP method may use the same weights as those in the SAW method. In that case, the ranking of the materials will be same as that suggested by the SAW method. However, if the decision maker decides to use the AHP method rather than SAW and the weights used in it, then he or she has to make pair-wise comparisons of the attributes to determine the weights (wj) of the attributes. Let the decision maker prepares the following matrix: H 1 3 1/2 1/2 M 1/3 1 1/4 1/4 C 2 4 1 1 CR 2 4 1 1

H M A34x4 = C CR

Following the procedure given in Section 3.2.3 of Chapter 3, the relative normalized weights (wj) of the attributes are calculated, and these are WH = 0.2195, WM = 0.5376, WC = 0.1214, and WCR = 0.1214. The value of max is 4.0206, and CR is 0.0077. As the calculated value of CR is less than the allowed CR value of 0.1, there is good consistency in the judgements made. Also there is no contradiction in the judgements.

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The value of the material selection index is now calculated using the above weights, and the normalized data of the attributes given in Table 5.6. This leads to the ranking given by the revised AHP or ideal mode of AHP. The materials are arranged in the descending order of the material selection index. Material 6: 0.7314 Material 5: 0.6777 Material 2: 0.6650 Material 3: 0.5931 Material 4: 0.6483 Material 1: 0.5509 It may be observed that the above ranking is for the given preferences of the decision maker. The ranking depends upon the judgements of relative importance of attributes made by the decision maker. For the weights of attributes used in this method, the simple AHP as well as the multiplicative AHP methods give the same ranking of materials, i.e., 6-5-2-4-31. 5.2.2.5 TOPSIS Method The quantitative values of the material selection attributes, which are given in Table 5.5, are normalized as explained in Section 3.2.6 and the normalized matrix R6x4 is shown below: 0.1868 0.1556 0.1734 0.1112 0.2668 0.1023 0.0786 0.1258 0.0940 0.1100 0.0943 0.1729 0.0883 0.0530 0.0530 0.0229 0.0389 0.0707 0.0730 0.0560 0.0628 0.0560 0.0560 0.0421

R6x4 =

The relative importance of attributes (aij) can be assigned values as explained in Section 3.2.6. Using the same weights as those used in SAW method, the ranking of materials is 5-3-2-1-6-4. Using the same weights as those used in the AHP method, the ranking of materials is 6-2-5-4-3-1. 5.2.2.6 Modified TOPSIS Method Using the same weights as those used in the SAW method, the ranking of materials is 5-2-3-4-6-1. Using the same weights as those used in the AHP method, the ranking of materials is 6-5-2-4-3-1. It may be noted here that for the same weights of importance of the attributes, all decision-making methods described in this example suggest material 5 as the first right choice. The choice may change when different weights are used. It is observed, from the application of GTMA and various MADM methods for material selection problems, that the relative importance (i.e., weights) of the material selection attributes decides the ranking of the alternative materials to a significant extent. The decision maker has to be clear about his or her preferences, and choose a particular decision-making method to select the best material for the given engineering application.

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References
Amen R, Vomacka P (2001) Case-based reasoning as a tool for materials selection. Materials & Design 22:353–358 Ashby MF (1992) Materials selection in mechanical design. Pergamon Press, New York Ashby MF (2000) Multi-objective optimization in material design and selection. Materials & Design 48:359–369 Ashby MF, Johnson K (2002) Materials and design: the art and science of materials selection in product design. Butterworth Heinemann, Oxford Ashby MF, Brechet YJM, Cebon D, Salvo L (2004) Selection strategies for materials and processes. Materials & Design 25:51–67 Bovea MD, Gallardo A (2006) The influence of impact assessment methods on materials selection for eco-design. Materials & Design 27:209–215 Chan JWK, Tong TKL (2006) Multi-criteria material selections and end-of-life product strategy: grey relational analysis approach. Materials & Design doi:10.1016/j.matdes.2006.02.016 Cheng AC, Chen CJ, Chen CY (2006) A fuzzy multiple criteria comparison of technology forecasting methods for predicting the new materials development. Technological Forecasting and Social Change doi:10.1016/j.techfore. 2006.08.002 Deng YM, Edwards KL (2007) The role of materials identification and selection in engineering design. Materials & Design 28:131–139 Edwards KL (2002) Linking materials and design: an assessment of purpose and progress. Materials & Design 23:255–264 Edwards KL (2005) Selecting materials for optimum use in engineering components. Materials & Design 26:469–473 Edwards KL, Deng M (2006), Supporting design decision-making when applying materials in combination. Materials & Design doi: 10.1016/ j.matdes.2005. 12.009 Edwards W, Newman JR, Snapper K, Seaver D (1982) Multiattribute Evaluation. SAGE Publications, Newbury Park, California Ermolaeva NS, Kaveline KG, Spoormaker JL (2002) Material selection combined with optimal structural design: concept and some results. Materials & Design 23:459–470 Farag M (1997) Materials selection for engineering design. Prentice-Hall, New York Giachetti RE (1998) A decision support system for material and manufacturing process selection. Journal of Intelligent Manufacturing 9:265–276 Giudice F, La Rosa G, Risitano A (2005) Materials selection in the lifecycle design process: a method to integrate mechanical and environmental performances in optimal choice. Materials & Design 26:9–20 Guisbiers G, Wautelet M (2007) Materials selection for micro-electromechanical systems. Materials & Design 28:246–248 Jalham IS (2006) Decision-making integrated information technology (IIT) approach for material selection. International Journal of Computer Applications in Technology 25:65–71

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Kumar S, Singh R (2006) A short note on an intelligent system for selection of materials for progressive die components. Journal of Materials Processing Technology doi:10.1016/j.jmatprotec.2006.09.004 Kuo TC, Chang SH, Huang SH (2006) Environmentally conscious design by using fuzzy multi-attribute decision-making. International Journal of Advanced Manufacturing Technology 29:209–215 Liao TW (1996) A fuzzy multicriteria decision-making method for material selection. Journal of Manufacturing Systems 15:1–12 Lin F, Lin L (2003) A discussion of the state-of-art research on environmentally conscious material selection methodologies for the reduction of products’ toxic impact. The Journal of Sustainable Product Design 3:119–134 Ljungberg LY (2005) Materials selection and design for development of sustainable products. Materials & Design doi:10.1016/j.matdes.2005.09.006 Manshadi BD, Mahmudi H, Abedian A, Mahmudi R (2007) A novel method for materials selection in mechanical design: combination of non-linear normalization and a modified digital logic method. Materials & Design 28:8– 15 Matos MJ, Simplicio MH (2006) Innovation and sustainability in mechanical design through materials selection. Materials & Design 27:74–78 Raj R (2000) An interdisciplinary framework for the design and life prediction of engineering systems. Trans ASME, Journal of Engineering Materials Technology 122:348–354 Raj R, Enright MP, Frangopol DM (2000) A system level partitioning approach for analyzing the origins of variability in life prediction of tungsten filaments for incandescent lamps. Materials & Design 21:9–18 Rao RV (2006) A material selection model using graph theory and matrix approach. Materials Science and Engineering A 431:248–255 Rao RV, Davim JP (2007) A decision making framework model for material selection using a combined multiple attribute decision making method. International Journal of Advanced Manufacturing Technology (in press) Sapuan SM (2001) A knowledge-based system for materials selection in mechanical engineering design. Materials & Design 22:687–695 Shanian A, Savadogo O (2006a) A material selection model based on the concept of multiple factor decision making. Materials & Design 27:329–337 Shanian A, Savadogo O (2006b) TOPSIS multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell. Journal of Power Sources 159:1095–1104 Shanian A, Savadogo O (2006c) A non-compensatory compromised solution for material selection of bipolar plates for polymer electrolyte membrane fuel cell (PEMFC) using ELECTRE IV. Electrochimica Acta 51:5307–5315 Trethewey KR, Wood RJK, Puget Y, Roberge PR (1998) Development of a knowledge-based system for materials management. Materials & Design 19:39–56 Zha XF (2005) A web-based advisory system for process and material selection in concurrent product design for a manufacturing environment. International Journal of Advanced Manufacturing Technology 25:233–243

6
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Evaluation of Product Designs

6.1 Introduction
Today’s world is characterized by major changes in market and economic conditions coupled with rapid advances in technology. As a natural result of this, companies have been forced to develop new products for current markets, principally technology-driven or high-tech markets. The changing economic conditions and technologies combined with increased domestic and global competition, changing customer needs, rapid product obsolescence and emergence of new markets require a very fast innovation process (Ayag, 2005). The final decision to select a particular design for a given product is perhaps the most critical stage in product design development. Obviously, such a decision is influenced by many factors, the specifics of which are not known a priori during the design stage. As such, a quantitative basis for comparison and selection of the best design solution among a host of alternatives could greatly impact on the eventual success or failure of a product in the market. The importance of this issue calls for more sophisticated design selection criteria, and methods to incorporate all important factors of interest into the selection of a single final design (Besharati et al., 2006). Thurston (1991) presented a more formal theory and methodology for design by mathematically modeling the functional relationships between design decisions and the ultimate overall worth of a design. A formal methodology for the evaluation of design alternatives (MEDA) was presented which could be used to evaluate design alternatives in the iterative design/redesign process. Multi-attribute utility analysis was employed to compare the overall utility or value of alternative designs as a function of the levels of several performance characteristics of a manufactured system. The evaluation function reflected the designer's preferences for sets of multiple attributes. A case study of materials selection and design in the automotive industry was presented, which illustrated the steps followed in application of the method. Hsiao (1998) proposed a fuzzy decision-making method for selecting an optimum design from various design alternatives. The development of a juicer was taken as an example in the study. The evaluation objectives were arranged in a hierarchical structure with several levels. The relative contribution of each

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objective to the overall value of the solution, and the rating or degree of approximation of a solution with respect to a given objective were quantified with the membership functions of a fuzzy set. A computer program based on a weighted generalized mean method was used to calculate the fuzzy probability level by level from the lowest-level objectives. After the fuzzy expected values of the top-level objectives were calculated, they were used to make a decision quantitatively on selecting the optimal design alternative. Matsatsinis and Siskos (1999) presented a new methodology for the development of new products, and an intelligent decision support system, named MARKEX, which was an implementation of the methodology. The system acted as a consultant for marketers, providing visual support to enhance understanding and to overcome lack of expertise. The databases of the system were the results of consumer surveys, as well as financial information of the enterprises involved in the decision-making process. Calantone et al. (1999) illustrated the use of the analytic hierarchy process (AHP) as a decision support model to aid managers in selecting new product ideas to pursue. The authors then presented an in-depth example of an actual application of AHP in new product screening, and discussed the usefulness of this process in gathering and processing knowledge for making new product screening decisions. Ozer (1999) conducted a survey on new product evaluation models. Several market-based decision support methodologies have been reported in the literature to aid product selection (Parameswaran et al., 2001; Choi et al., 2004), single product design selection (Balakrishnan and Jacob, 1995, 1996), and product line design (Alexouda, 2005). The selection criteria in these methods were mostly based on either maximization of the market share, or of the seller’s return or minimization of job completion time. Haque et al. (2000) described the development and application of case-based reasoning (CBR) to provide decision support for project managers and engineers during the early phases of new product development in a concurrent engineering (CE) environment. Suh (2001) introduced a metric known as a probability of success in product design which combined the uncertainty in each attribute level with a customer’s acceptable range. Edwards (2002) discussed the priorities for concurrent engineering towards more strategic product design for manufacture and assembly. Hsiao and Chou (2004) presented a creativity-based design process for innovative product design. Gulcin and Orhan (2004a) identified the decision points in the NPD process, and the uncertainty factors affecting those points. Next, the necessary decision models and techniques were determined to help the decision makers to reduce their risks. Finally, an integrated approach based on fuzzy logic to shape the decisions was presented, with an application in software development. In another work, Gulcin and Orhan (2004b) presented the uncertainty factors related to NPD, and proposed an integrated approach based on fuzzy logic, neural networks, and multi-criteria decision making to enable the most appropriate decision making. A case study in a toy manufacturing firm served to demonstrate the potential of the methodology. Petrick and Echols (2004) proposed that firms adopt a broader heuristic for making new product development choices. The heuristic approach required moving

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beyond traditional finance-based thinking, and suggested that firms concentrate on technological trajectories by combining technology roadmapping, information technology (IT), and supply chain management to make more sustainable new product development decisions. Pan and Santner (2004) considered applications where the product design or process design is considered to be seriously flawed if its performance is inferior at any level of the environmental factor. The authors developed a theory for a class of subset selection procedures that identify product designs maximizing the worstcase performance over environmental conditions for general combined array experiments. Ozer (2005) presented an integrated framework for understanding how various factors affect decision making in new product evaluation, and provided guidelines for reducing their negative impacts on new product decisions. The results indicated that the quality of new product evaluation decisions was affected by four major sets of factors, namely, the nature of the task, the type of individuals who are involved in the decisions, the way the individuals’ opinions are elicited, and the way the opinions are aggregated. Lo et al. (2006) reported a new idea-screening method for new product development (NPD), with a group of decision makers having imprecise, inconsistent and uncertain preferences. The authors presented a new method for new product screening in the NPD process by relaxing a number of assumptions, so that imprecise, inconsistent and uncertain ratings could be considered. In addition, a new similarity measure for vague sets was introduced to produce a ratings aggregation for a group of decision makers. The method was able to provide decision makers with consistent information and to model situations where vague and ill-defined information exists in the decision process. Maddulapalli et al. (2006) conducted sensitivity analysis for product design selection with an implicit value function. Besharati et al. (2006) proposed a generalized purchase modeling approach that considered three important factors (anticipated market demand for the design, designers’ preferences, and uncertainty in achieving predicted design attribute levels under different usage conditions and situations), and developed a customer-based expected utility metric that formed the basis for a decision support system for supporting the selection in product design. The objective of a product design selection procedure is to identify the product design selection attributes, and obtain the most appropriate combination of the attributes in conjunction with the real requirements. A product design selection attribute is defined as a factor that influences the selection of a product design for a given application. Efforts need to be made to determine attributes which influence product design selection for a given industrial application, using a logical approach, to eliminate unsuitable product designs, and to select a proper product design to strengthen the existing product design selection procedure. Pertinent attributes and the alternative product designs involved are to be identified. Values of the attributes and their relative importance are to be obtained. An objective or subjective value, or its range, may be assigned to each identified attribute as a limiting value, or threshold value, for its acceptance for the considered product design selection problem. An alternative product design with each of its selection attributes, meeting the acceptance value, may be short-listed. After short-listing the

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alternative product designs, the main task in choosing the alternative product design is to see how it serves the attributes considered. The next section presents the applications of the GTMA and fuzzy MADM methods for product design selection for a given application.

6.2 Example
Now, to demonstrate and validate the application of proposed decision-making methods, the case study presented by Besharati et al. (2006) is considered. Besharati et al. (2006) generated a number of product alternatives within the design process. The product attributes are both performance- and market- related, and were obtained using design simulation tools and marketing models. The objective of their work was to present a decision support system (DSS) that aggregates the three factors (market demand, uncertainty in achieving nominal attribute levels and designer’s preferences) into a single valued metric. The authors considered the problem of design and selection of a power electronic device based on three performance attributes. The attributes were: manufacturing cost, junction temperature, and thermal cycles to failure. Ten design alternatives were considered that had tradeoffs with respect to one another. Table 6.1 presents the data of the design alternatives.
Table 6.1. Description of design alternatives (from Besharati et al., 2006; reprinted with permission from Elsevier) __________________________________________________________________________ Design no. Junction temperature (°C) Cycles to failure Manufacturing cost($) __________________________________________________________________________ 1 126 22,000 85 2 105 38,000 99 3 138 14,000 65 4 140 13,000 60 5 147 10,600 52 6 116 27,000 88 32,000 92 7 112 8 132 17,000 75 9 122 23,500 85 10 135 15,000 62 __________________________________________________________________________

6.2.1 Graph Theory and Matrix Approach (GTMA) The attributes considered are the same as those of Besharati et al. (2006), and these are: manufacturing cost (MC), junction temperature (JT), and thermal cycles to failure (CF). The quantitative values of the product design selection attributes, given in Table 6.1, are to be normalized. In this example, CF is a beneficial attribute, and MC and JT are non-beneficial attributes. The values of these attributes are normalized, and are given in Table 6.2 in the respective columns.

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Table 6.2. Normalized values of the product design selection attributes ___________________________________________________ Design no. JT CF MC ___________________________________________________ 1 0.8333 0.5789 0.6118 2 1 1 0.5253 3 0.7609 0.3684 0.8 4 0.75 0.3421 0.8667 5 0.7143 0.2789 1 6 0.9052 0.7105 0.5909 7 0.9375 0.8421 0.5652 8 0.7955 0.4474 0.6933 9 0.8607 0.6184 0.6118 10 0.7778 0.3947 0.8397 ___________________________________________________

Let the designer chooses the following preferences (i.e., relative importance): JT CF MC JT --0.335 0.255 CF 0.665 --0.335 MC 0.745 0.665 --Manufacturing cost (MC) is considered more important to the designer than cycles to failure (CF), than junction temperature (JT). The product design selection attributes digraph, product design selection attributes matrix of the digraph and product design selection function for the matrix can be prepared. However, these are not shown here. The value of the product design selection index (PDSI) is calculated using the values of Ai and aij for each product design. The product design selection index values of different product designs are given below in descending order: 2 1.2514 7 1.1373 6 1.0447 9 0.9675 1 0.9234 10 0.8890 8 0.8598 4 0.8439 3 0.8383 5 0.8305 From the values of the product design selection index, it is understood that the product design designated as 2 is the best choice among the considered ten product designs for the given power electronic device. The next choice is 7, and the last choice is 5. However, the ranking obtained using GTMA differs from that obtained by Besharati et al. (2006), according to which the first choice was 5. The ranking proposed by Besharati et al. (2006) was 5-10-4-3-7-6-2-8-9-1. A close look at the values of the attributes of the alternative product designs 2 and 5 reveal that 2 is much better than 5 in the case of JT and CF attributes, and 5

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is better in the case of the MC attribute. In fact, the values of JT and CF for 5 are worst among all alternative product designs. At the same time, the values are best for 2 among all the alternative product designs considered. It appears that the results obtained by Besharati et al. (2006) are biased towards the MC attribute. In the above case, only the designer’s preferences are accounted. Besharati et al. (2006) presented a second scenario in which the market information was also accounted for in terms of customer’s purchase decision. The specific conditions are given below: The device has to endure at least 25,000 cycles, or its junction temperature must remain less than 130°C. or The customer is willing to purchase the device if the price is less than $170 (i.e., manufacturing cost less than $70), and it lasts at least 20,000 cycles. Applying the above conditions to the data in Table 6.2 gives only five product designs, 1, 2, 6, 7, and 9. These designs can be ranked as 2-7-6-9-1 using graph theory and the matrix approach. However, the ranking proposed by Besharati et al. (2006) was 7-6-9-1-2. Again, it appears that Besharati et al. (2006) had given much more importance to the MC attribute than to CF and JT. Besharati et al. (2006) presented a third scenario 3 with multiple segments. Four customer segments were assumed. The purchase decisions were defined as follows: Segment I: The device needs to tolerate at least 20,000 cycles. Its junction temperature should not exceed 130°C. The available budget for this purchase is no more than $185 per product item. Segment II: The desired device needs to have one of the following criteria: endure more than 35,000 cycles, junction temperature lower than 110°C, price less than $160. Segment III: The budget does not exceed $185 per product item, and the eligible device needs to satisfy either one of the following criteria: lasting more than 20,000 cycles, junction temperature lower than 130°C. Segment IV: The desired device should tolerate at least 30,000 cycles, and its junction temperature should not exceed 110°C. From Table 6.1, it can be understood that product design alternatives 1 and 9 lie within the customer’s range of segments I and III; 2 lies within the customer’s range of segments II and IV, and 4 and 5 lie within the customer’s range of segment II. Of these, product design 2 obtains the higher PDSI. 6.2.2 AHP Method Let the decision maker prepares the following relative importance matrix: JT 1 3 5 CF 1/3 1 3 MC 1/5 1/3 1

JT CF MC

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In this example, MC is given comparatively higher importance, and CF is given high importance. The normalized weights of each attribute are calculated, and these are: WJT = 0.1047, WCF = 0.2582, and WMC = 0.6371. The value of max is 3.0387 and CR = 0.0372, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. The value of PDSI is now calculated using the above weights and the normalized data of the attributes given in Table 6.2. This leads to the ranking given by the revised AHP or ideal mode of AHP methods. The alternative product designs are arranged in descending order of the PDSI: 5 0.7837 4 0.7186 10 0.7172 2 0.6962 3 0.6839 7 0.6744 6 0.6534 8 0.6396 9 0.6384 1 0.6254 The AHP method suggests product design 5 as the preferred design when no market information is considered. When market information is also considered, then the ranking will be 2-7-6-9-1 (which is the same as that given by GTMA). It may be noted that the ranking depends upon the judgements of relative importance of attributes made by the decision maker. 6.2.3 TOPSIS Method Various steps of TOPSIS methodology using the AHP method for assigning the relative importance of attributes are described below: Step 1: The objective is to evaluate the alternative product designs for the power electronic device. The attributes considered are the same as those of Besharati et al. (2006), and these are: manufacturing cost (MC), junction temperature (JT), and thermal cycles to failure (CF). Step 2: The next step is to represent all the information available on attributes in the form of a decision matrix. The data are shown in Table 6.1. Step 3: The quantitative values of the product design selection attributes, which are given in Table 6.1, are to be normalized. CF is a beneficial attribute, and higher values are desirable. MC and JT are non-beneficial attributes, and lower values are desirable. The values of these attributes for different product designs are normalized but are not shown here. Step 4: Let the decision maker assigns the relative importance weights using the AHP method described in Section 6.2.2. The normalized weights of each attribute are calculated, and these are: WJT = 0.1047, WCF = 0.2582, and WMC = 0.6371. The value of max is 3.0387 and CR = 0.0333, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made.

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Step 5: The weighted normalized matrix is calculated. 0.0326 0.0272 0.0357 0.0362 0.0380 0.0300 0.0289 0.0342 0.0316 0.0349 0.0786 0.1357 0.0500 0.0464 0.0373 0.0964 0.1143 0.0607 0.0839 0.0536 0.2202 0.2565 0.1684 0.1555 0.1347 0.2280 0.2384 0.1943 0.2202 0.1607

Step 6: The next step is to obtain the ideal (best) and negative ideal (worst) solutions. These are given as: V1+ = 0.0272 V1- = 0.0380 + V2 = 0.1357 V2- = 0.0379 + V3- = 0.2565 V3 = 0.1347 Step 7: The next step is to obtain the separation measures, and these are: S1+ = 0.1030 S1- = 0.0548 + S2- = 0.0985 S2 = 0.1218 + S3 = 0.0925 S3- = 0.0889 + S4 = 0.0921 S4- = 0.1014 + S5- = 0.1218 S5 = 0.0985 + S6 = 0.1013 S6- = 0.0656 + S7 = 0.1059 S7- = 0.0791 + S8- = 0.0664 S8 = 0.0961 + S9 = 0.1001 S9- = 0.0590 + S10 = 0.0865 S10- = 0.0972 Step 8: The relative closeness of a particular alternative to the ideal solution is calculated, and these are: P1 = 0.3473; P2 = 0.4471; P3 = 0.4902; P4 = 0.5241; P5 = 0.5529; P6 = 0.3933; P7 = 0.4276; P8 = 0.4086; P9 = 0.3709; P10 = 0.5292 This relative closeness to the ideal solution is named as the ‘product design selection index (PDSI)’ in the present example. Step 9: The scenarios are arranged in descending order of their PDSI. This can be arranged as 5-10-4-3-2-7-8-6-9-1. From the above values of PDSI, it is understood that product design 5 is the first choice when no market information is considered. When market information is also considered, then the ranking will be 2-7-6-9-11 (which is the same as that given by the GTMA and AHP methods).

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6.2.4 Modified TOPSIS Method For using the same weights of attributes as those used in the AHP and TOPSIS methods, the modified TOPSIS method leads to the following ranking order: 2 0.5311 7 0.4104 6 0.4154 5 0.4272 10 0.3522 4 0.4382 9 0.3747 3 0.4673 1 0.5618 8 0.3913 The modified TOPSIS method suggests product design 2 as the first choice for the given power electronic device when no market information is considered. When market information is also considered, then the ranking will be 2-7-6-9-1 (which is the same as that given by the GTMA, AHP, and TOPSIS methods).

References
Alexouda G (2005) A user-friendly marketing decision support system for product line design using evolutionary algorithms. Decision Support Systems 38:495– 509 Ayag Z (2005) An integrated approach to evaluating conceptual design alternatives in a new product development environment. International Journal of Operations Research 43:687–713 Balakrishnan PV, Jacob VS (1995) Triangulation in decision support systems: algorithms for product design. Decision Support Systems 14:313–327 Balakrishnan PV, Jacob VS (1996) Genetic algorithms for product design. Management Science 42:289–298 Besharati B, Azarm S, Kannan PK (2006) A decision support system for product design selection: a generalized purchase modeling approach. Decision Support Systems 42:333–350 Calantone RJ, Benedetto CAD, Schmidt JB (1999) Using the analytic hierarchy process in new producr screening. Journal of Product Innovation Management 16:65–76 Choi HR, Kim HS, Park BJ, Park YJ, Whinston AB (2004) An agent for selecting optimal order set in EC marketplace. Decision Support Systems 36:371–383 Edwards KL (2002) Towards more strategic product design for manufacture and assembly: priorities for concurrent engineering. Materials & Design 23:651– 656 Gulcin GB, Orhan F (2004a) A new approach based on soft computing to accelerate the selection of new product ideas. Computers in Industry 54:151– 167

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Gulcin GB, Orhan F (2004b) A fuzzy-logic-based decision making approach for new product development. International Journal of Production Economics 90: 27–45 Haque BU, Belecheanu RA, Barson RJ, Pawar KS (2000) Towards the application of case based reasoning to decision-making environment in concurrent product development (concurrent engineering). Knowledge-Based Systems 13:101– 112 Hsiao SW (1998) Fuzzy logic based decision model for product design. International Journal of Industrial Ergonomics 21:103–116 Hsiao SW, Chou JR (2004) A creativity-based design process for innovative product design. International Journal of Industrial Ergonomics 34:421–443 Lo CC, Wang P, Chao KM (2006) A fuzzy group-preferences analysis method for new-product development. Expert Systems with Applications 31:826–834 Maddulapalli AK, Azarm S, Boyars A (2006) Sensitivity analysis for product design selection with an implicit value function. European Journal of Operational Research doi:10.1016/j.ejor.2006.03.055 Matsatsinis NF, Siskos Y (1999) MARKEX: An intelligent decision support system for product development decisions. European Journal of Operational Research 113:336–354 Ozer M (1999) A survey of new product evaluation models. International Journal of Innovation Management 16:77–94 Ozer M (2005) Factors which influence decision making in new product evaluation. European Journal of Operational Research 163:784–801 Pan G, Santner J (2004) Theory of screening procedures to identify robust product designs using fractional factorial experiments. Journal of Statistical Planning and Inference 125:59–84 Parameswaran M, Stallaert J, Whinston AB (2001) A market based allocation mechanism for the DiffServ framework. Decision Support Systems 31:351– 361 Petrick IJ, Echols (2004) Technology roadmapping in review: a tool for making sustainable new product development decisions. Technological Forecasting & Social Change 71:81–100 Suh NP (2001) Axiomatic design: advances and applications. Oxford University Press, New York Thurston DL (1991) A formal method for subjective design evaluation with multiple attributes. Research in Engineering Design 3:105–122

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Machinability Evaluation of Work Materials

7.1 Introduction
Machining operations have been the core of the manufacturing industry since the industrial revolution. Machining is a process of material removal using cutting tools and machine tools to accurately obtain the required product dimensions with good surface finish. The manufacturing industries strive to achieve either a minimum cost of production or a maximum production rate, or an optimum combination of both, along with better product quality in machining. Appropriate selection of work piece and tool materials, machine tools, cutting fluids, cutting conditions, and sequences is a key factor in achieving these goals. Moreover, these goals have gained importance within the context of economic liberalization and globalization. In general, a manufacturing process for a product consists of several phases such as product design, process planning, machining operations, and quality control. The machinability aspect is related to all phases of manufacturing, especially to process planning and machining operations. The general objective of current research on machinability is to improve all phases of manufacturing by optimizing cost, productivity, and quality. Machinability is a measure of ease with which a work material can satisfactorily be machined. The machinability aspect is of considerable importance for production engineers to know in advance the machinability of work materials so that the processing can be planned in an efficient manner. The study can also be a basis for cutting tool and cutting fluid performance evaluation, and machining parameter optimization. In the process of product design, material selection is important for realizing the design objective and for reducing production costs. The machinability of engineering materials, owing to the marked influence on the production cost, needs to be taken into account in the product design, although it will not always be a criterion considered top priority in the process of material selection. If there are a finite number of work materials from among which the best material is to be chosen, and if each work material satisfies the required design and functionality of the product, then the main criterion to choose the work material is its operational performance during machining, i.e., machinability.

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The basis of machinability evaluation depends on the manufacturer’s interest, and many other aspects. For instance, some manufacturers consider tool life as the most important criterion to evaluate machinability, while others consider quality of surface cut the dominant factor. The solution to these difficulties has eluded practicing engineers for decades. Since there is no universally accepted methodology for evaluating machinability, and numerous new materials enter the market every year, many manufacturers are encountering difficulties in selecting the most appropriate material for their products. Machinability is influenced by the machining process input variables, Xr (r = 1, 2, …… , k), and the output variables, Yq (q = 1, 2, … , n), and the output variables are the functions of the input variables. Yq = f(X1,X2, … , Xk) (7.1)

The machining process is influenced by a number of variables. One may consider any number of machining process input or output variables for the purpose of machinability evaluation of work materials. Table 7.1 presents the most common machining process input and output variables.
Table 7.1. Machining process variables __________________________________________________________________________ Machining process input and output variables __________________________________________________________________________ Machining process input variables (process-independent variables): 1. Machine tool (rigidity, capacity, accuracy, etc.) 2. Cutting tool (material, coating, geometry, nature of engagement with the work material, tool rigidity, etc.) 3. Cutting conditions (speed, feed, and depth of cut) 4. Work material properties (hardness, tensile strength, chemical composition, microstructure, method of production, thermal conductivity, ductility, shape and dimensions of the job, work piece rigidity, etc.) 5. Cutting fluid properties and characteristics Machining process output variables (process-dependent variables): 1. Cutting tool life/tool wear/tool wear rate 2. Cutting forces/specific cutting forces 3. Power consumption/specific power consumption 4. Processed surface finish 5. Processed dimensional accuracy 6. Metal removal rate 7. Noise 8. Vibrations 9. Cutting temperature 10. Chip characteristics __________________________________________________________________________

However, it may be added that the machining process input variables may not precisely represent machinability. For example, materials of same composition but different metallographic structure may have different machinability characteristics. Machinability evaluation is based on the evaluation of certain economic and

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technical objectives (such as higher production rate, low operational cost, good product quality, etc.), which are the consequences of the machining operation on a given work material. Machining process output variables are nothing but the behavioral properties of the work materials during machining operations in terms of economic and technical consequences, and are directly related to machining operations, and hence to machinability. These machining process output variables are expressed in quantitative terms for the purpose of comparison. As the machining process output variables are directly related to the machining operations, it is quite appropriate to consider the output variables as the pertinent representatives of the machinability of work materials. Moreover, as the machining process output variables are functions of machining process input variables, the majority of researchers have preferred the machining process output variables for the machinability evaluation of work materials. Thus, the machining process output variables are the pertinent, and most commonly accepted measures of machinability. A machinability attribute is defined as a machining process variable. It can be any machining process input or output variable that affects the machinability. Machinability evaluation of work materials can be carried out using both types of variables. However, as mentioned above, machining process output variables are the pertinent machinability attributes (Table 7.1). These attributes are common to all machining operations, and only the terminology may vary for cutting tools and cutting forces in the machining operations. For example, the cutting tool is called single point tool in turning/shaping/planning/boring operations, drill in drilling operations, reamer in reaming operations, tap in tapping operations, milling cutter in milling operations, grinding wheel in grinding operations, etc. Similarly, the cutting forces are named differently in different machining operations: main cutting force, feed force, and thrust force in turning/shaping/planning/boring operations, torque and thrust in drilling/reaming/tapping operations, tangential force and axial force in milling operations, normal force and tangential force in grinding operations, etc. It is also noted from a literature review on machinability evaluation (Bech, 1963; Konig and Erinski, 1983; Mills and Redford, 1983; Ostafev et al. 1989; Malakooti et al. 1990; Notoya et al. 1990; Trent, 1991; Eyada, 1992; Kato et al. 1992; Shanmugam and Krishnamurthy, 1992; Jin and Sandstrom, 1994; Yoshikawa et al. 1994; Enache et al. 1995; Hung et al. 1995; Liao, 1996; Arunachalam and Mannan, 2000; Ong and Chew, 2000; Dravid and Utpat, 2001; Kim et al. 2002; Rao and Gandhi, 2002; Boubekri et al. 2003; Davim and Reis, 2004; Rech et al. 2004; Davim and Mata, 2005; Manna and Bhattacharya, 2005; Rao, 2005; Stoi et al. 2005; Özdemir and Özek, 2006; Šalak et al. 2006; eker and Hasirci, 2006; Morehead et al. 2007) that the criteria, in general, for the machinability assessment of different work materials include tool life, tool wear/tool wear rate, cutting forces/specific cutting forces, power consumption/specific energy consumption, processed surface finish, dimensional accuracy of the processed surface, etc. So far, research has been based mainly on experimental work to characterize the machinability of work materials. Some researchers have evaluated the machinability of different work materials considering ‘any one’ of the above criteria only (Ostafev et al. 1989; Notoya et al.

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190; Eyada, 1992; Kato et al. 1992; Jin and Sandstrom, 1994; Yoshikawa et al. 1994; Hung et al. 1995; Dravid and Utpat, 2001). Depending on the techno-needs of a process, some criteria may play a primary or secondary role in the machinability evaluation. However, realistic estimation of the machinability can be carried out only by considering all the criteria and their interrelations. The selection procedures suggested by other researchers considered a number of (i.e., more than one) machining process output variables, and these output variables were examined with respect to the work material properties and characteristics. So far, work materials have been evaluated by researchers considering their performance with respect to each machining process output variable separately, and then the final decision regarding the selection of work material (i.e., machinability evaluation) was taken, in a subjective manner, keeping in mind the overall performance. It is clear that there is a need to develop a scientific/mathematical tool for machinability evaluation that is capable of considering the requirements of a given machining operation. Considerable work in this direction, i.e., simultaneous consideration of machinability attributes using mathematical models, has been reported by a few researchers (Malakooti et al. 1990; Enache et al. 1995; Liao, 1996; Ong and Chew, 2000; Rao and Gandhi, 2002; Rao, 2005). It was recommended by Rao (2005) to short-list various work materials on the basis of satisfying the required design and functionality of the product. Machining process input variables such as work material variables play an important role in short-listing. After short-listing the materials, the main criterion to choose the work material is its operational performance while being machined, i.e., the resulting machining process output variables.

7.2 Examples
Now, to demonstrate and validate the application of decision making-methods, two examples are considered. In both examples, GTMA is applied first, and subsequently a few MADM methods are applied to rank and select the work materials from a machinability point of view. 7.2.1 Example 1 Konig and Erinski (1983) listed and discussed the general machining characteristics of aluminum pressure die-cast and die-cast alloys under various machining conditions for turning, face milling, and drilling operations. The authors used the results of turning data (Bech, 1963) of non-ferrous and ferrous alloys machined with high-speed machining tools. The results are given in Table 7.2. One-hour cutting speeds determined from machining tests on aluminummagnesium die-cast alloy (GK-A1Mg5) and magnesium-aluminum die-cast alloy (GK-MgA19Zn) are the highest compared with the corresponding values for aluminum-silicon die-cast alloys, gray cast iron (GG26) and carbon steel (C35). The one-hour cutting speeds for aluminum-silicon die-cast alloys are higher than for GG26 and C35. The specific cutting forces (i.e., cutting force per unit area of the material removed) when machining aluminum-silicon die-cast alloys and GK-

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A1Mg5 are very low compared to those for GG26 and C35, and for GKMgA19Zn, the specific cutting force is the lowest. Machining of aluminum-silicon die-casting alloys required power 3 to 4.5 times higher than for GG26, and 1.5 to 2 times higher than C35. The alloys GK-A1Mg5 and GK-MgA19Zn required comparatively very high power. This example is considered to demonstrate the application of the GTAM and MADM methods.
Table 7.2. Objective data of the attributes of example 7.2.1 _________________________________________________________________ Work material VC (m/min) CF (N/m2) PI (kW) _________________________________________________________________ W1 710 400 28 W2 900 415 38 W3 1630 440 59 W4 1720 235 43 W5 120 1150 8 W6 160 1750 19 _________________________________________________________________ W1: GK-AlSi10Mg (aluminum-silicon die-cast alloy) W2: GK-AlSi6Cu4 (aluminum-silicon die-cast alloy) W3: GK-AlMg5 (aluminum-magnesium die-cast alloy) W4: GK-MgAl9Zn (magnesium-aluminum die-cast alloy) W5: GG26 (gray cast iron with lamellar graphite); W6: C35 (low-carbon steel) VC: One-hour cutting speed; CF = Specific cutting force; CI = Cutting power input Cutting conditions: dry, tool material–K10, feed–0.175 mm/rev, and depth of cut–2 mm

7.2.1.1 Application of Graph Theory and the Matrix Approach (GTMA) Pertinent machinability attributes are identified. The attributes considered are: onehour cutting speed (VC), specific cutting force (CF), and cutting power input (PI). The quantitative values of these attributes are given in Table 7.2, and these are to be normalized. One-hour cutting speed (VC) is a beneficial attribute. A work material is said to possess higher machinability if it allows very high cutting speeds for a specified tool life. So, higher values are desired. Specific cutting force (CF) and cutting power input (PI) are non-beneficial attributes, and lower values are desirable. The values of the three attributes are normalized, and are given in Table 7.3 in their respective columns. Table 7.3 shows the values of Ai for different work materials.

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Table 7.3. Normalized data of the attributes of example 7.2.1 ____________________________________________________ Work material VC CF PI ____________________________________________________ W1 0.4128 0.5875 0.2857 W2 0.5233 0.5663 0.2105 W3 0.9477 0.5341 0.1356 W4 1 1 0.1860 W5 0.0698 0.2043 1 W6 0.0932 0.1343 0.4211 ____________________________________________________

The relative importance of attributes (i.e., aij) is assigned values as explained in Section 2.4. Let the decision maker select the following assignments: VC 0.255 0.255 CF 0.745 0.5 PI 0.745 0.5 -

VC CF PI

For example, one-hour cutting speed is considered much more important than the specific cutting force in turning operations. This is because the one-hour cutting speed is related to high cutting speeds for a specified tool life of one-hour. If a work material permits high cutting speeds for a specified tool life then production time will be reduced, and production costs will also be reduced. Thus, a one-hour cutting speed is considered very important, compared to the other attributes, i.e., specific cutting force and the cutting power input, and thus a relative importance value of 0.745 is assigned to a one-hour cutting speed over specific cutting force and cutting power input (i.e., a12 = 0.745 and a13 = 0.745), and a relative importance value of 0.255 is assigned to the specific cutting force (i.e., a21 = 0.255) and cutting power input (i.e., a31 = 0.255). The specific cutting force and cutting power input are considered as equally important in turning operations and thus equal relative importance is assigned to these attributes (i.e., a23 = a32 = 0.5). It may be added that these values can be decided by the decision maker, depending on the requirements. The machinability attributes digraph, machinability attributes matrix of the digraph, and machinability function for the matrix can be prepared. The value of the machinability index is calculated using the values of Ai and aij for each work material. The machinability index values of different work materials are given below in descending order: W4: 0.8513 W3: 0.6228 W2: 0.5308 W1: 0.5284 W5: 0.4504 W6: 0.3241

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From the above values of the machinability index, it is clear that the work material W4 (i.e., GK – Mg A19Zn: magnesium-aluminum die-cast alloy) is the best choice among the considered materials for the turning operation under the given conditions. The next choice is W3 (i.e., GK-AlMg5: aluminum-magnesium die-cast alloy), and W6 (i.e., low-carbon steel) is the last choice. Following graph theory and the matrix approach, the coefficients of similarity/dissimilarity are also calculated for different work materials using Equations 2.15 and 2.16. The coefficient of similarity values are given in Table 7.4. These are useful for work materials documentation, and for easy storage and retrieval of the work materials data for turning operations under the given conditions.
Table 7.4. Values of the coefficient of similarity for the work materials of example 7.2.1 ________________________________________________________ Work material W2 W3 W4 W5 W6 ________________________________________________________ W1 0.9955 0.8483 0.6206 0.8524 0.6134 W2 0.8522 0.6234 0.8486 0.6106 W3 0.7316 0.7232 0.5204 W4 0.5291 0.3807 W5 0.7196 ________________________________________________________ 7.2.1.2 SAW Method

The procedure suggested by Edwards et al. 1982) to assess weights for each of the attributes to reflect their relative importance to the work material selection decision is as follows. The attributes are ranked in order of importance, and 10 points are assigned to the least important attribute PI. CF is also considered least important and equal to PI in this example. The attribute VC is given 50 points to reflect its relative importance. The final weights are obtained by normalizing the sum of the points to one. For example, the weight for attribute VC is calculated by 50/(50+10+10) = 0.7142. The weights of CF and PI are calculated as 0.1429 each. Using these weights, and the normalized data of the attributes for different work materials, the machinability index values are calculated, and are arranged in descending order of the index. W4: 0.8838 W3: 0.7726 W2: 0.4848 W1: 0.4196 W5: 0.2219 W6: 0.1458 The SAW method also suggests W4 as the best machinable work material. 7.2.1.3 WPM The same weights as were used in the SAW method are selected for this method and the values of machinability index are calculated. The values are arranged in descending order.

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W4: 0.7863 W3: 0.5693 W2: 0.4646 W1: 0.4119 W5: 0.1190 W6: 0.1216 The ranking of work materials suggested by both the SAW and WPM methods is the same in this example. 7.2.1.4 AHP and its Versions If the same weights as were used in the SAW method are selected for in this method, then the ranking of work materials obtained by using the relative as well as ideal mode AHP will be same. The multiplicative AHP method also yields the same ranking. 7.2.1.5 TOPSIS Method Rao (2005) applied the TOPSIS and AHP methods together for machinability evaluation of work materials. The AHP method was used for finding the weights of importance of the attributes. The procedure is given below: Step 1: The objective is to evaluate the machinability of different non-ferrous and ferrous alloys. The attributes considered are: VC, CF, and PI. VC is the beneficial attribute, and CF and PI are non-beneficial attributes. Step 2: The next step is to represent all the information available on attributes in the form of a decision matrix. The data given in Table 7.2 are represented as a matrix D16x3, but not shown here. Step 3: The quantitative values of the machinability attributes, which are given in Table 7.2, are normalized as explained in Section 3.2.6. Step 4: The relative importance of attributes (aij) are assigned values using the AHP method as explained in Section 7.2.4. Let the decision maker select the following assignments: VC 1 1/5 1/5 CF 5 1 1 PI 5 1 1

VC CF PI

Once again, it may be added that, in actual practice, these values of relative importance can be judiciously decided upon by the user/experts, depending on the requirements. The assigned values in this chapter are for demonstration purposes only. The normalized weight for each attribute is: WVC = 0.7142, WCF = 0.1429, and WPI = 0.1429. The value of max is 3.0 and CR = 0.0, and there exists absolute consistency in the judgements made. Step 5: The weighted normalized matrix V16x3 is calculated.

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0.1921 0.2435 0.4410 0.4654 0.0325 0.0433

0.0256 0.0266 0.0282 0.0151 0.0737 0.1122

0.0448 0.0608 0.0943 0.0688 0.0128 0.0304

Step 6: The next step is to obtain the ideal (best) and the negative ideal (worst) solutions, and these are given as: VVC+ = 0.4654 VVC- = 0.0325 + VCF- = 0.1122 VCF = 0.0151 + VPI- = 0.0943 VPI = 0.0128 Step 7: Here, the separation measures are obtained as: SW1+ = 0.2753 SW1- = 0.1882 + SW2 = 0.2273 SW2- = 0.2302 + SW3 = 0.0861 SW3- = 0.4171 + SW4 = 0.0559 SW4- = 0.4444 + SW5 = 0.4368 SW5- = 0.0902 + SW6 = 0.4335 SW6- = 0.0649 Step 8: The relative closeness of a particular alternative to the ideal solution (i.e., machinability index) is calculated, and these are: P W1 = 0.4060 P W2 = 0.5032 P W3 = 0.8289 P W4 = 0.8882 PW5 = 0.1711 P W6 = 0.1302 Step 9: The work materials are arranged in descending order of their machinability index, and this can be arranged as W4-W3-W2-W1-W5-W6. Thus, the TOPSIS method also suggests W4 as the first right-choice work material from the machinability point of view. 7.2.1.6 Modified TOPSIS Method In this process, the positive ideal solution (R+) and the negative ideal solution (R-), which are not dependent on the weighted decision matrix, are given by using Equations 3.19 and 3.20. RVC+ = 0.6515 RVC= 0.0455 + RCF = 0.1055 RCF= 0.7853 RPI+ = 0.0895 RPI= 0.6603 The weighted Euclidean distances are calculated as DW1+ = 0.3354 DW1= 0.3245 + = 0.3486 = 0.2932 DW2DW2 DW3+ = 0.2205 DW3= 0.5320 DW4+ = 0.1481 DW4= 0.5770 = 0.2386 = 0.5352 DW5DW5+ DW6+ = 0.5636 DW6= 0.1697 The relative closeness of a particular alternative to the ideal solution is calculated (i.e., machinability index), and these are: PW1-mod = 0.4918 PW2-mod = 0.5432 PW3-mod = 0.7070 PW4-mod = 0.7958 PW5-mod = 0.3083 PW6-mod = 0.2315

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The alternative materials are arranged in descending order of their machinability index. This can be arranged as W4-W3-W2-W1-W5-W6. 7.2.2 Example 2 Enache et al. (1995) conducted turning experiments on titanium alloys using different cutting tools of different geometries, and presented a mathematical model for assessing the machinability of various work-tool combinations. The work-tool combinations, experimental conditions, and test results are given in Table 7.5. The various steps of the methodology are carried out as described below.
Table 7.5. Objective data of the machinability attributes of example 7.2.2 (from Enache et al., 1995; with permission from CIRP) ___________________________________________________________________ Work-tool Tool wear rate Specific energy Surface roughness combination (m/min) consumed (N) ( m) ___________________________________________________________________ 1 0.061 219.74 5.8 2 0.093 3,523.72 6.3 3 0.064 2,693.21 6.8 4 0.028 761.46 5.8 5 0.034 1,593.48 5.8 6 0.013 2,849.15 6.2 ___________________________________________________________________ 1: TiAl6V4-P20; 2: TiMo32-P20; 3: TiAl5Fe2.5-P20; 4: TiAl6V4-P20 (TiN); 5: TiAl6V4-K20; 6: TiAl6V4-K20* (K20* is a special form of tool without top in contrast with other tools). Cutting conditions: dry, cutting speed–150 m/min, feed– 0.15 mm/rev, and depth of cut–0.5 mm

7.2.2.1 Application of SAW Method Pertinent machinability attributes are identified. The attributes considered are the same as those of Enache et al. (1995), and these are tool wear rate (TW), specific energy consumed (SE), and processed surface roughness (SR). These three attributes are non-beneficial, and low values are most desired. In other words, a work material is said to possess higher machinability if it produces very low values of tool wear rate, specific energy consumption, and surface roughness in the turning operation. The objective values of these attributes, given in Table 7.5, are to be normalized. The values of the three attributes are normalized, and are given in Table 7.6 in their respective columns.

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Table 7.6. Normalized data of the attributes of example 7.2.2 ________________________________________________________________ Work-tool combination TW SE SR ________________________________________________________________ 1 0.2131 1 1 2 0.1398 0.0624 0.9206 3 0.2031 0.0816 0.8529 4 0.4643 0.2886 1 0.3824 0.1379 1 5 6 1 0.0771 0.9355 ________________________________________________________________

The same weights as those selected by Enache et al. (1995) are used in this method, and the values of machinability index are calculated. The values are arranged in descending order as given below: 6: 0.8213 4: 0.4747 1: 0.4248 5: 0.3865 3: 0.2329 2: 0.1885 The above ranking obtained using the SAW method matches very well with the results presented by Enache et al. (1995). These show that TiAl6V4 possesses better machinability than TiMo32 and TiAl5Fe2.5. Comparing the machinability of the same work material with different tools, the maximum machinability is obtained with tool K20*, followed by P20 (TiN), P20, and K20. 7.2.2.2 WPM The same weights as those selected by Enache et al. (1995) are used in this method, and the values of the machinability index are calculated. The values are arranged in descending order as given below: 6: 0.6143 4: 0.4518 5: 0.3412 1: 0.3230 3: 0.1922 2: 0.1399 WPM also suggests that work-tool combination designated by 6 possesses better machinability than the other work-tool combinations in this example. 7.2.2.3 AHP and its Versions If the same weights as those used in the SAW method are selected in this method, then the ranking of work-tool combinations obtained by using the relative as well as ideal mode AHP will be same. The multiplicative AHP method also yields the same ranking as that given by WPM.

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7.2.2.4 TOPSIS Method Rao (2005) applied the TOPSIS and AHP methods together for machinability evaluation of work materials. The AHP method was used to determine the weights of importance of the attributes. The procedure is given below: Step 1: The objective is to evaluate the machinability of different titanium work materials and work-tool combinations. The attributes considered are the same as those of Enache et al. (1995), namely, tool wear rate (TW), specific energy consumed (SE), and processed surface roughness (SR). Step 2: The next step is to represent all the information available on attributes in the form of a decision matrix. The data given in Table 7.5 are represented as matrix D26x3, but not shown here. Step 3: The quantitative values of the machinability attributes, given in Table 7.5, are normalized as explained in Section 3.2.6. 0.4476 0.6824 0.4696 0.2054 0.2495 0.0954 0.0395 0.6333 0.4841 0.1369 0.2864 0.5121 0.3862 0.4195 0.4528 0.3862 0.3862 0.4129

Step 4: The relative importance of attributes (aij) is assigned. Let the decision maker select the following assignments: TW SE SR TW 1 5 7 SE 1/5 1 3 SR 1/7 1/3 1 Once again, it may be added that the assigned values in this example are for demonstration purposes only.The normalized weights of each attribute are WTW = 0.7306, WSE = 0.1884, and WSR = 0.0810. The value of max is 3.0649 and CR = 0.0624, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. Step 5: The weighted normalized matrix V26x3 is calculated. 0.3270 0.4986 0.3431 0.1501 0.1823 0.0697 0.0074 0.1193 0.0912 0.0258 0.0539 0.0965 0.0313 0.0339 0.0367 0.0313 0.0313 0.0334

Step 6: The next step is to obtain the ideal (best) and negative ideal (worst) solutions, and these are given as: VTW+ = 0.0697 VTW- = 0.4986 + VSE = 0.0074 VSE- = 0.1193 + VSR = 0.0313 VSR- = 0.0367

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Step 7: Here, the separation measures are obtained as: SNr1+ = 0.2573 SNr1- = 0.2049 + SNr2 = 0.4432 SNr2- = 0.0027 + SNr3 = 0.2860 SNr3- = 0.1579 + SNr4 = 0.0825 SNr4- = 0.3608 + SNr5 = 0.1218 SNr5- = 0.0891 + SNr6 = 0.3230 SNr6- = 0.4295 Step 8: The relative closeness of a particular alternative to the ideal solution (i.e., machinability index) is calculated, and these are: PNr1 = 0.4433 PNr2 = 0.0060 PNr3 = 0.3558 PNr4 = 0.8139 PNr6 = 0.8252 PNr5 = 0.7262 Step 9: The work-tool combinations are arranged in descending order of their machinability index, and this can be arranged as 6-4-5-1-3-2. Thus, the TOPSIS method also suggests Nr6 as the best work-tool combination from the machinability point of view. 7.2.2.5 Modified TOPSIS Method In this process, the positive ideal solution (R+) and the negative ideal solution (R-), which are not dependent on the weighted decision matrix, are used. RTW+ = 0.0954 RTW= 0.6824 + = 0.6333 = 0.0395 RSERSE RSR+ = 0.3862 RSR= 0.4528 The weighted Euclidean distances are calculated as: = 0.3280 0.3009 DNr1DNr1+ = + DNr2 = 0.5645 DNr2= 0.0094 0.3743 DNr3= 0.1931 DNr3+ = = 0.4618 0.1032 DNr4DNr4+ = DNr5+ = 0.1700 DNr5= 0.4000 DNr6+ = 0.2061 DNr6= 0.5044 The relative closeness of a particular alternative to the ideal solution is calculated (i.e., machinability index), and these are: PNr1-mod = 0.5216 PNr2-mod = 0.01642 PNr3-mod = 0.3403 PNr4-mod = 0.8174 PNr5-mod = 0.7017 PNr6-mod = 0.7099 The alternative work-tool combinations are arranged in descending order of their machinability index. This can be arranged as 4-6-5-1-3-2. Thus, the modified TOPSIS method suggests 4 as the first right choice, and 6 as the second choice.

References Arunachalam R, Mannan MA (2000) Machinability of nickel-based high temperature alloys. Machining Science and Technology 4:127–168 Bech HG (1963) Untersuchung derZerspanbarkeit von Leichtmetallegierungen. Dissertation, RWTH, Aachen

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Boubekri N, Rodriguez J, Asfour S (2003) Development of an aggregate indicator to assess the machinability of steels. Journal of Materials Processing Technology 134:159–165 Davim JP, Mata F (2005) A new machinability index in turning fiber reinforced plastics. Journal of Materials Processing Technology 170:436–440 Davim JP, Reis P (2004) Machinability study on composite (polyetheretherketone reinforced with 30% glass fibre–PEEK GF 30) using polycrystalline diamond (PCD) and cemented carbide (K20) tools. International Journal of Advanced Manufacturing Technology 23:412–418 Dravid SV, Utpat LS (2001) Machinability evaluation based on the surface finish criterion. Journal of the Institution of Engineers (India), Production Engineering Division 81:47–51 Edwards W, Newman JR, Snapper K, Seaver D (1982) Multiattribute Evaluation. SAGE Publications, Newbury Park, California Enache S, Strajescu E, Opran C, Minciu C, Zamfirache M (1995) Mathematical model for the establishment of the materials machinability. CIRP Annals 44:79–82 Eyada OK (1992) Reliability of cutting forces in machinability evaluation. Flexible Automation and Information Management 20:937–946 Hung NP, Boey FYC, Khor KA, Oh CA, Lee HF (1995) Machinability of cast and powder-formed aluminum alloys reinforced with SiC particles. Journal of Materials Processing Technology 48:291–297 Jin L, Sandstrom R (1994) Machinability data applied to materials selection. Materials & Design 15:339–346 Kato K, Tokisue H, Chiba I (1992) Effect of side cutting edge angle of tools on the turning machinability of magnesium alloy castings MC2. Journal of Japan Institute of Light Metals 42:453–458 Kim KK, Kang MC, Kim JS, Jung YH, Kim NK (2002) A study on the precision machinability of ball end milling by cutting speed optimization. Journal of Materials Processing Technology 130-131:357–362 Konig W, Erinski D (1983) Machining and machinability of aluminum cast alloys. CIRP Annals 32:535–540 Liao TW (1996) A fuzzy multi criteria decision making method for material selection. Journal of Manufacturing Systems 15:1–12 Malakooti B, Wang J, Tandler EC (1990) Sensor-based accelerated approach for multiattribute machinability and tool life evaluation. International Journal of Production Research 28:2373–2392 Manna A, Bhattacharya B (2003) A study on machinability of Al/SiC-MMC. Journal of Materials Processing Technology 140:711–716 Mills B, Redford AH (1983) Machinability of engineering materials. Applied Science Publishers, London Morehead M, Huang Y, Hartwig KT (2007) Machinability of ultrafine-grained copper using tungsten carbide and polycrystalline diamond tools. International Journal of Machine Tools and Manufacture 47:286–293 Notoya H, Yamada S, Yoshikawa K, Takatsuji Y (1990) Effects of tool materials on machinability of commercially pure titanium. Journal of the Japan Institute of Metals 54:596–602

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Ong SK, Chew LC (2000) Evaluating the machinability of machined parts and their setup plans. International Journal of Production Research 38:2397–2410 Ostafev VA, Minaev AA, Kokarovtsev VV (1989) Fast method for determining machinability of materials. Soviet Engineering Research 9:113–114 Özdemir N, Özek C (2006) An investigation on machinability of nodular cast iron by WEDM. International Journal of Advanced Manufacturing Technology doi:10.1007/s00170-004-2446-3 Rao RV (2005) Machinability evaluation of work materials using a combined multiple attribute decision making method. International Journal of Advanced Manufacturing Technology 28:221–227 Rao RV, Gandhi OP (2002) Digraph and matrix methods for machinability evaluation of work materials. International Journal of Machine Tools and Manufacture 42:321–330 Rech J, Calvez CL, Dessoly M (2004) A new approach for the characterization of machinability-application to steels for plastic injection molds. Journal of Materials Processing Technology 152:66–70 Šalak A, Vasilko K, Selecká M, Danninger H (2006) New short time face turning method for testing the machinability of PM steels. Journal of Materials Processing Technology 176:62–69 eker U, Hasirci H (2006) Evaluation of machinability of austempered ductile irons in terms of cutting forces and surface quality. Journal of Materials Processing Technology 173:260–268 Shanmugam S, Krishnamurthy R (1992) Machinability study on pearlitic spheroidal graphite cast iron. International Journal of Production Research 30:189–197 Stoi A, Kopa J, Cukor G (2005) Testing of machinability of mould steel 40CrMnMo7 using genetic algorithm. Journal of Materials Processing Technology 164-165:1624–1630 Trent EM (1991) Metal cutting. Butterworth-Heinemann, London Yoshikawa T, Miyazawa S, Mori K (1994) Machinability of Ni3Al-based intermetallic compounds. Journal of Mechanical Engineering Laboratory 48:190–196

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Cutting Fluid Selection for a Given Machining Application

8.1 Introduction
Much heat is generated in metal cutting operations due to plastic deformation of work materials, friction at the tool-chip interface, and friction between the clearance face of the tool and the work piece. The heat generation increases the temperature of both the work piece and the tool point, resulting in decrease in hardness, and hence tool life. The machined surface will also be less smooth, and the possibility of built-up edge increases. So, the use of a cutting fluid during a machining operation very essential. The major factors that govern the selection of cutting fluids are: (i) the machining process, (ii) cutting tool material, and (iii) work piece material. Other factors, such as compatibility with the machine tool, performance requirements, operator interaction, environment friendliness, and economy must also be looked into. Nowadays, ever increasing environmental problems are becoming a serious threat to the survival and development of society. After the publishing of ISO 9000 quality management standards, the ISO 14000 environmental management system standards, and the OHSAS 18001 occupational health and safety assessment series, one of our greatest strategic challenges is to apply the three series integrated into a management system in enterprises, not only from an engineering but also from a business and marketing perspective. The manufacturing industry is one of the main roots of environmental pollution. Therefore, minimizing the environmental impact of the manufacturing industry has become an important topic for all manufacturers. During these critical times, an advanced manufacturing mode - green manufacturing - suitable for a sustainable development strategy has been presented. Green manufacturing is a modern manufacturing strategy, essential for 21st century manufacturing industries, integrating all issues of manufacturing, its ultimate goal being to reduce and minimize environmental impact and resource consumption during a product’s life cycle, which includes design, synthesis, processing, packaging, transportation, and the use of products in continuous or discrete manufacturing industries.

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As cutting fluids are widely used in industrial machining operations, and because of their negative effects on health, safety, and environment, legislation and public environmental concerns now have great impacts on their development. Dry machining and minimum quantity lubrication (MQL) machining have been successfully applied in some kinds of machining processes. However, in others, such as grinding, it is very difficult to obtain good results without the help of cutting fluids, because of the high amount of heat generated during grinding. As for MQL machining, although progress is being made, we have a long way to go before this problem is solved in applications workshops. Therefore, research on the composition, supply techniques, selection, cleaning, and maintenance of cutting fluids is still active at present. The selection of cutting fluids is more an art, than a science, because there is almost no standardized method available for this purpose. Numerous methods have been proposed in the past, yet very few of these gave reasonably satisfactory results. Different metal cutting operations have been used to evaluate cutting fluids. Nagpal and Sharma (1973) presented the results of a series of short- and long-run cylindrical turning tests for the evaluation of most common, commercially available metal cutting fluids, namely, water soluble, straight mineral, chlorinated and sulfo-chlorinated oils. Peters and Aerens (1976) made an attempt to evaluate grinding fluids based on grinding charts obtained in cylindrical plunge grinding. The authors considered performance parameters, roughness, tangential force, normal force, grinding ratio, specific energy, metal removal rate, tool life, and cost for grinding conditions in the middle of the practical usable range. From the comparison, it appeared that the large variety of grinding fluids offered by the market was not justified commercially or technologically. The use of oils led to a significantly lower cost price, and an increased surface quality in external as well as internal grinding, especially when high wheel speed was used. de Chiffre (1978) studied a series of hole-making operations (drilling, boring, reaming, and tapping) in order to evaluate different types of cutting fluids. After measuring performance parameters such as number of holes to failure, cutting force, and surface finish, the author concluded that the effectiveness of a coolant greatly depended on the machining process and on the performance measures. Sutcliffe et al. (1979) used the criterion of catastrophic drill failure, or a maximum of 120 holes. Different feeds, speeds, and types of cutting fluids were tested, including a nitrite-free synthetic coolant that performed very well. Rowe (1982) performed cutting fluids testing for cylindrical grinding operations, involving the coordination of various chemical and physical properties of the grinding fluids, their physiological actions and their mechanical performance. A simplified databank was also proposed, allocating each result under one of seven categories, and combining these by means of a software program. Various weighting factors were also applied to the practical requirements of specific grinding processes. Rapp (1984) discussed the general criteria for the selection of cutting fluids for machine tools, and identified the advantages offered by an appropriate selection of cutting fluids (e.g., cost reduction, higher productivity, better safety, lower rate of rejects, and less frequent sharpening of tools).

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Yuhta et al. (1984) carried out experiments on the grinding abilities of grinding fluids (water miscible and insoluble in water). The effects of each component of the grinding fluid on the grindability were discussed. The experimental results showed that when the commercial grinding fluid with the highest grindability was used, oxy-ferric hydroxide formed in the surface layer of the work piece, and the surface layer was thinner than that produced by means of other grinding fluids. This suggested that when grinding steel with a diamond wheel, grindability was improved under conditions in which oxy-ferric hydroxide was produced in the surface layer of the work piece. Lorenz (1985) compared various cutting fluids by tapping test, taking into consideration also the tapping speed. It was shown that the statistical treatment of torque measurements as a function of cutting speed provides a good comparative basis for assessing cutting fluids when machining a particular material, or a particular group of materials. The author discussed the selection of testing tools and test pieces, and also proposed the standardization of test procedure. Ghio (1986) studied cutting fluids for operations on metal with flexible abrasive belts. Compared with dry grinding, the use of a cutting oil ensured high production, economy, increased belt life, and a better finish. The author suggested the use of very low-viscosity straight mineral oils for materials that tend to clog the belt, and highly fluid compounded oils for carbon steels and non-ferrous metals. Bennett (1987) also presented results of testing of cutting fluids. The coolants tested were synthetic, semi-synthetic, soluble, and straight grinding oils. The three parameters monitored were grinding ratio, surface finish, and load on the wheel head. Narheim and Kendig (1987) evaluated the cutting fluid effectiveness in machining using electrochemical techniques. A correlation was found between the degree of electro-absorption of surfactants from cutting fluids at metal surfaces, and cutting forces in machining. The effectiveness of cutting fluids, as characterized by cutting forces, was assessed using rapid electrochemical techniques, thereby reducing the need for time-consuming and costly machinability tests. Wakabayashi and Ogura (1990) evaluated cutting fluids in terms of consumption energy in tapping tests. The consumption energy was estimated by integration of the total torque-time curve as an alternative to the tapping torque commonly used to evaluate cutting fluids. It was pointed out that cutting fluids influence the overall cutting process, rather than causing only a reduction of friction on the interface. Based on consumption energy, it was possible to account for the overall cutting process. Cholakov et al. (1992) compared lubricating properties of 16 oil- and water-based fluids, tap water, and air in surface grinding of En9 steel specimens. The oils showed an overall better lubricity, which was less affected by changes of operation parameters. Some water-based fluids, under particular operating conditions, were equal to or better than the oils in lowering forces and in wheel protection, but none achieved the surface quality obtained with oil. Okuyama et al. (1993) studied the cooling action of grinding fluid in shallow grinding. A new method was proposed for measuring the heat transfer coefficient in the vicinity of the wheel-work piece contact zone. The experiments were performed under a variety of conditions during which grinding fluid was supplied

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and the authors recommended certain measures for increasing the cooling efficiency (i.e., setting the velocity of the coolant higher than the critical value to penetrate the air flow layer formed around the wheel periphery, using a nozzle with a thin throat and attaching a scrapper plate above the nozzle outlet, choosing a wheel of larger grain size, and setting a higher wheel speed). de Chiffre et al. (1994) used a reaming test for cutting fluid evaluation, as an alternative to tapping torque measurement and thread finish evaluation. Davinson (1995) provided some guidelines for choosing the correct cutting fluids, and disposing of the used coolants, including waste minimization and elimination. Research into the effects of a coherent cutting fluid jet as opposed to a dispersed jet, upon exit from the nozzle, was carried out by Webster et al. (1995). Compared with a dispersed jet, the authors reported that when a coherent jet was maintained, the grinding temperature was reduced. Sheng and Oberwalleney (1997) reviewed the basic components, performance and health effects, and post-processing options for non-water-miscible and water mixed fluids. Time-based degradation mechanisms for cutting fluid performance were examined, and disposal pre-treatment options for cutting fluids were discussed. Maekawa (1998) reviewed computational aspects of tribological phenomena in metal machining. Emphasis was laid on the interaction between the mechanical aspects of tribology, and the characteristics of the cutting process. Brinksmeier et al. (1999) discussed aspects of cooling lubrication reduction in machining advanced materials, e.g., titanium alloys and extreme low-sulfur steels. The authors focused the research on cutting tool performance and wear mechanism at high cutting speeds, while using different lubricants and cooling supply strategies. The investigations contributed to increasing process stability and tool life, improving of machined surface finish, and avoiding tensile residual stresses. Yamanaka et al. (1996) developed a new, easy, and accurate method to evaluate the performance of grinding fluids by means of a block-on test ring machine and an electro-plated CBN wheel. Based on this, the authors developed a new grinding fluid for the CBN wheel. In another work, Yamanaka et al. (1997) had provided reasons for the outstanding properties of extreme-pressure agents based on the analysis of specimen surfaces after the tests. Further, Yamanaka et al. (1998) evaluated the grinding performances of 11 typical metal working additives, and found that sulfur-type EP additives and phosphorous-type EP additives showed excellent grinding performance, even at low concentration. Yamanaka et al. (2000a), reported on whether or not any synergic effect can be observed in grinding performance when two different types of metal working additives are used together. The results showed that there was no synergic effect on grinding performance in a total of 12 cases. Further, Yamanaka et al. (2000b) studied the grinding performance of various types of carboxylic acids, and found that among those tested, straight chain saturated higher fatty acids with carbon atom numbers exceeding that of lauric acid are the best in grinding performance. Ebbrell et al. (2000) studied the effects of cutting fluid application method on the grinding process. Results from three experiments with different quantities of cutting fluid passing through the grinding zone were presented. Michigan Technological University developed a cutting fluid evaluation software test bed. Upton (2000) described a new drilling test for the evaluation of cutting fluids. The

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technique was based on a procedure that relied on gathering performance data from tests using the same drill with different cutting fluids, or lubricant concentrations, rather than on the life time or wear rate of individual tools. Chen et al. (2001) presented an analytical model for the prediction of shop floor aerosol generation rate, and particulate size distribution associated with the spin-off motion of cutting fluid from a rotational work piece in a turning operation. The predictive models developed can be used as a basis for human exposure and health hazard analysis. Belluco and de Chiffre (2001) presented the results of cutting fluid testing through subsequent hole-making operations. AISI 316L stainless steel specimens were machined with drilling, core drilling, reaming and tapping using HSS-E tools. The effect of different lubricants on cutting force and power was investigated in connection with the development of vegetable-based cutting oils. de Chiffre et al. (2001) aimed to ream austenitic stainless steel using water-based fluids, and to evaluate the effect of cutting fluid on cutting forces, surface finish, and hole diameter. Results showed that torque and thrust measurements offer a reliable description of the lubricating properties of cutting fluids, while conventional surface roughness evaluation was associated with a large scatter in the data. Eppert et al. (2001) presented a methodology using the cluster analysis in a hierarchical agglomerative form, for the development of a classification scheme based on physical properties of a wide array of cutting fluids. Bartz (2001) described ecological and environmental aspects of cutting fluids, and suggested that all components, base oils and additives, have to be selected very carefully in order to minimize any health problems and any impact to the environment. Rao and Gandhi (2001) presented a cutting fluid selection index using digraph and matrix methods, which can serve for the evaluation and selection of cutting fluids. Sun et al. (2001) presented a two-grade fuzzy synthetic decision-making method using AHP for evaluation of grinding fluids. Varadarajan et al. (2002) investigated hard turning operations with MQL, and made a comparison with dry and wet turning. Tan et al. (2002) presented a decision-making framework model for cutting fluid selection for green manufacturing, together with a case study. Sokovic and Mijanovic (2001) studied ecological aspects of cutting fluids, and their influence on quantifiable parameters of cutting processes. Rao (2004) presented a combined MADM method for the selection of environmentally conscious cutting fluids using the TOPSIS and AHP methods. Dhar et al. (2006) studied the effect of minimum quantity lubrication (MQL) on tool wear and surface roughness while machining AISI 4340 steel. In another work, Dhar and Kamruzzaman (2006) conducted turning experiments on AISI 4037 steel using cryogenic cooling by liquid nitrogen jets. Haq and Tamizharasan (2005) investigated the effects of cooling in hard turning operations. Reddy and Rao (2006) studied the effects of solid lubricants on cutting forces and surface quality in end milling. The results indicated that there was a considerable improvement in process performance with solid lubricant-assisted machining, compared to that of machining with cutting fluids. Obikawa et al. (2006) investigated high-speed grooving operations with minimum quantity lubrication (MQL). Heinemann et al. (2006) studied the effect of MQL on the tool life of small twist drills in deep-hole drilling.

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It is evident from the above that existing procedures of cutting fluid selection for a given machining application focus mainly on identifying the cutting fluid matching with a tool, work material, and machining operation. Different metal cutting operations have been used to evaluate cutting fluids, and the performance of a cutting fluid judged by the resulting machining process output variables such as: tool life (i.e., life of single point tool in turning/boring, drill in drilling, reamer in reaming, tap in tapping, grinding wheel in grinding), cutting forces (i.e., main cutting force and/or thrust in turning/boring, torque and/or thrust in drilling/reaming/tapping, normal force and/or tangential force in grinding), power consumption, cost per unit volume of material removed, surface finish, cutting temperature, dimensional accuracy, etc. The selection procedures suggested by earlier researchers considered either a single machining process output variable, or a number of machining process output variables, and these output variables were examined with respect to cutting fluid properties and characteristics. So far, cutting fluids have been evaluated in terms of their performance with respect to each machining process output variable separately, and then the final decision regarding selection was taken, in a subjective manner, keeping in mind the overall performance. It is clear that there is a need to develop a mathematical tool for cutting fluid selection that is capable of considering the requirements of a given machining application. The objective of a cutting fluid selection procedure is to identify cutting fluid properties, and obtain the most appropriate combination of cutting fluid properties in conjunction with the real requirement of a machining application. Thus, efforts need to be extended to determine attributes that influence cutting fluid selection for a given machining application, using a logical approach, to eliminate unsuitable cutting fluids and to select an appropriate cutting fluid to strengthen the existing cutting fluid selection procedure. A few researchers, such as Rowe (1982), Sun et al. (2001), Rao and Gandhi (2001), Tan et al. (2002) and Rao (2004), have presented some mathematical models for cutting fluid selection. A cutting fluid attribute is defined as a property or characteristic of the cutting fluid, or a machining process variable on which the cutting fluid has influence. Cutting fluid attributes can be broadly classified into two types, and are listed below: 1. Cutting fluid properties and characteristics such as viscosity, viscosity index, composition, flash point, specific heat, thermal conductivity, lubricity, durability, film formation, anti-foaming characteristics, anti-contamination characteristics, cooling capacity, evaporation rate, toxicity, degradation, disposability, corrosion resistance, compatibility, cost of cutting fluid, molecular size, thermal stability, emulsion stability, chemical stability, handling qualities, physiological properties, operator acceptability, and ecological and environmental characteristics. 2. Machining process variables on which the cutting fluid has influence such as tool life (i.e., life of single point tool in turning/boring, drill in drilling, reamer in reaming, tap in tapping, grinding wheel in grinding), cutting forces (i.e., main cutting force and/or thrust in turning/boring, torque and/or thrust in drilling/reaming/tapping, normal force and/or tangential force in grinding), power consumption, cost per unit volume of material removed, surface finish, cutting temperature, dimensional accuracy, metal removal rate, etc.

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Rao (2004) proposed that the cutting fluids be short-listed for a given machining application, on the basis of cutting fluid attributes of first type, i.e., properties or characteristics of the cutting fluid satisfying the machining application requirements. The machining application involves the machining process, tool, and work materials. An objective or subjective value, or its range, may be assigned to each identified attribute as a limiting value, or threshold value, for acceptance in the cutting fluid selection problem considered. A cutting fluid with each of its selection attribute, meeting the acceptance value, may be shortlisted. After short-listing, the main criterion to choose the cutting fluid for a given machining application is its operational performance during machining. The operational performance of the cutting fluid is indicated by the cutting fluid attributes of second type, i.e., machining process output variables. The next section describes the application of graph theory and the matrix approach, and fuzzy MADM methods for cutting fluid selection in a given machining application.

8.2 Examples
Now, to demonstrate and validate the application of decision making methods, two examples are considered. For a start, GTMA is applied, and subsequently a few MADM methods are applied to rank and select the cutting fluids for a given machining application.

8.2.1 Example 1 A cylindrical grinding operation is considered in which four grinding fluids are tested. Eight cutting fluid attributes are considered, of which four are the machining process output variables wheel wear (WW), tangential force (TF), grinding temperature (GT), and surface roughness (SR), and four are the cutting fluid properties and characteristics recyclability (R), toxic harm rate (TH), environment pollution tendency (EP), and stability (S). The cutting fluid properties and characteristics are expressed in linguistic terms. Table 8.1 presents the data on cutting fluid selection attributes for the four grinding fluids tested.
Table 8.1. Data of cutting fluid selection attributes of example 8.2.1 __________________________________________________________________________ Cutting fluid WW TF GT SR R TH EP S (mm) (N) (°C) (µm) __________________________________________________________________________ 1 0.035 34.5 847 1.76 L A AA AA 2 0.027 36.8 834 1.68 L H H H 3 0.037 38.6 808 2.40 AA AA BA A 4 0.028 32.6 821 1.59 A AA AA BA __________________________________________________________________________ L: Low; BA: Below average; A: Average; AA: Above average; H: High

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The linguistic terms are converted to fuzzy scores as explained in Chapter 4 using Table 4.3. Table 8.2 presents the objective data of cutting fluid selection attributes accordingly.
Table 8.2. Objective data of cutting fluid selection attributes of example 8.2.1 ________________________________________________________________ Cf WW TF GT SR R TH EP S ________________________________________________________________ 1 0.035 34.5 847 1.76 0.335 0.500 0.590 0.590 2 0.027 36.8 834 1.68 0.335 0.665 0.665 0.665 3 0.037 38.6 808 2.40 0.590 0.590 0.410 0.500 4 0.028 32.6 821 1.59 0.500 0.590 0.590 0.410 ________________________________________________________________ Cf: Cutting fluid

8.2.1.1 Application of Graph Theory and Matrix Approach (GTMA) Various steps of the methodology, proposed in Section 2.6, are carried out as described below. In the present work, the attributes considered are wheel wear (WW), tangential force (TF), grinding temperature (GT), surface roughness (SR), recyclability (R), toxic harm rate (TH), environment pollution tendency (EP), and stability (S). The objective values of the cutting fluid selection attributes, which are given in Table 8.2, are to be normalized. R and S are beneficial attributes, and higher values are desirable. Values of these attributes are normalized, as explained in Section 2.4, and are given in Table 8.3 in the respective columns. WW, TF, GT, SR, TH, and EP are non-beneficial attributes and lower values are desirable. The values of these attributes for different cutting fluids are normalized, and given in Table 8.3 in the respective columns.
Table 8.3. Normalized data of cutting fluid selection attributes of example 8.2.1 ___________________________________________________________________ TF GT SR R TH EP S Cf WW ___________________________________________________________________ 1 0.7714 0.9449 0.9539 0.9034 0.5678 1 0.6949 0.8872 2 1 0.8859 0.9688 0.9464 0.5678 0.7519 0.6165 1 3 0.7297 0.8445 1 0.6625 1 0.8475 1 0.7519 4 0.9643 1 0.9842 1 0.8475 0.8475 0.6949 0.6165 ___________________________________________________________________ Cf: Cutting fluid

Relative importance of attributes (aij) is also assigned the values as explained in Section 2.4. Let the decision maker (i.e., user organization) makes the following assignments:

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WW TF GT SR R TH EP S

WW 0.255 0.335 0.255 0.255 0.335 0.335 0.255

TF 0.745 0.665 0.5 0.41 0.59 0.59 0.41

GT 0.665 0.335 0.335 0.335 0.41 0.41 0.335

SR 0.745 0.5 0.665 0.41 0.59 0.59 0.41

R 0.745 0.59 0.665 0.59 0.665 0.665 0.5

TH 0.665 0.41 0.59 0.41 0.335 0.5 0.335

EP 0.665 0.41 0.59 0.41 0.335 0.5 0.335

S 0.745 0.59 0.665 0.59 0.5 0.665 0.665 -

However, it may be added that the above-assigned values are for demonstration purposes only. The cutting fluid attributes digraph, cutting fluid attributes matrix of the digraph and cutting fluid function for the matrix can be prepared. The value of the cutting fluid selection index is calculated using the values of Ai and aij for each cutting fluid. The cutting fluid selection index values of different cutting fluids are given below in descending order: Cutting fluid 4: 246.8591 Cutting fluid 3: 238.2171 Cutting fluid 2: 233.2670 Cutting fluid 1: 231.1462 From the above values of the cutting fluid selection index, it is clear that the cutting fluid, designated as 4 is the best choice among the cutting fluids considered for the cylindrical grinding operation under the given conditions. The next choice is cutting fluid 3, and cutting fluid 1 is the last choice. It may be observed that this ranking is based upon simultaneous consideration of the machining process output variables on which the cutting fluid has influence, as well as the environmental properties and characteristics of the cutting fluids. Following graph theory and the matrix approach, the coefficients of similarity/dissimilarity are also calculated for different cutting fluids, using Equations 2.15 and 2.16. The coefficient of similarity values are given in Table 8.4. These are useful for cutting fluids documentation, for easy storage, and for retrieval of cutting fluids data for cylindrical grinding operations under the given conditions.
Table 8.4. Values of coefficient of similarity for the cutting fluids of example 8.2.1 ______________________________________________________ Cutting fluid 2 3 4 ______________________________________________________ 1 0.9909 0.9703 0.9363 2 0.9792 0.9449 3 0.9650 ______________________________________________________

8.2.1.2 SAW Method The procedure suggested by Edwards et al. (1982) to assess weights for each of the attributes to reflect relative importance to the cutting fluid selection decision is

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followed. The attributes are ranked in order of importance and 10 points are assigned to the least important attribute S. R is also considered least important and equal to S in this example. The attribute WW is given 60 points to reflect its relative importance. GT is given 30 points, TH and EP are given 25 points each and TF and SR are given 15 points each. The final weights are obtained by normalizing the sum of the points to one. For example, the weight for attribute WW is calculated by 60/(60+30+25+25+15+15+10+10) = 0.316. The weight for attribute GT is 0.158, the weights for TH and EP are 0.132 each, those for TF and SR are 0.079 each, and those for S and R are 0.053 each. Using these weights and the normalized data of the attributes for different cutting fluids, the cutting fluid selection index values are calculated, and are arranged in descending order. Cutting fluid 4: 0.8994 Cutting fluid 2: 0.8775 Cutting fluid 3: 0.8443 Cutting fluid 1: 0.8413 From the above values of the cutting fluid selection index, it is clear that the cutting fluid, designated as 4 is the best choice among the cutting fluids considered for the cylindrical grinding operation under the given conditions. 8.2.1.3 WPM Using the same weights of attributes as selected for the SAW method, the following ranking of cutting fluids is obtained: Cutting fluid 4: 0.8884 Cutting fluid 2: 0.8603 Cutting fluid 3: 0.8332 Cutting fluid 1: 0.8300 The ranking is the same as that obtained by using the SAW method. 8.2.1.4 AHP and its Versions If the same weights as those used in the SAW method are selected for this method, then the ranking of cutting fluids obtained by using the relative as well as ideal mode AHP will be the same. The multiplicative AHP method yields the same ranking as that given by WPM. However, if the decision maker decides to use the AHP method, rather than the weights used in the SAW method, then he or she has to make pair-wise comparisons of the attributes to determine the weights (wj) of the attributes. Let the decision maker prepare the following matrix: WW 1 1/5 1/3 1/5 1/5 1/3 1/3 1/5 TF 5 1 3 1 1/2 2 2 1/2 GT 3 1/3 1 1/3 1/3 1/2 1/2 1/3 SR 5 1 3 1 1/2 2 2 1/2 R 5 2 3 2 1 3 3 1 TH 3 1/2 2 1/2 1/3 1 1 1/3 EP 3 1/2 2 1/2 1/3 1 1 1/3 S 4 2 3 2 1 3 3 1

WW TF GT SR R TH EP S

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Wheel wear (WW) is strongly more important than the tangential force (TF) in the grinding operation. Reducing WW is strongly more important than reducing TF. Attention should be paid to reducing the value of WW so as to reduce the machining cost. So, a relative importance value of 5 is assigned to WW over TF (i.e., a12 = 5), and a relative importance value of 1/5 is assigned to TF over WW (i.e., a21 = 1/5). Wheel wear (WW) is moderately more important than the grinding temperature (GT). So, a relative importance value of 3 is assigned to WW over GT (i.e., a13 = 3), and a relative importance value of 1/3 is assigned to GT over WW (i.e., a31 = 1/3). Similarly, the relative importance among other attributes can be explained. It may be added that these values are to be arrived at judiciously after careful analysis. The assigned values in this chapter are for demonstration purposes only. The normalized weights of each attribute are calculated following the procedure presented in Section 3.2.3, and these are Www = 0.3306, WTF = 0.0718, WGT = 0.1808, WSR = 0.0718, WR = 0.0459, WTH = 0.1260, WEP = 0.1260, and WS = 0.0472. The value of max is 8.19 and CR = 0.0194, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. The value of the cutting fluid selection index is now calculated using the above weights, and the normalized data of the attributes given in Table 8.3. This leads to the ranking given by the revised AHP or ideal mode of AHP methods. The alternative cutting fluids are arranged in descending order of the cutting fluid selection index. Cutting fluid 4: 0.9027 Cutting fluid 2: 0.8830 Cutting fluid 3: 0.8444 Cutting fluid 1: 0.8417 From the above values of the cutting fluid selection index, it is clear that the cutting fluid designated as 4 is the best choice among the cutting fluids considered for the cylindrical grinding operation under the given conditions. For the above weights of importance of attributes, multiplicative AHP also leads to the same ranking order of 4-3-2-1. It may be observed that the above ranking is for the given preferences of the decision maker. The ranking depends upon the judgements of relative importance of attributes made by the decision maker. 8.2.1.5 TOPSIS Method Step 1: The objective is to evaluate the four alternative cutting fluids, the pertinent attributes considered being WW, TF, GT, SR, R, TH, EP, and S. Step 2: The next step is to represent all the information available on attributes in the form of a decision matrix. The data given in Table 8.2 can be represented as matrix D4x8. However, the matrix is not shown here, as it is nothing but the repetition of data given in Table 8.2 but represented in a matrix form. Step 3: The quantitative values of the flexible manufacturing system selection attributes, which are given in Table 8.2, are normalized as explained in Section 3.2.6. Step 4: Relative importance of attributes (aij) is assigned using the AHP method as explained in Section 8.2.1.3, and these are Www = 0.3306, WTF =

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0.0718, WGT = 0.1808, WSR = 0.0718, WR = 0.0459, WTH = 0.1260, WEP = 0.1260, and WS = 0.0472. The value of max is 8.19 and CR = 0.02, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. Step 5: The weighted normalized matrix, V4x8 is calculated, and is shown below: 0.1806 0.1393 0.1909 0.1445 0.0347 0.0370 0.0388 0.0328 0.0925 0.0911 0.0883 0.0897 0.0335 0.0320 0.0457 0.0303 0.0170 0.0170 0.0298 0.0253 0.0535 0.0710 0.0631 0.0631 0.0650 0.0732 0.0450 0.0650 0.0253 0.0285 0.0215 0.0176

Step 6: The next step is to obtain the ideal (best) and negative ideal (worst) solutions, and these are given as: VWW+ = 0.1393 VWW- = 0.1909 + VTF = 0.0328 VTF= 0.0388 + VGT = 0.0883 VGT= 0.0925 = 0.0457 = 0.0303 VSRVSR+ VR+ = 0.0298 VR= 0.0169 VTH+ = 0.0535 VTH= 0.0711 = 0.0733 = 0.0452 VEPVEP+ VS+ = 0.0285 VS= 0.0176 Step 7: The next step is to obtain the separation measures, and these are: S1- = 0.0267 S1+ = 0.0480 + S2 = 0.0360 S2- = 0.0545 + S3 = 0.0555 S3- = 0.0325 + S4- = 0.0514 S4 = 0.0256 Step 8: The relative closeness of a particular alternative to the ideal solution is calculated and these are P1 = 0.3571, P2 = 0.6024, P3 = 0.3691, and P4 = 0.6675. This relative closeness to ideal solution can be named ‘cutting fluid selection index’ in the present work. Step 9: The alternative cutting fluids are arranged in descending order of their cutting fluid selection index. This can be arranged as 4-2-3-1. 8.2.1.6 Modified TOPSIS Method In this method, the positive ideal solution (R+) and the negative ideal solution (R-) are used, and the values are given below: RWW+ RTF+ RGT+ RSR+ RR+ RTH+ REP+ RS+ = = = = = = = = 0.4213 0.4566 0.4881 0.4218 0.6505 0.4243 0.3587 0.6049 RWWRTFRGTRSRRRRTHREPRS= = = = = = = = 0.5774 0.5407 0.5117 0.6367 0.3694 0.5644 0.5818 0.3729

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D1+ D2+ D3+ D4+

The weighted Euclidean distances are calculated as = 0.1114 D1= 0.0831 = 0.1152 = 0.1127 D2= 0.1041 = 0.1169 D3= 0.0833 D4= 0.1138 The relative closeness of a particular alternative to the ideal solution is calculated (i.e., cutting fluid selection index), and these are: P1-mod = 0.4272 P2-mod = 0.5054 P3-mod = 0.4709 P4-mod = 0.5774 The alternative cutting fluids are arranged in the descending order of their cutting fluid selection index. This can be arranged as: 4-2-3-1. 8.2.2 Example 2 The results of a cylindrical turning test are presented in Table 8.5. This test is conducted for the purpose of evaluation of most common, commercially available metal cutting fluids, namely, water soluble, straight mineral, chlorinated and sulfochlorinated oils.
Table 8.5. Data of cutting fluid attributes of example 8.2.2 __________________________________________________________ Cutting fluid Fc (N) Ft (N) WL (mm*100) Rrms (µm) __________________________________________________________ Dry 1,324 725 7 9 Water soluble 1,082 485 16 7 Straight mineral oil 1,098 516 8 4.7 Chlorinated oil 1,158 494 15 4.9 Sulfo-chlorinated oil 962 393 6 8 __________________________________________________________ Fc: Cutting force; Ft: Thrust force; WL: Wear land; Rrms: Processed surface roughness expressed in rms value. Work material: medium-carbon steel; Tool: HSS; Cutting conditions: speed–33.5 m/min, feed–0.24 mm/rev

This example is considered to demonstrate further the application of the GTMA and MADM methods for cutting fluid selection. 8.2.2.1 GTMA In the present work, the attributes considered are cutting force (FC), thrust force (TF), wear land (WL), and processed surface roughness (R). The objective values of the cutting fluid selection attributes, which are given in Table 8.5, are to be normalized. All four attributes are of non-beneficial type, and lower values are desirable. Values of these attributes are normalized, as explained in Section 2.4, and are given in Table 8.6 in the respective columns.

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Table 8.6. Normalized data of cutting fluid attributes of example 8.2.2 ______________________________________________________________ Cutting fluid FC (N) TF (N) WL (mm * 100) R (µm) ______________________________________________________________ Dry 0.7251 0.5489 1 0.5222 Water soluble 0.9074 0.8206 0.4375 0.6714 Straight mineral oil 0.8743 0.7713 0.875 1 Chlorinated oil 0.8290 0.8057 0.4667 0.9592 Sulfo-chlorinated oil 1 1 1 0.5875 ______________________________________________________________

Relative importance of attributes (aij) is assigned values as explained in Section 2.4. Let the decision maker select the following assignments: FC --0.335 0.665 0.410 TF 0.665 --0.745 0.590 WL 0.335 0.255 --0.335 R 0.590 0.410 0.665 ---

FC TF WL R

Finally, the cutting fluid selection index values of different cutting fluids are calculated, and are given below in descending order: Sulfo-chlorinated oil 2.8871 Straight mineral oil 2.8172 Chlorinated oil 2.1483 Water soluble 1.9204 Dry 1.9076 From the above values of the cutting fluid selection index, it is understood that the sulfo-chlorinated oil is the best choice among the cutting fluids considered for the cylindrical turning operation under the given conditions. The last choice is dry cutting. Following graph theory and the matrix approach, the coefficients of similarity/dissimilarity are also calculated, and are given in Table 8.7.
Table 8.7. Values of coefficient of similarity for the cutting fluids of example 8.2.2 ______________________________________________________________________ Cutting fluid Water Straight Chl. oil Sulfo-chlorinated oil Soluble min. oil ______________________________________________________________________ Dry 0.9933 0.6671 0.8879 0.6607 Water soluble 0.6817 0.8939 0.6652 0.7626 0.9758 Straight mineral oil Chlorinated oil 0.7441 ______________________________________________________________________

8.2.2.2 SAW Method The procedure suggested by Edwards and Newman (1982) to assess weights for each of the attributes to reflect relative importance to the cutting fluid selection

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decision is followed here. The attributes are ranked in order of importance, and 10 points are assigned to the least important attribute TF. R is considered the nextleast important attribute, and is given 20 points. FC is given 30 points, and WL 40 points. The final weights are obtained by normalizing the sum of the points to one. For example, the weight for attribute WL is calculated by 40/(40+30+20+10) = 0.40. The weight for attribute FC is 0.30, that for R 0.20 and that for TF 0.10. Using these weights, and the normalized data of the attributes for different cutting fluids, the cutting fluid selection index values are calculated, and are arranged in descending order of the index. Sulfo-chlorinated oil 0.9588 Straight mineral oil 0.8561 Water soluble 0.7638 Chlorinated oil 0.7626 Dry 0.7069 The SAW method also suggests sulfo-chlorinated oil as the first choice for the cylindrical turning operation under the given conditions. 8.2.2.3 WPM Using the same weights of attributes as those selected for the SAW method, the following ranking of cutting fluids is obtained: Sulfo-chlorinated oil 0.9482 Straight mineral oil 0.8536 Chlorinated oil 0.7435 Water soluble 0.7383 Dry 0.6883 This method also suggests sulfo-chlorinated oil as the right choice in this example. 8.2.2.4 AHP and its Versions If the same weights as those used in the SAW method are selected for this method, then the ranking of cutting fluids obtained by using the relative as well as ideal mode AHP methods will be same. The multiplicative AHP method yields the same ranking as that given by WPM. 8.2.2.5 TOPSIS Method Following the steps of the TOPSIS method, the following ranking is obtained: Sulfo-chlorinated oil 0.7976 Straight mineral oil 0.7933 Dry 0.6502 Chlorinated oil 0.2979 Water soluble 0.2108 This method also suggests sulfo-chlorinated oil as the right choice. However, the water-soluble fluid is shown as the last choice (unlike dry cutting as given by the other methods). This may be due to TOPSIS being normally biased towards the alternative having a higher value of attribute with higher relative importance. In this example, attribute WL is given maximum weight of importance, and as far as this attribute is concerned, dry cutting is better than the water-soluble fluid.

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8.2.2.6 Modified TOPSIS Method Following the steps of the modified TOPSIS method, the following ranking is obtained: Sulfo-chlorinated oil 0.7892 Straight mineral oil 0.7285 Chlorinated oil 0.4500 Dry 0.4468 Water soluble 0.4084 This method also suggests sulfo-chlorinated oil as the right choice in this example.

References
Bartz WJ (2001) Ecological and environmental aspects of cutting fluids. Lubrication Engineering 57:13–16 Belluco W, de Chiffre L (2001) Testing of vegetable based cutting fluids by hole making operations. Lubrication Engineering 57:12–16 Bennett BG (1987) Effects of coolants and application in using vitrified CBN grinding wheels. Carbide and Tool Journal 19:23–26. Brinksmeier E, Waiter A, Janssen R, Diersen P (1999) Aspects of cooling lubrication reduction in machining advanced materials. Proc. IME., Journal of Engineering Manufacture 213:769–778. Chen Z, Wong K, Li W, Liang SY, Stephenson DA (2001) Cutting fluid aerosol generation due to spin-off in turning operation: analysis for environmentally conscious machining. Journal of Manufacturing Science and Engineering 123:507–512 Cholakov GS, Guest TL, Rowe GW (1992) Lubricating properties of grinding fluids. 1. Comparison of fluids in surface grinding experiments. STLE Transactions 48:155–163 Davinson JF (1995) Cutting fluids and coolants. Tooling and Production 60:4–8 de Chiffre L (1978) Testing the overall performance of cutting fluids. STLE Transactions 34:244–251 de Chiffre L, Lassen S, Pedersen KB, Skade S (1994) Reaming test for cutting fluid evaluation. Journal of Synthetic Lubrication 11:17–34 de Chiffre L, Belluco W, Zeng Z (2001) An investigation of reaming test parameters used for cutting fluid evaluations. Lubrication Engineering 57:24– 28 Dhar NR, Kamruzzaman M (2006) Cutting temperature, tool wear, surface roughness and dimensional deviation in turning AISI-4037 steel under cryogenic condition. International Journal of Machine Tools and Manufacture doi:10.1016/j.ijmachtools.2006.09.018 Dhar NR, Kamruzzaman M, Ahmed M (2006) Effect of minimum quantity lubrication (MQL) on tool wear and surface roughness in turning AISI-4340 steel. Journal of Materials Processing Technology 172:299–304 Ebbrell S, Woolley NH, Tridimas YD, Allanson DR, Rowe WB (2000) The effects of cutting fluid application methods on the grinding process. International Journal of Machine Tools & Manufacture 40:209–223

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Edwards W, Newman JR, Snapper K, Seaver D (1982) Multiattribute Evaluation. SAGE Publications, Newbury Park, California Eppert JJ, Gunter KL, Sutherland JW (2001) Development of a cutting fluid classification system using cluster analysis. Tribology Transactions 44:375– 382 Ghio F (1986) Cutting fluids for operations on metal with flexible abrasive belts. Australian Machinery and Production Engineering 38:19–20 Haq AN, Tamizharasan T (2005) Investigation of the effects of cooling in hard turning operations. International Journal of Advanced Manufacturing Technology 30:808–816 Heinemann N, Hinduja S, Barrow G, Petuelli G (2006) Effect of MQL on the tool life of small twist drills in deep-hole drilling. International Journal of Machine Tools and Manufacture 46:1–6 Lorenz G (1985) Reliable cutting fluid rating. CIRP Annals 34:95–99 Maekawa K (1998) Computational aspects of tribology in metal machining. Proc. of I.Mech.E., Journal of Engineering Tribology 212:307–318 Nagpal BK, Sharma CS (1973) Evaluation of four common, commercially available cutting fluids used in flooding. Journal of the Institution of Engineers (India) 23:249–253 Narheim Y, Kendig M (1987) Evaluation of the cutting fluid effectiveness in machining using electrochemical techniques. Wear 114:51–57 Obikawa T, Kamata Y, Shinozuka J (2006) High-speed grooving with applying MQL. International Journal of Machine Tools and Manufacture 46:1854–1861 Okuyama S, Nakamura Y, Kawamura S (1993) Cooling action of grinding fluid in shallow grinding. International Journal of Machine Tools & Manufacture 33:13–23 Peters J, Aerens R (1976) An objective method for evaluating grinding coolants. CIRP Annals 25:247–250 Rao RV (2004) Performance evaluation of cutting fluids for green manufacturing using a combined multiple attribute decision making method. International Journal of Environmentally Conscious Design and Manufacturing 12:526–535 Rao RV, Gandhi OP (2001) Digraph and matrix method for selection, identification and comparison of metal cutting fluids. Proc. IME, Journal of Engineering Tribology 212:307–318 Rapp W (1984) Selection of cooling lubricants. VDI - Z 126:213–220 Reddy NSK, Rao PV (2006) Experimental investigation to study the effect of solid lubricants on cutting forces and surface quality in end milling. International Journal of Machine Tools and Manufacture 46:189–198 Rowe GW (1982) Lubricant testing for grinding operations. Wear 77:73–80 Sheng PS, Oberwalleney S (1997) Life-cycle planning of cutting fluids - a review. Journal of Manufacturing Science and Engineering 119:791–800 Sokovic M, Mijanovic K (2001) Ecological aspects of the cutting fluids and its influence on quantifiable parameters of the cutting processes. Journal of Materials Processing Technology 109:181–189 Sun J, Ge P, Zhenchang L (2001) Two-grade fuzzy synthetic decision-making system with use of an analytic hierarchy process for performance evaluation of grinding fluids. Tribology International 34:683–688

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Sutcliffe T, Barber SJ, Dycan W (1979) Coolants laboratory evaluation by drill test technique using high speed drills. STLE Transactions 35:145–152 Tan XC, Liu F, Cao HJ, Zhang H (2002) A decision-making framework model of cutting fluid selection for green manufacturing and a case study. Journal of Materials Processing Technology 129:467–470 Upton DP (2000) Optimization of cutting fluid performance. International Journal of Production Research 38:1219–1223 Varadarajan AS, Philip PK, Ramamoorthy B (2002) Investigations on hard turning with minimal cutting fluid application (HTMF) and its comparison with dry and wet turning. International Journal of Machine Tools and Manufacture 42:193–200 Wakabayashi T, Ogura S (1990) Evaluation of cutting fluids by consumption energy in tapping test. STLE Transactions 46:715–720 Webster JA, Cui C, Mindek RB (1995) Grinding fluid application system design. CIRP Annals 4:333–338 Yamanaka Y, Oi T, Sakai Y, Mukai D (1996) Development of a new grinding fluid for the CBN grinding wheel. Part I. STLE Transactions 52:359–364 Yamanaka Y, Hayama M, Oi T, Sakai Y, Satoh M (1997) Development of a new grinding fluid for the CBN grinding wheel. Part II. STLE Transactions 53:20– 26 Yamanaka Y, Hayama M, Oi T, Imai J, Satoh M (1998) Development of a new grinding fluid for the CBN grinding wheel. Part III. STLE Transactions 54:24– 30 Yamanaka Y, Hayama M, Oi T, Imai J, Satoh M (2000) Development of a new grinding fluid for the CBN grinding wheel. Part IV. STLE Transactions 56:17–24 Yamanaka Y, Oi T, Nanao H, Satoh M (2000) Development of a new grinding fluid for the CBN grinding wheel. Part V. STLE Transactions 56:25–31 Yuhta T, Igarashi S, Hukushima, H, Satoh T (1984) On the influence of grinding fluid in grinding carbon steel with a diamond wheel. Japan Society of Precision Engineering 1:363–368

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Evaluation and Selection of Modern Machining Methods

9.1 Introduction
Traditional machining processes, such as turning, grinding, drilling, milling, etc., remove material by chip formation, abrasion, or micro-chipping. There are situations, however, where these processes are not satisfactory, economical, or even possible, for the following reasons (Kalpakjian and Schmid, 2000): 1. The hardness and strength of the material is very high (typically above 400 HB) or the material is too brittle. 2. The work piece is too flexible, slender, or delicate to withstand the cutting or grinding forces, or the parts are too difficult to fix. 3. The shape of the part is complex . 4. Surface finish and dimensional tolerance requirements are more rigorous than those obtained by other processes. 5. Temperature rise and residual stresses in the work piece are not desirable or acceptable. These requirements have led to the development of chemical, electrical, laser and other means of material removal. Beginning in the 1940s, these advanced methods are called non-traditional or unconventional machining processes. Over the last four decades, there has been a large increase in the number of nontraditional machining processes (NTMPs). Today, NTMPs with vastly different capabilities and specifications are available for a wide range of applications. Effective utilization of the capabilities of NTMPs needs careful selection of a suitable process for the application (Benedict, 1987; Yurdakul and Cogun, 2003). The lack of versatility of NTMPs, uncertainties regarding the capabilities of NTMPs, and different cost elements of operating NTMPs make the comparison and ranking of NTMPs a challenging task. An increasing shortage of experienced experts in the field of NTMPs makes the selection of appropriate NTMPs a critical problem. There is not enough published work on the selection of NTMPs. A few attempts have been made to suggest a systematic procedure for selection of a particular NTMP for a given application. Alder et al. (1986) outlined the

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background, and some of the problems associated with the selection of conventional processes and NTMPs. A range of material types to achieve a given task by means of a knowledge-based expert system was also examined. Cogun (1994) developed a procedure that identifies suitable alternative NTMPs for the user, with a list of suitable processes for parts with relatively slack design requirements. The main objective of the work was to remove unsuitable NTMPs from consideration, but not the ranking of the NTMPs. Jain and Jain (2001) reviewed the modeling of material removal in mechanical-type advanced machining processes, and gave a brief summary of research work on these processes. Yurdakul and Cogun (2003) developed a multi-attribute selection procedure for NTMP selection using the technique for order preference by similarity to ideal solution (TOPSIS) and the analytic hierarchy process (AHP) methods. AHP was used to assign weights of relative importance to various process selection attributes, and TOPSIS was used to obtain a ranking score for each of the alternative NTMPs. However, the authors had not considered the subjective attributes. Further, the authors had made certain mistakes in applying the basic technique of TOPSIS. Chakraborthy and Dey (2006) suggested a quality function deployment (QFD) based expert system for NTMP selection. The developed expert system employs the use of a house of quality (HOQ) matrix for comparison of relevant product and process characteristics. The weights obtained for various process characteristics were utilized to estimate an overall score for each of the NTMPs, and the process having the maximum score was selected as the optimal choice. However, the procedure is knowledge-intensive and may go beyond the capabilities of the non-expert user. There is a need for a simple scientific method or mathematical tool to guide users in taking a proper NTMP selection decision. The objective of an NTMP selection procedure is to identify the NTMP selection attributes, and obtain the most appropriate combination of attributes in conjunction with the real requirements of the machining application. Efforts need to be extended to determine attributes that influence NTMP selection for a given machining application, using a logical approach, to eliminate unsuitable NTMPs, and for the selection of a proper NTMP to strengthen the existing NTMP selection procedure. This is considered in this chapter using the GTMA and other fuzzy MADM methods. An NTMP selection attribute is defined as a factor that influences the selection of an NTMP for a given industrial application. NTMP attributes include work piece material, cost involved, and process capability attributes such as tolerance, surface finish, surface damage, corner radii, taper, hole diameter, depth/diameter ratio for cylindrical holes, depth/width ratio for blind cavities, width of cut, material removal rate, part size, part exterior and interior shape details, etc. As a first step in NTMP selection, the decision maker has to identify the NTMP selection attributes for a given industrial application, and short-list the NTMP processes on the basis of identified attributes satisfying the requirements. A quantitative or qualitative value, or its range, may be assigned to each identified attribute as a limiting value, or threshold value, for its acceptance in the application

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considered. An NTMP process with each of its attributes, meeting the criterion, may be short-listed. Now, an example is included to demonstrate and validate the proposed decision making-methods for the selection of an NTMP process for a given industrial application.

9.2 Examples
Two examples of NTMP selection are considered. 9.2.1 Example 1 Yurdakul and Cogun (2003) developed a multi-attribute selection procedure for NTMP selection using the TOPSIS and AHP methods. The authors presented different case studies, one of which is considered here. The details of the case study are given in Table 9.1. The NTMPs eliminated on the basis of the work material were ECM, ECG, ECH, EDM, WEDM, and PAC. The NTMP eliminated on the basis of the shape applications was WJM. No NTMPs were eliminated on the basis of process capabilities. This elimination procedure is similar to the shortlisting of alternative NTMPs as described in Section 9.1. Feasible NTMPs to be ranked are AJM, USM, CHM, EBM, and LBM.
Table 9.1. Data of the NTMP selection attributes of example 9.2.1 (from Yurdakul and Cogun 2003; permission of the Council of the Institution of Mechanical Engineers, UK) ____________________________________________________________ NTMP T SF SD TR MR WM C ____________________________________________________________ AJM 0.05 0.6 2.5 0.005 50 3 4 USM 0.013 0.5 25 0.005 500 3 5 CHM 0.03 2 5 0.3 40 1 2 EBM 0.02 3 100 0.02 2 3 1 LBM 0.02 1 100 0.05 2 3 1 ____________________________________________________________ Work material: Ceramic (non-conductive); Shape application: Cylindrical through hole drilling; Process requirements: 930 holes of 0.64 mm diameter, L/D = 5.7 T: Tolerance (mm); SF: Surface finish (µm); SD: Surface damage (µm); TR: Taper (mm/mm); MR: Material removal rate (mm3/min); WM: Work material (NTMP process suitability is assigned on a scale of 1–3, 1 for poor and 3 for good application); C: Cost (on a scale of 1–9, 1 for low, 5 for medium and 9 for very high) USM: Ultrasonic machining; AJM: Abrasive jet machining; LBM: Laser beam machining; EBM: Electron beam machining; CHM: Chemical machining

9.2.1.1 Graph Theory and Matrix Approach (GTMA) Now, various steps of the proposed procedure are carried out as described next:

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1. The NTMP selection attributes considered are the same as those of Yurdakul and Cogun (2003) and these are: tolerance (T), surface finish (SF), surface damage (SD), taper (TR), material removal rate (MR), work material (WM), and cost (C). 2. The quantitative values of the NTMP selection attributes, which are given in Table 3, are to be normalized. MR and WM are beneficial attributes, and higher values are desirable. Values of these attributes are normalized, and are given in Table 9.2 in the respective columns. T, SF, SD, TR, and C are non-beneficial attributes, and lower values are desirable. The values of these attributes for different NTMPs are normalized, and are given in Table 9.2 in the respective columns.
Table 9.2. Normalized data of the NTMP selection attributes of example 9.2.1 _______________________________________________________________ NTMP T SF SD TR MR WM C _______________________________________________________________ AJM 0.26 0.83 1 1 0.1 1 0.25 USM 1 1 0.1 1 1 1 0.2 CHM 0.43 0.25 0.5 0.02 0.08 0.33 0.5 EBM 0.65 0.17 0.03 0.25 0.004 1 1 LBM 0.65 0.5 0.03 0.1 0.004 1 1 _______________________________________________________________

Relative importance of attributes (aij) is also assigned values, as explained in Chapter 4. Let the decision maker (i.e., user organization) select the following assignments: T 0.410 0.135 0.135 0.410 0.335 0.335 SF 0.59 0.255 0.255 0.500 0.410 0.410 SD 0.865 0.745 0.500 0.745 0.665 0.665 TR 0.865 0.745 0.5 0.745 0.665 0.665 MR 0.59 0.5 0.255 0.255 0.41 0.41 WM 0.665 0.590 0.335 0.335 0.590 0.500 C 0.665 0.590 0.335 0.335 0.590 0.500 -

T SF SD TR MR WM C

The assigned values in this example are for demonstration purposes only. 3. The NTMP selection attributes digraph, showing the presence as well as relative importance of the above attributes, is similar to Fig. 2.2 but with seven attributes. However, it is not shown here. 4. The NTMP selection attributes matrix of this digraph is written. However, it is not shown here. 5. The NTMP selection attributes function is written. However, as a computer program is developed for calculating the permanent function value of a matrix, this step can be skipped. 6. The NTMP selection index (NTMP-SI) is calculated using the values of Ai and aij for each alternative NTMP and the values are given in descending order. Ultrasonic machining (USM) 40.50211 Abrasive jet machining (AJM) 31.76501

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Laser beam machining (LBM) 21.05954 Electron beam machining (EBM) 20.13952 Chemical machining (CHM) 15.90063 From the above values of the NTMP selection index, USM is understood as the best choice among the alternatives considered for the given hole making operations. The ranking of NTMPs based on the proposed methodology is USMAJM-LBM-EBM-CHM; by contrast, the ranking presented by Yurdakul and Cogun (2003) was USM-LBM-EBM-CHM-AJM. Both the methods suggest USM as the first right choice. However, the ranking of certain alternative NTMPs obtained by using the proposed procedure is different from that reported by Yurdakul and Cogun (2003). For example, AJM is the second choice based on the proposed procedure, whereas it was LBM in Yurdakul and Cogun (2003), and AJM was proposed as the last choice by these authors. A closer look at the quantitative data of the attributes of LBM and AJM reveals that AJM is better than LBM in the case of four out of seven attributes (i.e., SF, SD, T, and MR), and equal to LBM in the case of attribute WM. LBM is better than AJM only in the case of two attributes (i.e., T and C). Thus, keeping in mind the values of the attributes and the relative importance of the attributes, proposing AJM as the second choice by the proposed method based on the method used here seems to be more appropriate, compared to LBM as proposed by Yurdakul and Cogun (2003). Thereby, the differences in the ranking of alternatives between the procedure proposed here and that suggested by Yurdakul and Cogun (2003) can be explained. It may be added here, however, that the weights of relative importance used by Yurdakul and Cogun (2003) were different from those used in the present work. Further, it may be mentioned that ranking depends upon the judgements of relative importance made by the decision maker (i.e., user organization). The ranking may change if the decision maker assigns different relative importance values to the attributes. The same is true with the approach proposed by Yurdakul and Cogun (2003). Yurdakul and Cogun (2003) had made certain mistakes in applying the basic technique of TOPSIS in their model (e.g., in normalization of the attributes, and calculation of final ranking scores). 9.2.1.2 SAW Method To start with, the attributes are ranked in order of importance, and 10 points each are assigned to the least important attributes SD and TR. The attributes WM and C are considered as equally important in the present example, and given 20 points each to reflect their relative importance. SF and MR are considered as equally important, and given 30 points each, and T is given 40 points. The final weights are obtained by normalizing the sum of the points to one. Thus, the weights of T, SF, MR, WM, C, SD, and TR are calculated as 0.25, 0.1875, 0.1875, 0.125, 0.125, 0.0625, and 0.0625, respectively. Using these weights, and the normalized data of the attributes for different NTMPs, the NTMP-SI values are calculated, and are arranged in descending order of the index. Ultrasonic machining (USM) 0.8438 Abrasive jet machining (AJM) 0.5206 Laser beam machining (LBM) 0.5151

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Electron beam machining (EBM) 0.4626 Chemical machining (CHM) 0.3056 The SAW method also suggests USM as the right choice for the given NTMP selection problem. 9.2.1.3 WPM Using the same weights of attributes as those selected for the SAW method, the NTMP-SI value for each NTMP is calculated, and the values are given below: Ultrasonic machining (USM) 0.7082 Abrasive jet machining (AJM) 0.4478 Chemical machining (CHM) 0.2328 Laser beam machining (LBM) 0.1948 Electron beam machining (EBM) 0.1685 WPM also suggests USM as the right choice for the given NTMP selection problem. However, CHM is proposed as the third choice, and EBM as the last choice. 9.2.1.4 AHP and its Versions The AHP method may use the same weights as those selected for the SAW method. In that case, the ranking of the NTMPs will be same. However, if the decision maker decides to use the AHP method for determining the weights, rather than adopting the weights used in SAW method, then he or she has to make pairwise comparisons of the attributes to determine the weights (wj) of the attributes. Let the decision maker prepare the following matrix: T 1 1/2 1/7 1/7 1/2 1/3 1/3 SF 2 1 1/5 1/5 1 1/2 1/2 SD 7 5 1 1 5 3 3 TR 7 5 1 1 5 3 3 MR 2 1 1/5 1/5 1 1/2 1/2 WM 3 2 1/3 1/3 2 1 1 C 3 2 1/3 1/3 2 1 1

T SF SD TR MR WM C

The normalized weights of each attribute are calculated following the procedure presented in Section 3.2.3 and these are WT = 0.3224, WSF = WMR = 0.1938, WWM = WC = 0.1063, and WSD = WTR = 0.0387. The value of max is 7.028 and CR = 0.003457, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. The value of NTMP-SI is now calculated using the above weights, and the normalized data of the attributes given in Table 9.3. The alternative NTMPs are arranged in descending order of the NTMP-SI: Ultrasonic machining (USM) 0.8801 Laser beam machining (LBM) 0.5249 Abrasive jet machining (AJM) 0.4743 Electron beam machining (EBM) 0.4667 Chemical machining (CHM) 0.3109

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For the above weights of importance of attributes, the multiplicative AHP method leads to the following ranking order: Ultrasonic machining (USM) 0.7709 Abrasive jet machining (AJM) 0.3451 Chemical machining (CHM) 0.2466 Laser beam machining (LBM) 0.2084 Electron beam machining (EBM) 0.1752 It may be observed that the ranking order given by multiplicative AHP for the given weights is similar to that given by WPM. 9.2.1.5 TOPSIS Method Using the same weights as those selected for the AHP method, and following the steps of the methodology given in Section 3.2.6, the TOPSIS method gives the following ranking order of NTMPs: Ultrasonic machining (USM) 0.7709 Abrasive jet machining (AJM) 0.3451 Chemical machining (CHM) 0.2466 Laser beam machining (LBM) 0.2084 Electron beam machining (EBM) 0.1752 This ranking order is similar to that given by the multiplicative AHP method. 9.2.1.6 Modified TOPSIS Method For the same weights as those used in the AHP method, the modified TOPSIS method gives the following ranking order: Ultrasonic machining (USM) 0.7693 Laser beam machining (LBM) 0.4893 Abrasive jet machining (AJM) 0.4231 Electron beam machining (EBM) 0.4180 Chemical machining (CHM) 0.3594 This ranking order is similar to that given by the AHP method. 9.2.2 Example 2 Another case study presented by Yurdakul and Cogun (2003) is considered here. No NTMPs were eliminated on the basis of the work material. The NTMPs eliminated on the basis of the shape applications were WJM, ECM, ECG, ECH, CHM, WEDM, and PAC. The NTMP eliminated on the basis of process capability was AJM. This elimination procedure is similar to the short-listing of alternative NTMPs described in Section 9.1. Feasible NTMPs to be ranked are USM, EDM, EBM, and LBM. The details of the case study are given in Table 9.3.

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Table 9.3. Data of the NTMP selection attributes of example 9.2.2 (from Yurdakul and Cogun 2003; permission of the Council of the Institution of Mechanical Engineers, UK) _______________________________________________________ NTMP SF SD TR MR WM C _______________________________________________________ USM 0.5 25 0.005 500 2 5 EDM 2 20 0.001 800 3 7 EBM 3 100 0.02 2 2 1 LBM 1 100 0.05 2 2 1 _______________________________________________________ Work material: Hardened 52100 steel; Shape application: Cylindrical through hole drilling; Process requirements: 800 holes of 0.175 mm diameter, L/D = 5.7 SF: Surface finish (µm); SD: Surface damage (µm); TR: Taper (mm/mm); MR: Material removal rate (mm3/min); WM: Work material (NTMP process suitability is assigned on a scale of 1–3, 1 for poor and 3 for good application); C: Cost (on a scale of 1–9, 1 for low, 5 for medium and 9 for very high) USM: Ultrasonic machining; EDM: Electric discharge machining; EBM: Electron beam machining; LBM: Laser beam machining

9.2.2.1 Graph Theory and the Matrix Approach (GTMA) In the present work, the attributes considered are the same as those of Yurdakul and Cogun (2003) and these are: surface finish (SF), surface damage (SD), taper (TR), material removal rate (MR), work material (WM), and cost (C). The quantitative values of the NTMP selection attributes, which are given in Table 9.3, are to be normalized. SF, SD, TR, and C are non-beneficial attributes, and MR and WM are beneficial attributes. The values of the attributes are normalized, and are shown in Table 9.4.
Table 9.4. Normalized data of the NTMP selection attributes of example 9.2.2 __________________________________________________________________ NTMP SF SD TR MR WM C __________________________________________________________________ USM 1 0.8 0.2 0.625 0.6667 0.2 EDM 0.25 1 1 1 1 0.1428 EBM 0.1667 0.2 0.05 0.0025 0.6667 1 LBM 0.5 0.2 0.02 0.0025 0.6667 1 __________________________________________________________________

Let the decision maker select the following assignments of relative importance:

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SF SD TR MR WM C

SF 0.41 0.5 0.59 0.335 0.59

SD 0.59 0.59 0.665 0.41 0.665

TR 0.5 0.41 0.59 0.335 0.59

MR 0.41 0.335 0.41 0.255 0.41

WM 0.665 0.59 0.665 0.745 0.745

C 0.41 0.335 0.41 0.59 0.255 -

The NTMP selection attributes digraph, NTMP selection attributes matrix of the digraph, and NTMP selection function for the matrix can be prepared. The value of the NTMP selection index is calculated using the values of Ai and aij for each NTMP. The NTMP selection index values of different NTMPs are given below in descending order: EDM 14.0184 USM 10.4897 LBM 7.1186 EBM 6.4465 From the above values of the NTMP selection index, EDM is identified as the best choice among the alternatives considered for the given operations. The ranking of NTMPs based on the methodology proposed is EDM-USM-LBM-EBM. 9.2.2.2 TOPSIS Method The same relative importance matrix as in Yurdakul and Cogun (2003) is used here. SF SD TR MR WM C SF 1 2 1 1/2 4 1/2 SD 1/2 1 1/2 1/3 2 1/3 TR 1 2 1 1/2 3 1/2 MR 2 3 2 1 6 2 WM 1/4 1/2 1/3 1/6 1 1/6 C 2 3 2 1/2 6 1 The normalized weights of each attribute are calculated following the procedure presented in Section 3.2.3, and these are WSF = 0.155, WSD = 0.0853, WTR = 0.1478, WMR = 0.3162, WWM = 0.0447, and WC = 0.251. The value of max is 6.0725 and CR = 0.0116, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. Following the steps of the methodology given in Section 3.2.6, the TOPSIS method gives the following ranking order of NTMPs: EDM 0.6250 USM 0.6121 EBM 0.3932 LBM 0.3865 This ranking order also suggests EDM as the first choice. However, Yurdakul and Cogun (2003) who also used the above relative importance matrix and the TOPSIS method, obtained a different ranking order, i.e., EDM-USM-LBM-EBM. As

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explained in Section 9.2.1.1, Yurdakul and Cogun (2003) had made certain mistakes in applying the basic technique of TOPSIS in their model. 9.2.2.3 Modified TOPSIS Method For the same weights as those used in the TOPSIS method, the modified TOPSIS method gives the following ranking order: USM 0.6467 EDM 0.6215 EBM 0.4100 LBM 0.3959 This ranking order suggests USM as the first right choice. However, a closer look at the values of the attributes for USM, and the corresponding values of the attributes for EDM indicates that proposing USM is not logical. Thus, it can be said that modified TOPSIS method does not provide logical results for the example considered here.

References
Alder GM, McGeough JA, Spencer CA (1986) Selection of machining processes by intelligent knowledge base systems. In: Proc. International Conference on Computer Aided Production Engineering, University of Edinburgh, Edinburgh pp 61–66 Benedict GF (1987) Non-traditional manufacturing processes. Marcel Dekker, New York Chakraborthy S, Dey S (2006) QFD-based expert system for non-traditional machining processes selection. Expert Systems with Applications doi:10.1016/j.eswa.2006.02.010 Cogun C (1994) Computer aided preliminary selection of non traditional machining processes. International Journal of Machine Tools and Manufacture 34:315–326 Jain NK, Jain VK (2001) Modeling of material removal in mechanical type advanced machining processes: a state-of-art review. International Journal of Machine Tools and Manufacture 41:1573–1635 Kalpakjian S, Schmid SR (2000) Manufacturing engineering and technology. Addison Wesley Longman (Singapore), Indian branch, Delhi Yurdakul M, Cogun C (2003) Development of a multi-attribute selection procedure for non-traditional machining processes. Proc. IME, Journal of Engineering Manufacture 217:993–1009

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Evaluation of Flexible Manufacturing Systems

10.1 Introduction
A flexible manufacturing system (FMS) consists of a group of processing work stations (usually CNC machine tools) interconnected by an automated material handling and storage system, and controlled by a distributed computer system. The reason the FMS is called ‘flexible’ is that it is capable of processing a variety of different part styles simultaneously at the various work stations, and the mix of part styles and quantities of production can be adjusted in response to changing demand patterns. The evolution of flexible manufacturing systems offers great potential for increasing flexibility and changing the basis of competition by ensuring both costeffective and customized manufacturing at the same time. The decision to invest in FMS and other advanced manufacturing technology has been an issue in the practitioner and academic literature for over two decades. An effective justification process requires the consideration of many quantitative attributes (e.g., costs involved, floor space requirements, etc.) and qualitative attributes (e.g., product-mix flexibility, routing flexibility, etc.). An FMS selection attribute is defined as a factor that influences the selection of a flexible manufacturing system for a given application. These attributes include: costs involved, floor space requirements, labor requirements, throughput time, work-inprocess, setup cost, quality, volume flexibility, product-mix flexibility, process/routing flexibility, expansion flexibility, utilization rate, risk, ease of operation, maintenance aspects, payback period, reconfiguration time, company policy, etc. To help address this issue of effective evaluation and justification of flexible manufacturing systems, various mathematical and systems modeling approaches have been proposed. Kochan (1987) discussed the importance of selection of flexible manufacturing and CAD/CAM systems. Troxler (1990) estimated the cost impact of flexible manufacturing systems. Dhavale (1990) proposed a manufacturing cost model for computer-integrated manufacturing systems. Layek and Wolf (1991) evaluated flexibility of alternative FMS designs using a comparative measure. Sriram and Gupta (1991) discussed the impact of FMS and its implications in terms of information reporting, strategic cost analyses, and

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control. Suresh and Kaparthi (1992) presented a procedure that combined a general mixed integer goal programming (GP) formulation with the analytic hierarchy process (AHP) for use in deciding upon flexible automation investments. Gerwin and Kolodny (1992) discussed the aspects of management of advanced manufacturing technologies. Elango and Meinhart (1994) proposed a strategic framework for selecting an FMS. Kuula (1993) presented a risk management model for FMS selection decisions using a multiple criteria decision-making approach. Tabucanon et al. (1994) proposed a decision support system for multiple criteria machine selection for flexible manufacturing systems. The approach presented combined the analytic hierarchy process (AHP) technique with the rule-based technique for creating Expert Systems (ES). Myint and Tabucanon (1994) used AHP method and goal programming (GP) model to determine the satisfactory FMS configuration from the short-listed FMS configurations. Shang and Sueyoshi (1995) proposed a unified framework to facilitate decision-making in the design and planning stage of FMS. The recommended framework contains three individual modules: an analytic hierarchy process (AHP), a simulation module, and an accounting procedure. These modules were unified through an efficiency measurement method called data envelopment analysis (DEA). The AHP model examines the non-monetary criteria associated with corporate goals and long-term objectives, while the simulation model was employed to analyze the tangible benefits. Both the AHP and simulation models were used to generate the necessary outputs for the DEA, whereas the accounting procedure determines the required inputs, such as expenditures and resources for realizing the potential benefits. Albayrakoglu (1996), and Mohanty and Venkataraman (1996) proposed the application of AHP for justification of new manufacturing technologies. Sarkis (1997) presented an illustrative problem for evaluating flexible manufacturing systems for an industrial application using DEA. The problem considered 24 alternative flexible manufacturing systems, and eight selection attributes. Perego and Rangone (1998) presented a reference framework for the application of three categories of fuzzy MADM techniques to select advanced manufacturing technologies. Talluri et al. (2000) proposed a method based on the combined application of data envelopment analysis (DEA) and nonparametric statistical procedures for FMS evaluation. Chan et al. (2000) developed intelligent decision support tools to aid the design of flexible manufacturing systems. Karsak and Tolga (2001) proposed a fuzzy multiple criteria decision-making procedure for evaluating advanced manufacturing system investments. Karsak and Kuzgunkaya (2002) proposed a fuzzy multiple objective programming approach for the selection of a flexible manufacturing system. The model proposed by the authors determines the most appropriate FMS alternative through maximization of objectives such as reduction in labor cost, reduction in setup cost, reduction in work-in-process (WIP), increase in market response and improvement in quality, and minimization of capital and maintenance costs as well as floor space used. These objectives were assigned priorities indicating their importance levels based on linguistic variables.

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Sarkis and Talluri (1999) presented a decision model using DEA for evaluation of flexible manufacturing systems in the presence of both cardinal and ordinal factors. Karsak (2002) presented a distance-based fuzzy MCDM approach for evaluating flexible manufacturing system alternatives. The method is similar to the TOPSIS method. Tseng (2004) presented the details of strategic choice of flexible manufacturing technologies. Laosirihongthong et al. (2003) presented case studies related to new manufacturing technology implementation. Lloréns et al. (2005) described the aspects of flexibility of manufacturing systems, strategic change, and performance. The authors showed that manufacturing flexibility at system level can be a critical factor in the process of strategic change, which means that it can have an impact on the desirability of strategic change, or on the more specific strategic fit. Bayazit (2005) used AHP to implement FMS in a tractor manufacturing plant. Also a sensitivity analysis was conducted to assess how realistic the final outcome was. Kulak and Kahraman (2005) proposed axiomatic design (AD) principles for multiple attribute comparison of advanced manufacturing systems. The comparison was made for cases of both complete and incomplete information. The crisp AD approach for complete information, and the fuzzy AD approach for incomplete information were developed. Rao (2006) presented a decision-making model for FMS selection using digraph and matrix methods. A ‘flexible manufacturing system selection index’ was proposed that evaluates and ranks flexible manufacturing systems for a given industrial application. In another work, Rao (2007) used the TOPSIS and AHP methods in combination for evaluating flexible manufacturing systems. Now, to demonstrate and validate the application of decision-making methods, two examples are considered. In both, GTMA is applied first, and then a few MADM methods are applied to rank and select the flexible manufacturing systems.

10.2 Examples
Two examples are considered to demonstrate the application of the GTMA and fuzzy MADM methods. 10.2.1 Example 1 Karsak and Kuzgunkaya (2002) proposed a fuzzy multiple objective programming approach for the selection of a flexible manufacturing system. The authors had considered eight alternative flexible manufacturing systems and seven attributes. Five attributes were expressed objectively, and two attributes were expressed subjectively. Table 10.1 presents the data.

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Table 10.1. Data of attributes of example 10.2.1 (from Karsak and Kuzgunkaya 2002; reprinted with permission from Elsevier) __________________________________________________________________ FMS RLC RWP RSC IMR IQ CMC FSU __________________________________________________________________ 1 30 23 5 Good Good 1,500 5,000 2 18 13 15 Good Good 1,300 6,000 3 15 12 10 Fair Fair 950 7,000 4 25 20 13 Good Good 1,200 4,000 5 14 18 14 Worst Good 950 3,500 6 17 15 9 Good Fair 1,250 5,250 7 23 18 20 Fair Good 1,100 3,000 8 16 8 14 Worst Fair 1,500 3,000 __________________________________________________________________ RLC: Reduction in labor cost (%) RWP: Reduction in WIP (%) RSC: Reduction in set up cost (%) IMR: Increase in market response IQ: Increase in quality CMC: Capital and maintenance cost ($1,000) FSU: Floor space used (sq. ft.) The above data for RLC, RWP, RSC, CMC, and FSU are actually the middle values of the range presented by Karsak and Kuzgunkaya (2002)

10.2.1.1 Application of Graph Theory and Matrix Approach (GTMA) Various steps of the methodology, proposed in Section 2.6, are carried out as described below: Step 1: In the present work, the attributes considered are the same as those of Karsak and Kuzgunkaya (2002), and these are: reduction in labor cost (RLC), reduction in WIP (RWP), reduction in setup cost (RSC), increase in market response (IMR), increase in quality (IQ), capital and maintenance cost (CMC), and floor space used (FSU). The subjective data of the two attributes IMR and IQ are converted into appropriate objective data using Table 4.3, and the objective data for all seven attributes are given in Table 10.2.
Table 10.2. Objective data of attributes of example 10.2.1 __________________________________________________________________ FMS RLC RWP RSC IMR IQ CMC FSU __________________________________________________________________ 1 30 23 5 0.745 0.745 1,500 5,000 2 18 13 15 0.745 0.745 1,300 6,000 3 15 12 10 0.500 0.500 950 7,000 25 20 13 0.745 0.745 1,200 4,000 4 5 14 18 14 0.255 0.745 950 3,500 6 17 15 9 0.745 0.500 1,250 5,250 7 23 18 20 0.500 0.745 1,100 3,000 16 8 14 0.255 0.5 1,500 3,000 8 __________________________________________________________________

The objective values of the FMS selection attributes, which are given in Table 10.2, are to be normalized. RLC, RWP, RSC, IMR, and IQ are beneficial attributes, and higher values are desirable. CMC and FSU are non-beneficial attributes, and lower values are desirable. The values of the attributes for different FMSs are normalized, and given in Table 10.3 in the respective columns.

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Table 10.3. Normalized data of attributes of example 10.2.1 __________________________________________________________________ FMS RLC RWP RSC IMR IQ CMC FSU __________________________________________________________________ 1 1 1 0.25 1 1 0.6333 0.6 2 0.6 0.5652 0.75 1 1 0.7308 0.5 3 0.5 0.5217 0.5 0.6711 0.6711 1 0.4286 4 0.83333 0.8696 0.65 1 1 0.7917 0.75 5 0.4667 0.7826 0.7 0.3423 1 1 0.8571 6 0.5667 0.6527 0.45 1 0.6711 0.76 0.5714 7 0.7667 0.7826 1 0.6711 1 0.8636 1 8 0.5333 0.3478 0.7 0.3423 0.6711 0.6333 1 __________________________________________________________________

Relative importance of attributes (aij) is also assigned values, as explained in Section 2.4. Let the decision maker (i.e., user organization) select the following assignments: RLC 0.5 0.335 0.5 0.665 0.665 0.335 RWP 0.5 0.335 0.5 0.665 0.665 0.335 RSC 0.665 0.665 0.665 0.745 0.745 0.5 IMR 0.5 0.5 0.335 0.665 0.665 0.335 IQ 0.335 0.335 0.255 0.335 0.5 0.255 CMC 0.335 0.335 0.255 0.335 0.5 0.255 FSU 0.665 0.665 0.5 0.665 0.745 0.745 -

RLC RWP RSC IMR IQ CMC FSU

As was assigned by Karsak and Kuzgunkaya (2002), more relative importance is given to IQ and CMC, less to RLC, RWP, and IMS, and even lesser to RSC and FSU. However, the above-assigned values are for demonstration purposes only. Step 2: 1. The FMS selection attributes digraph, showing the presence as well as relative importance of the above attributes is similar to Figure 2.2 but with seven attributes is not shown here due to obvious reasons. 2. The FMS selection attributes matrix of this digraph is written based on Equation 2.10. This is not shown here due to space restriction. 3. The FMS selection attributes function is written but not shown here. However, it may be added that as a computer program is developed for calculating the permanent function value of a matrix, this step can be skipped. 4 & 5. The flexible manufacturing system selection index (FMS-SI) is calculated using the values of Ai and aij for each alternative flexible manufacturing system. The FMS-SI values of different flexible manufacturing systems are given in descending order: 7 61.2188 4 57.2741 1 48.9012 5 45.6628

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6 39.3644 2 45.5043 3 35.2635 8 34.7198 From the above values of FMS-SI, it is understood that the flexible manufacturing system designated as 7 is the right choice for the given industrial application under the given conditions, and the second choice is 4. These results are similar to those suggested by Karsak and Kuzgunkaya (2002) using the fuzzy multiple objective programming approach. However, it may be mentioned that the ranking depends upon the judgments of relative importance made by the user. The ranking may change if the user assigns different relative importance values to the attributes. The same is true with the approach proposed by Karsak and Kuzgunkaya (2002). The fuzzy method proposed by Karsak and Kuzgunkaya (2002) is cumbersome in terms of the mathematical equations involved, representation of weights of relative importance, fuzzy distributions, etc. Further, the authors had converted the available objective values of the attributes (of RLC, RWP, RSC, CMC, and FSU) into fuzzy values which violates the basic rule of fuzzy logic, i.e., the available objective values need not be fuzzified (i.e., the actual objective values of the attributes are to be taken as is). Comparatively, the GTMA proposed here provides a simple, straight-forward and logical procedure for the FMS selection problem. 10.2.1.2 AHP and its Versions Let the decision maker prepare the following relative importance matrix: RLC 1 1 1/3 1 3 3 1/3 RWP 1 1 1/3 1 3 3 1/3 RSC 3 3 1 3 5 5 1 IMR 1 1 1/3 1 3 3 1/3 IQ 1/3 1/3 1/5 1/3 1 1 1/5 CMC 1/3 1/3 1/5 1/3 1 1 1/5 FSU 3 3 1 3 5 5 1

RLC RWP RSC IMR IQ CMC FSU

RLC is considered moderately more important than RSC in FMS selection. So, a relative importance value of 3 is assigned to RLC over RSC (i.e., a13 = 3), and a relative importance value of 1/3 is assigned to RSC over RLC (i.e., a31 = 1/3). RLC and RWP are considered equally important attributes in FMS selection. So, a relative importance value of 1 is assigned to RLC over RWP (i.e., a12 = 1), and a relative importance value of 1/1 is assigned to RWP over RLC (i.e., a21 = 1/1=1). Similarly, the relative importance among other attributes can be explained. However, it may be added that, in actual practice, these values of relative importance can be judiciously decided upon by the user/expert depending on the requirements. The normalized weights of each attribute are calculated following the procedure presented in Section 3.2.3, and these are WRLC = 0.1181, WRWP =

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0.1181, WRSC = 0.046, WIMR = 0.1181, WIQ = 0.3, WCMC = 0.3, and WFSU = 0.046, and good consistency is found in the judgments made. The value of the FMS selection index is now calculated using the above weights, and the normalized data of the attributes given in Table 10.2. This leads to the ranking given by the revised AHP or ideal mode of AHP method. The alternative FMS configurations are arranged in descending order of the FMS selection index: 4 0.9211 7 0.9133 1 0.8834 5 0.8596 2 0.8324 3 0.7440 6 0.7384 8 0.6140 For the above weights of importance of attributes, multiplicative AHP leads to the following ranking order: 4 0.8684 7 0.7993 1 0.7990 2 0.7657 5 0.7641 6 0.6826 3 0.6728 8 0.5495 It may be observed that the above ranking is for the given preferences of the decision maker. The ranking depends upon the judgements of relative importance of attributes made by the decision maker. 10.2.2 Example 2 Now another example is considered to further demonstrate the potential of the proposed GTMA and fuzzy MADM methods. Kulak and Kahraman (2005) proposed axiomatic design (AD) principles for multiple attribute comparison of advanced manufacturing systems. The authors presented the case study of a company manufacturing tractor components that wished to renew the manufacturing system. In order to produce a group of products, the company had to decide and select the most appropriate one among the different alternative FMSs. The attributes considered were: annual depreciation and maintenance costs (ADM), quality of results (Q), ease of use (E), competitiveness (C), adaptability (A), and expandability (X). The linguistic expressions of the attributes are given in Table 10.4.

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Table 10.4. System data of the attributes (from Kulak and Kahraman 2005; reprinted with permission from Elsevier)

__________________________________________________________________
FMS ADM Q E C A X _________________________________________________________________________ FMS-I High Excellent Very good Excellent Very good Very good FMS-II Very low Very good Good Very good Very good Very good FMS-III Medium Good Good Very good Excellent Good FMS-IV Low Fair Good Very good Very good Good _________________________________________________________________________ ADM: annual depreciation and maintenance costs Q: quality of results E: ease of use C: competitiveness A: adaptability X: expandability

10.2.2.1 Application of GTMA In the present work, the attributes considered are the same as those of Kulak and Kahraman (2005), and these are: annual depreciation and maintenance costs (ADM), quality of results (Q), ease of use (E), competitiveness (C), adaptability (A), and expandability (X). The linguistic terms given in Table 10.4 are converted into appropriate fuzzy scores (using Table 4.3). Table 10.5 gives the fuzzy scores, and these scores are to be normalized. ADM is a non-beneficial attribute, and lower values are desirable. The remaining attributes are beneficial, and higher values are desirable. The fuzzy scores are normalized, as explained in Section 2.4, and are given in Table 10.6 in the respective columns.
Table 10.5. Fuzzy scores of the attributes of example 10.2.2

__________________________________________________________
FMS ADM Q E C A X ________________________________________________________________ FMS-I 0.665 0.955 0.865 0.955 0.865 0.865 FMS-II 0.255 0.865 0.745 0.865 0.865 0.865 FMS-III 0.5 0.745 0.745 0.865 0.955 0.745 FMS-IV 0.335 0.5 0.745 0.865 0.865 0.745 ________________________________________________________________

Table 10.6. Normalized values of the attributes of example 10.2.2

_________________________________________________
FMS ADM Q E C A X ______________________________________________________ FMS-I 0.3835 1 1 1 0.9058 1 FMS-II 1 0.9058 0.8613 0.9058 0.9058 1 FMS-III 0.51 0.7801 0.8613 0.9058 1 0.8613 FMS-IV 0.7612 0.5236 0.8613 0.9058 0.9058 0.8613 ______________________________________________________

Relative importance of attributes (aij) is also assigned values, as explained in Section 2.4. Let the decision maker (i.e., user organization) select the following assignments:

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ADM Q E C A X

ADM 0.335 0.255 0.335 0.255 0.255

Q 0.665 0.335 0.5 0.335 0.335

E 0.745 0.665 0.665 0.5 0.5

C 0.665 0.5 0.5 0.335 0.335

A 0.745 0.665 0.5 0.665 0.5

X 0.745 0.665 0.5 0.665 0.5 -

The assigned values are for demonstration purposes only. Following the procedure of GTMA, the flexible manufacturing system selection index (FMS-SI) is calculated using the values of Ai and aij for each alternative flexible manufacturing system. The FMS-SI values of different flexible manufacturing systems are given below in descending order: FMS-II 22.5201 FMS-I 19.2912 FMS-III 17.3958 FMS-IV 17.0109 From the above values of FMS-SI, it is understood that the flexible manufacturing system designated as FMS-II is the right choice under the given conditions. This result matches with that suggested by Kulak and Kahraman (2005). In fact, FMS-I has taken the second position mainly because of its very low normalized fuzzy score for its ADM attribute. Otherwise, it would have become the first choice. In their work, Kulak and Kahraman (2005) had eliminated FMS-I after performing all calculations, reasoning that the value of ADM for this alternative was beyond the acceptable limit. However, this discarding of FMS-I could have been done at the initial short-listing stage itself, as suggested in step 1 of the GTMA methodology presented in Section 2.6. This could be the case for FMS-IV, too. 10.2.2.2 AHP and its Versions The AHP method may use the same weights as those selected for the SAW method. In that case, the ranking of the materials will be same. However, if the decision maker decides to use the AHP method, rather than SAW method and the weights used in it, then he or she has to make pair-wise comparisons of the attributes to determine the weights (wj) of the attributes. Let the decision maker prepare the following pair-wise comparison matrix: ADM 1 1/3 1/5 1/3 1/5 1/5 Q 3 1 1/3 1 1/3 1/3 E 5 3 1 3 1 1 C 3 1 1/3 1 1/3 1/3 A 5 3 1 3 1 1 X 5 3 1 3 1 1

ADM Q E C A X

The assigned values are for demonstration purposes only. The normalized weight of each attribute is calculated following the procedure presented in step 4 of

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Section 3.2.3, and these are: WADM = 0.4188, WQ = 0.1873, WE = 0.0688, WC = 0.1873, WA = 0.0688, and WX = 0.0688. The value of max is 6.0578 and CR = 0.00933, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. The value of FMS selection index is now calculated using the above weights and the normalized data of the attributes given in Table 10.5. The alternative FMS configurations are arranged in descending order of the FMS selection index: FMS-II 0.9485 FMS-I 0.7351 FMS-IV 0.7673 FMS-III 0.7167 Thus, the revised AHP or ideal mode AHP method also suggest FMS-II as the first choice. For the same weights of importance of attributes, the SAW method also gives the same ranking as that given by AHP method. For the same weights of importance of attributes, multiplicative AHP leads to the following ranking order: FMS-II 0.9473 FMS-IV 0.7548 FMS-III 0.6924 FMS-I 0.6648 Thus, multiplicative AHP also suggests FMS-II as the first choice. WPM also suggests the same ranking as that given by the multiplicative AHP method. It may be observed that the above ranking is for the given preferences of the decision maker. The ranking depends upon the judgements of relative importance of attributes made by the decision maker. 10.2.2.3 TOPSIS & Modified TOPSIS Methods Application of the TOPSIS and modified TOPSIS methods also suggests FMS-II as the first choice. 10.2.2.4 Compromise Ranking Method (VIKOR) Step 1: The objective is to evaluate the four flexible manufacturing systems, and the attributes are: annual depreciation and maintenance costs (ADM), quality of results (Q), ease of use (E), competitiveness (C), adaptability (A), and expandability (X). ADM is a non-beneficial attribute, and lower values are desirable. The remaining attributes are beneficial, and higher values are desirable. Table 10.4 gives the fuzzy scores. The best, i.e., (mij)max, and the worst, i.e., (mij)min, values of all attributes are also determined. Step 2: The values of Ei and Fi are calculated using Equations 3.26 and 3.27, and are given below. The same weights used in the AHP method are considered, and these are: WADM = 0.4188, WQ = 0.1873, WE = 0.0688, WC = 0.1873, WA = 0.0688, and WX = 0.0688. E1 = 0.42 + 0 + 0 + 0 + 0.07 + 0 = 0.49 E2 = 0 + 0.0376 + 0.07 + 0.19 + 0.07 + 0 = 0.3676 E3 = 0.251 + 0.0877 + 0.07 + 0.19 + 0 + 0.07 = 0.6687

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E4 = 0.0819 + 0.19 + 0.07 + 0.19 + 0.07 + 0.07 = 0.6719 Ei-min = 0.3676 Ei-max = 0.6719 R1 = 0.42 R2 = 0.19 R3 = 0.251 R4 = 0.19 Fi-max = 0.42 Fi-min = 0.19 Step 3: The values of Pi are calculated using Equation 3.28, and for v = 0.5. P1 = 0.7011 P2 = 0 P3 = 0.6274 P4 = 0.5 Step 4: The alternatives are arranged in ascending order, according to the values of Pi. Similarly, the alternatives are arranged according to the values of Ei and Fi separately. Thus, three ranking lists are obtained. The best alternative, ranked by Pi, is the one with the minimum value of Pi. P2 = 0 E2 = 0.3676 F2 = 0.19 P4 = 0.5 E1 = 0.49 F4 = 0.19 E3 = 0.6687 F3 = 0.251 P3 = 0.6274 P1 = 0.7011 E4 = 0.6719 F1 = 0.42 Step 5: For the given attribute weights, FMS-II is suggested as the compromise solution, as it satisfies both conditions given in Section 3.2.7.

References
Albayrakoglu M (1996) Justification of new manufacturing technology: a strategic approach using the analytical hierarchy process. Production and Inventory Management Journal 37:71–77 Bayazit O (2005) Use of AHP in decision-making for flexible manufacturing systems. Journal of Manufacturing Technology Management 16:808–819 Chan FTS, Jiang B, Tang NKH (2000) The development of intelligent decision support tools to aid the design of flexible manufacturing systems. International Journal of Production Economics 65:73–84 Dhavale DG (1990) A manufacturing cost model for computer-integrated manufacturing systems. International Journal of Operations and Production Management 10:5–18. Elango B, Meinhart WA (1994) Selecting a flexible manufacturing system - A strategic approach. Long Range Planning 27:118–126 Gerwin D, Kolodny H (1992) Management of advanced manufacturing technology: strategy, organization, and innovation. Wiley, New York Karsak EE (2002) Distance-based fuzzy MCDM approach for evaluating flexible manufacturing system alternatives. International Journal of Production Research 40:3167–3181 Karsak EE, Kuzgunkaya O (2002) A fuzzy multiple objective programming approach for the selection of a flexible manufacturing system. International Journal of Production Economics 79:101–111 Karsak EE, Tolga E (2001) Fuzzy multi-criteria decision-making procedure for evaluating advanced manufacturing system investments. International Journal of Production Economics 69:49–64 Kochan D (1987) Flexible manufacturing and CAD/CAM-evaluation and selection of systems. Computers in Industry 8:201–207

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Kulak O, Kahraman C (2005) Multi-attribute comparison of advanced manufacturing systems using fuzzy vs. crisp axiomatic design approach. International Journal of Production Economics 95:415–424 Kuula M (1993) A risk management model for FMS selection decisions: A multiple-criteria decision-making approach. Computers in Industry 23:99–108 Laosirihongthong T, Paul H, Speece MW (2003) Evaluation of new manufacturing technology implementation: an empirical study in the Thai automotive industry. Technovation 23:321–331 Layek AM, Wolf C (1991) Evaluating flexibility of alternative FMS designs-A comparative measure. International Journal of Production Economics 23:3–10 Lloréns FJ, Molina LM, Verdú AJ (2005) Flexibility of manufacturing systems, strategic change and performance. International Journal of Production Economics 98:273–289 Mohanty RP, Venkataraman S (1996) Use of the analytic hierarchy process for selecting automated manufacturing systems. International Journal of Operations & Production Management 13:45–57 Myint S, Tabucanon MT (1994) A multiple-criteria approach to machine selection for flexible manufacturing systems source. International Journal of Production Economics 33:121–131 Perego A, Rangone A (1998) A reference framework for the application of MADM fuzzy techniques to selecting AMTS. International Journal of Production Research 36:437–458 Rao RV (2006) A decision-making framework model for evaluating flexible manufacturing systems using digraph and matrix methods. International Journal of Advanced Manufacturing Technology 30:1101–1110 Rao RV (2007) Evaluating flexible manufacturing systems using a combined multiple attribute decision-making method. International Journal of Production Research (In Press) Sarkis J (1997) Evaluating flexible manufacturing systems using data envelopment analysis. The Engineering Economist 43:25–46 Sarkis J, Talluri S (1999) A decision model for evaluation of flexible manufacturing systems in the presence of both cardinal and ordinal factors. International Journal of Production Research 37:2927–2938 Shang J, Sueyoshi T (1995) A unified framework for the selection of a flexible manufacturing system. European Journal of Operational Research 85:297–315 Sriram RS, Gupta YP (1991) Strategic cost measurement for flexible manufacturing systems. Long Range Planning 24:34–40 Suresh NC, Kaparthi S (1992) Flexible automation investments: a synthesis of two multi-objective modeling approaches. Computers & Industrial Engineering 22:257–272 Tabucanon MT, Batanov DN, Verma DK (1994) A decision support system for multicriteria machine selection for flexible manufacturing systems. Computers in Industry 25:131–143 Talluri S, Whiteside MM, Seipel SJ (2000) A nonparametric stochastic procedure for FMS evaluation. European Journal of Operational Research 124:529–538 Troxler JW (1990) Estimating the cost impact of flexible manufacturing. Journal of Cost Management 4:26–35

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Tseng MC (2004) Strategic choice of flexible manufacturing technologies. International Journal of Production Economics 91:201–298

Part 2
Applications of GTMA and Fuzzy MADM Methods in the Manufacturing Environment

11
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Machine Selection in a Flexible Manufacturing Cell

11.1 Introduction
Machine selection has been a very important issue for manufacturing companies due to the fact that improperly selected machines can negatively affect the overall performance of a manufacturing system. In addition, the outputs of a manufacturing system (i.e., the rate, quality and cost) depend mostly oan appropriate selection of machines and its implementation (Ayag and Ozdemir, 2006). On the other hand, the selection of a new machine is a time-consuming and difficult process requiring advanced knowledge and experience deeply. So, the process can be a difficult task for engineers and managers. For a proper and effective evaluation, the decision maker may need a large amount of data to be analyzed, and many attributes to be considered. The decision maker should be an expert, or at least be very familiar with the specifications of machines to select the most suitable one. In this chapter, the machine selection problem in a flexible manufacturing cell (FMC) is considered to describe the systematical methods offering the best solution. In this chapter, the word ‘machine’ in a flexible manufacturing cell may be understood as a group of machines required to form the cell. Flexible manufacturing cells have been used as a tool to implement flexible manufacturing processes to increase the competitiveness of manufacturing systems. Flexible manufacturing cells represent a class of highly automated systems. The increased importance of these highly automated manufacturing systems to the survival of modern industries has resulted in growing research efforts that address the many issues inherent in flexible manufacturing. One of the key issues is the problem of machine selection in a flexible manufacturing cell, which involves a number of attributes, e.g., purchasing cost, machine type, number of machines in a group, floor space requirement, time needed for production, etc. To help address this issue, various mathematical and systems modeling approaches have been proposed to date. Sarkis (1997) used the data envelopment analysis (DEA) method for evaluating flexible manufacturing systems. However, DEA requires more computation, and if the number of factors that the decision maker wishes to consider is very large, and the number of alternatives small, then DEA may be a

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poor discriminator of good and poor performers. Again, DEA may be at a disadvantage in terms of the method’s rationale if the decision maker is unfamiliar with linear programming concepts. Talluri et al. (2000) proposed a framework based on the combined application of DEA and nonparametric statistical procedures, for the selection of flexible manufacturing systems. Wang et al. (2000) presented a real case of machine selection in a flexible manufacturing cell using a fuzzy multiple attribute decision-making method. However, the method was cumbersome in terms of the representation of weights of relative importance of the factors, fuzzy distributions, rating and ranking models, computation time, etc. Malek and Resare (2000) presented an algorithm-based decision support system for the concerted selection of equipment in machining/assembly cells. Karsak and Tolga (2001) proposed a fuzzy decision algorithm to select the most suitable advanced manufacturing system alternative. Both an economic evaluation criterion and strategic criteria such as flexibility, quality improvement, were considered for selection. Karsak and Kuzgunkaya (2002) proposed a fuzzy multiple objective programming approach for the selection of a flexible manufacturing system. Karsak (2002) presented a distancebased fuzzy multiple criteria decision-making (MCDM) approach based on the concepts of ideal and anti-ideal solutions for the selection of a flexible manufacturing system from a set of mutually exclusive alternatives. Rai et al. (2002) proposed a fuzzy goal-programming model using a genetic algorithm for machine tool selection and operation allocation in FMS. Yurdakul (2004) proposed AHP as a strategic decision-making method for machine tool selection. Tseng (2004) proposed a game theoretical model for selection of flexible manufacturing technologies. Chtourou et al. (2005) developed an expert system for manufacturing systems machine selection. Chan and Swarnkar (2005) presented a fuzzy goal-programming approach to model the machine tool selection and operation allocation problem of a flexible manufacturing system. An ant colony optimization (ACO)-based approach was applied to optimize the model. Chan et al. (2005) presented a fuzzy goal-programming approach to model a machine tool selection and operation allocation problem; the model was optimized using an approach based on artificial immune systems (AIS). Djassemi (2005) examined the performance of cellular manufacturing systems in a variable demand and flexible work force environment using simulation modeling. Mishra et al. (2006) presented a fuzzy goal-programming model having multiple conflicting objectives and constraints pertaining to a machine tool selection and operation allocation problem, and a new random search optimization methodology termed quick converging simulated annealing (QCSA) was used. Ayag and Ozdemir (2006) proposed a fuzzy AHP method for evaluating machine tool alternatives. Even though precision-based methods such as expert systems, neural networks, goal programming methods, fuzzy algorithms, genetic algorithms, simulated annealing, etc. have been proposed in the past to address the issue of selection of flexible manufacturing technologies, these methods are knowledgeintensive, complicated, require a high level of computation, and may go beyond the capabilities of the real decision maker (i.e., user organization). Also, most research work has concentrated on flexible manufacturing systems (FMS), and only a few

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authors have considered the problem of machine selection in a flexible manufacturing cell (FMC), once the alternative machines are developed. Thus, there is a need for a simple, systematic and logical method or mathematical tool to guide user organizations in taking a proper decision involving a number of machine selection attributes and their interrelations. This is considered in this chapter using the GTMA and other fuzzy MADM methods.

11.2 Example
Wang et al. (2000) presented a real case of a machine group selection in a flexible manufacturing cell including two CNC milling machine groups, a CNC lathe, and a robot for material handling. The constraints were described as explained below: Constraint 1: The total purchasing cost should not exceed 600,000 dollars Constraint 2: for CNC milling machine Vertical/horizontal: horizontal Spindle speed : 4,500 rpm X/Y/Z axis travel : 630/630/500 Feed rate : 5,000 mm/min Tool capacity : 40 Maximum tool diameter : 130 mm Constraint 3: for CNC lathe Maximum swing : 520 mm Maximum turning diameter : 350 mm Maximum turning length : 500 mm Hole through spindle : 70 mm Chuck size : 8” Spindle speed : 4,500 rpm Feed rate : 4,500 mm/min Constraint 4: for robot Configuration : arm-like Max. load capacity at wrist : 60 kg Allowable load moment of wrist : 36 kg-m Horizontal reach : 150 cm Repeatability : 1.0 Drive method : Electrical Furthermore, in the allowance for the operating procedure, the two milling machines can be replaced with a multifunctional machining center. After incorporating the above constraints into the total purchasing cost, and into the specifications of the milling machine, lathe machine, and robot, suitable machine groups of FMC were composed into 10 possible alternatives. Table 11.1 presents these 10 short-listed possible alternatives.

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Table 11.1. Objective data of attributes of the example considered (Wang et al., 2000; with permission from Taylor & Francis Ltd., http:www.tandf.co.uk/journals) __________________________________________________________________________ Alternative Total purchasing Total floor MN Productivity* cost ($) space (m2) (mm/min) __________________________________________________________________________ 1 581,818 54.49 3 5,500 2 595,454 49.73 3 4,500 3 586,060 51.24 3 5,000 4 522,727 45.71 3 5,800 5 561,818 52.66 3 5,200 6 543,030 74.46 4 5,600 7 522,727 75.42 4 5,800 8 486,970 62.62 4 5,600 9 509,394 65.87 4 6,400 10 513,333 70.67 4 6,000 __________________________________________________________________________ MN: Total number of machines in a machine group of the flexible manufacturing cell *Productivity (mm/min): the value corresponds to the machine with the slowest feed rate in the machine group

Now, application of the GTMA and other fuzzy MADM methods is carried out as explained below. 11.2.1 Application of GTMA The machine selection attributes considered are the same as those of Wang et al. (2000), and these are total purchasing cost (PC), total floor space (FS), total machine number (MN) and productivity (P). The machines short-listed are also the same as those of Wang et al. (2000). The objective values of the machine selection attributes, which are given in Table 11.1, are to be normalized. Productivity (P) is a beneficial attribute and higher values are desirable. Values of these attributes are normalized, and given in Table 11.2 in the respective column. PC, FS, and MN are non-beneficial attributes, and lower values are desirable. The values of these attributes for different alternative machines are normalized, and given in Table 11.2 in the respective columns. Relative importance of attributes (aij) is assigned the values using Table 4.4. Let the decision maker (i.e., user organization) select the following assignments: PC --0.335 0.255 0.410 FS 0.665 --0.410 0.590 MN 0.745 0.590 --0.665 P 0.590 0.410 0.335 ---

PC FS MN P

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Table 11.2. Normalized data of the machine selection attributes of the example considered _________________________________________________________________ Alternative PC FS MN P _________________________________________________________________ 1 0.854 0.839 1.000 0.859 2 0.835 0.919 1.000 0.703 3 0.848 0.892 1.000 0.781 4 0.951 1.000 1.000 0.906 5 0.885 0.868 1.000 0.812 6 0.915 0.614 0.750 0.875 7 0.951 0.606 0.750 0.906 8 1.000 0.730 0.750 0.875 9 0.976 0.694 0.750 1.000 10 0.968 0.647 0.750 0.938 _________________________________________________________________

The machine selection attributes digraph, machine selection attributes matrix of the digraph, and machine selection function for the matrix can be prepared. The value of machine selection index is calculated using the values of Ai and aij for each alternative machine, and these are given below in descending order: Alternative 4: 3.488808 Alternative 5: 3.002258 Alternative 1: 2.981451 Alternative 3: 2.930671 Alternative 2: 2.825410 Alternative 9: 2.755053 Alternative 8: 2.679458 Alternative 10: 2.597028 Alternative 7: 2.478609 Alternative 6: 2.411448 From the above values of the machine selection index, alternative 4 is the best choice among the alternatives considered for the flexible manufacturing cell under the given conditions. The ranking of machines based on the proposed methodology is 4-5-1-3-2-9-8-10-7-6; the ranking presented by Wang et al. (2000) was 4-5-3-12-8-9-10-7-6. The above results suggest the selection of alternative 4 for the FMC as the first right choice, alternative 5 as the second right choice, and alternative 6 as the last choice. These results are consistent with those presented by Wang et al. (2000). However, the ranking of certain alternatives obtained by using the proposed procedure is different from that proposed by Wang et al. (2000). For example, the third choice is alternative 1 as per the procedure proposed here, whereas it was alternative 3 in Wang et al. (2000). A closer look at the objective data of the four attributes PC, FS, MN, and P of these two alternatives reveals that there are significant differences between the two alternatives 1 and 3 in the case of PC ($581,818 vs. $586,060) and P (5,500 mm/min vs. 5,000 mm/min), that the difference is not high in the case of FS (54.49 m2 vs. 51.24 m2) and that there is no difference in the case of MN. Alternative 1 is best from the PC and P points of view, and alternative 3 is better from the FS point of view, and both alternatives are equal from the MN point of view. Thus, keeping in mind the relative importance of

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the attributes, proposing alternative 1 as the third choice based on the method proposed here seems to be more meaningful, compared to alternative 3 as proposed by Wang et al. (2000). Similarly the differences in the ranking of alternatives between the proposed procedure and the procedure suggested by Wang et al. (2000) can be explained. However, it may be added here that the weights of relative importance used by Wang et al. (2000) were different from those used in the present work. Further, it may be mentioned that the ranking depends upon the judgements of relative importance made by the decision maker. The fuzzy method proposed by Wang et al. (2000) is cumbersome in terms of the representation of weights of relative importance, fuzzy distributions, rating and ranking models, computation time, etc. Further, the authors had converted the available objective values of the attributes, after normalization, into fuzzy values, which violates the basic rule of fuzzy logic, i.e., the available objective values need not be fuzzified. Comparatively, the proposed GTMA provides a simple, straightforward and logical procedure for the machine selection problem in a flexible manufacturing cell. Following graph theory and the matrix approach, the coefficients of similarity/dissimilarity can also be calculated for different machines using Equations 2.15 and 2.16. It may be noted that GTMA offers a general methodology, and is applicable to any type of machine selection problem involving any number of machine selection attributes. 11.2.2 SAW Method For start, the attributes are ranked in order of importance and 10 points are assigned to the least important attribute MN. The attribute FS is given 15 points to reflect its relative importance. P and PC are given 25 and 30 points, respectively. Thus, the weights of PC, FS, MN, and P are calculated as 0.375, 0.1875, 0.125, and 0.3125 respectively. Using these weights, and the normalized data of the attributes for different machines, the machine selection index values are calculated, and are arranged in descending order of the index. Alternative 4: 0.9523 Alternative 9: 0.9024 Alternative 8: 0.8791 Alternative 5: 0.8734 Alternative 10: 0.8712 Alternative 1: 0.8710 Alternative 3: 0.8543 Alternative 7: 0.8471 Alternative 2: 0.8301 Alternative 6: 0.8254 From the above values of the machine selection index, it is clear that the alternative machine, designated as 4 is the best choice among the machines considered.

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11.2.3 WPM Using the same weights of the attributes as those selected for the SAW method, the following ranking of machines is obtained: Alternative 4: 0.9515 Alternative 9: 0.8927 Alternative 5: 0.8716 Alternative 1: 0.8697 Alternative 10: 0.8609 Alternative 3: 0.8517 Alternative 7: 0.8356 Alternative 8: 0.8266 Alternative 2: 0.8240 Alternative 6: 0.8167 This method also suggests alternative 4 as the first choice and alternative 9 as the second choice. 11.2.4 AHP and its Versions If the weights selected for the SAW method are used also in this method, then the ranking of machines obtained by using the relative as well as ideal mode AHP will be same. The multiplicative AHP method yields the same ranking as that given by WPM. However, let the decision maker prepare the following matrix: PC 1 1/3 1/4 1/2 FS 3 1 1/2 2 MN 4 2 1 3 P 2 1/2 1/3 1

PC FS MN P

The normalized weights of each attribute are calculated following the procedure presented in Section 3.2.3, and these are: WPC = 0.467, WFS = 0.16, WMN = 0.095, and WP = 0.278. The value of the machine selection index is now calculated using the above weights, and the normalized data of the attributes given in Table 11.2. The alternative machines are arranged in descending order of the machine selection index. Alternative 4: 0.9509 Alternative 9: 0.9161 Alternative 8: 0.8983 Alternative 10: 0.8876 Alternative 5: 0.8729 Alternative 1: 0.8669 Alternative 7: 0.8642 Alternative 3: 0.8508 Alternative 6: 0.8400 Alternative 2: 0.8274

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From the above values of the machine selection index, it is clear that the machine, designated as 4 is the best choice among the alternatives considered. It may be observed that the above ranking is for the given preferences of the decision maker. 11.2.5 TOPSIS Method The quantitative values of the machine selection attributes, which are given in Table 11.1, are normalized as explained in Section 3.2.6. Relative importance of attributes (aij) is assigned using the AHP method as explained in Section 11.2.4. After performing the calculations, the alternative machines are arranged in descending order of their machine selection index. This can be arranged as 4-9-8-10-7-5-1-6-3-2. 11.2.6 Modified TOPSIS Method Following the procedure of the modified TOPSIS method and using the same weights as those of the TOPSIS method, the following ranking of alternative machines is obtained: Alternative 4: 0.7842 Alternative 9: 0.5755 Alternative 5: 0.5526 Alternative 1: 0.5475 Alternative 8: 0.5415 Alternative 3: 0.5038 Alternative 10: 0.4806 Alternative 2: 0.4557 Alternative 7: 0.4045 Alternative 6: 0.3471 It can be observed that all the above decision-making methods propose machine designated as 4 as the first right choice. The example problem considered in this chapter is related to the selection of a group of machines required for a flexible manufacturing cell. However, the proposed decision-making methods are quite general, and can be applied also for the selection of a single machine tool for a given industrial application. For example, if a CNC machining center is required to be purchased by a firm, and a finite number of alternative CNC machining center configurations are available with objective as well as subjective information of the attributes, then the decisionmaking methods proposed in this chapter can be useful to the firm. Ayag and Ozdemir (2006) considered the problem of selection of a CNC vertical turning center for general use by a company. Nineteen machine selection attributes were considered, and these were: productivity (spindle speed, power, cutting feed, traverse speed), flexibility (number of tools, rotary table), space (machine dimensions, adaptability, CNC type, taper number); precision (repeatability, thermal deformation), reliability (bearing failure rate, reliability of drive system, safety and environment, mist collector, safety door, fire extinguisher, training), and maintenance and service (repair service, regular

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maintenance). Three machine alternatives (Maho, Hass, and Seiki) were evaluated by Ayag and Ozdemir (2006) using the fuzzy AHP method. However, the fuzzy version of AHP proposed by Ayag and Ozdemir (2006) is a complicated one. Once the objective and/or subjective data of the above 19 attributes are available, then the decision-making methods proposed in this book can be used for machine selection. The pair-wise comparison of the 19 attributes can also be made easily. It may be worth mentioning here that fuzzy set theory has serious difficulties in producing valid answers in decision-making based on fuzzifying judgements. No theorems are available dealing with its workability when applied indiscriminately as a number-crunching approach to numerical measurements that represent judgements. When numerical representation of judgements is allowed to vary in choice over the values of a fundamental scale, as in the analytic hierarchy process, these judgements are themselves already fuzzy. To make these even fuzzier can decrease the validity of the outcome, when the actual outcome is known. Also, improving the consistency of a judgement matrix does not necessarily increase the validity of the outcome. Validity is the goal in decision making, not consistency, which can be successively improved by manipulating the judgements as the answer becomes even farther removed from reality. Ayag and Ozdemir (2006) had not considered this fact in their work. Making fuzzy judgements fuzzier does not lead to a better outcome, and indeed often leads to a worse one. That is why this book proposes a logical method in Chapter 4 to take care of the above points, while assigning objective values to the subjective data of the attributes as well as deciding the relative importance of attributes.

References
Ayag Z, Ozdemir RG (2006) A fuzzy AHP approach to evaluating machine tool alternatives. Journal of Intelligent Manufacturing 17:179–190 Chan FTS, Swarnkar R (2005) Ant colony optimization approach to a fuzzy goal programming model for a machine tool selection and operation allocation problem in an FMS. Robotics & Computer Integrated Manufacturing doi:10.1016/j.rcim.2005.08.01 Chan FTS, Swarnkar R, Tiwari MK (2005) A fuzzy goal-programming model with an artificial immune system (AIS) approach for a machine tool selection and operation allocation problem in a flexible manufacturing system. International Journal of Production Research 43:4147–4163 Chtourou H, Masmoudi W, Maalej A (2005) An expert system for manufacturing systems machine group selection. Expert Systems with Applications 28:461– 467 Djassemi M (2005) A simulation analysis of factors influencing the flexibility of cellular manufacturing. International Journal of Production Research 43:2101– 2111 Karsak EE (2002) Distance-based fuzzy MCDM approach for evaluating flexible manufacturing system alternatives. International Journal of Production Research 40:3167–3181

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Karsak EE, Kuzgunkaya O (2002) A fuzzy multiple objective programming approach for the selection of a flexible manufacturing system. International Journal of Production Economics 79:101–111 Karsak EE, Tolga E (2001) Fuzzy multi-criteria decision-making procedure for evaluating advanced manufacturing system investments. International Journal of Production Economics 69:49–64 Malek LA, Resare LJ (2000) Algorithm based decision support system for the concerted selection of equipment in machining/assembly cells. International Journal of Production Research 38:323–339 Mishra A, Prakash N, Tiwari MK, Lashkari RS (2006) A fuzzy goal-programming model of machine-tool selection and operation allocation problem in FMS: a quick converging simulated annealing-based approach. International Journal of Production Research 44:43–76 Rai R, Kameshwaran S, Tiwari MK (2002) Machine-tool selection and operation allocation in FMS: solving a fuzzy goal-programming model using a genetic algorithm. International Journal of Production Research 40:641–665 Sarkis J (1997) Evaluating flexible manufacturing systems using data envelopment analysis. The Engineering Economist 43:25–46 Talluri S, Whiteside MM, Seipel SJ (2000) A nonparametric stochastic procedure for FMS evaluation. European Journal of Operational Research 124:529–538 Tseng MC (2004) Strategic choice of flexible manufacturing technologies. International Journal of Production Economics 91:223–227 Wang T, Shaw CF, Chen YL (2000) Machine group selection in flexible manufacturing cell: a fuzzy multiple attribute decision-making approach. International Journal of Production Research 38:2079–2097 Yurdakul M (2004) AHP as a strategic decision-making tool to justify machine tool selection. Journal of Materials Processing Technology 146:365–376

12
__________________________________________________________________

Failure Cause Analysis of Machine Tools

12.1 Introduction
Machine tool reliability and maintainability significantly affect the three elements of competitiveness: quality, cost, and production time. Well-maintained machines produce tolerances better, help reduce scrap and reworking, and raise the consistency and quality of the part. Further, such machine tools increase uptime and yield good parts, thereby reducing total production cost. Machine tools form a complex system consisting of various subsystems/components, and failure of a machine tool may occur due to failure(s) in any of the subsystems/components. For example, a CNC machine tool will invariably incorporate some, if not all, of the following subsystems: Electronic subsystems: microprocessor- or mini-computer-based controllers, input/output devices (displays, keyboards, disk and tape drives, data ports), memory components, analog systems (A/D, D/A converters and power amplifiers). Electrical subsystems: motors, contactors, relays, limit switches, servofeedback components, etc. Mechanical subsystems: gear boxes, slides and slide ways, drives, spindles, work holding devices, tool magazines and changers, swarf controllers, pallet systems, etc. Hydraulic subsystems: reservoirs, filters, pumps, valves, pressure relief valves, actuators, piston-cylinder arrangement, etc. Lubrication subsystems Coolant subsystems. Failure of a machine tool may occur due to failure(s) in any of the elements of the subsystems. The failure may be attributed to specific failure causes. A failure cause is defined as a reason that makes the machine tool unable to perform its intended function. This may be attributed to failure events contributed by its subsystems, assemblies, or components, including the cutting process and the cutting conditions. In the present work, machine tool failures are examined by analyzing the contributing events for their failure cause.

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There are numerous failure-causing elements in a machine tool. Some important common failure causes of a machine tool are given below: Faulty components, wear between mating parts, fatigue of the components, casting and welding defects in the machine tool structure, thermal stresses, high cutting temperatures, excessive cutting forces, low rigidity, vibrations, noise, electrica1 and electronic troubles, geometrical inaccuracy, low hydraulic and pneumatic pressure (for clamping devices, rotating devices, and feed drives), failure of bearings, contamination of slideways (e.g., due to swarf), loss of lubrication (slides, racks, ball-screw bearings, gears, and chains), malfunctions of valves, filter problems, cooling problems, pump cavitation, imbalance and disturbance in rives, chip conveying problems, clamping and indexing problems, tensioning problems in belts and chains, contactor troubles, motion control troubles, encoder problems, software troubles, servo adjustments, main process-related mechanisms, feed process-related mechanisms, auxiliary mechanisms, materials transportation system, environmental conditions, incorrect cutting conditions, nature of the machining process, incompatible cutting fluids, operator errors leading to poor operation, poor maintenance, etc. A failure manifests itself as a deviation of the machine tool behavior from its specified behavior. Martin (1994) distinguished between two different types of machine tool failures. The soft or gradual failure develops gradually with time, and this is characteristic of many mechanical and hydraulic elements of the machine tool where wear takes place, causing a gradual degradation of the operation of the element. The hard or catastrophic failure takes place instantaneously, and the element is either on or off, this is characteristic of many electrical circuit elements, but does occur also in mechanical elements, e.g., brittle fracture. Interest in machine tool failure data was shown by an early study of machine tool reliability undertaken by the Machine Tool Industry Research Associates (Stewart, 1977) and reported that the average downtime due to breakdowns was of the order of 7.6%, and the failure rate was 1-2 breakdowns per NC machine per month. A study of 35 CNC machines (1981), based upon service engineers’ records during one year warranty, quoted “an average availability of around 83%”. Kilmartin and Hannan (1981) invoked the poor diagnostics of electronics in explaining much of the downtime, but over the following years evidence supporting the development of diagnostics in the domain was reported by Kegg (1984). Continued interest in the reliability of machine tools gave rise to an initiative by the National Center for the System Reliability (NCSR) in the UK. This brought together a consortium of machine tool users and manufacturers, NCSR providing staff to collect the appropriate data. A report of NCSR (1988) provided data on the reliability of the CNC machine centers. The data were confidential to consortium members, but in general did highlight the more significant failure areas. A machine tool is a complex system, and it is not possible to contemplate the condition monitoring of all parameters that describe the behavior of a machine tool. Consequently, a limited choice has to be made, and this should be based upon the information available on failures, their frequency, and the resulting downtime. Johansson (1981) proposed parameters for monitoring CNC lathes, such as: feed drive current, mains voltage, hydraulic oil pressure, acceleration time for spindle

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motor, interval for central lubrication, tool change time, temperature of spindle bearings, temperature of control box, temperature of spindle motor, temperature of hydraulic oil, oil filter degree of purity, and number of movements of X and Y slides. Martin et al. (1990) applied the techniques of failure modes and effects analysis to analyze the catastrophic failures of machine tools. These are essentially logical decisions based upon system knowledge, and lend themselves to computerization and automatic decision making. Majstorovic and Milacic (1990) defined the basic architecture of expert systems for diagnosis and maintenance, and reviewed the current uses of expert systems. The authors reviewed 87 different expert systems; of 4.6% machine tool systems. Freyermuth (1991) described an expert system type analysis to define failures based on ‘fault-symptom trees’, which have similarities with fault trees. Angeli and Chatzinkikoraou (1985) developed an expert system to diagnose the faults in hydraulic systems. Marczewsky (1988) developed and implemented an expert system called 'Charley' to track machine tool conditions using vibration signatures from the machine tools. Puetz and Eichhorn (1987) proposed expert system shells for the failure diagnosis of CNC machine tools. The main techniques used for the diagnosis of soft or gradual failures are: pattern recognition techniques (using artificial neural networks and fuzzy logic), expert systems, and mathematical model-based detection techniques. Williams (1990) had described different methods of automatic recognition of failure patterns. Pattern recognition techniques generally rely upon the use of failure dictionarystored information upon the reaction of the system to certain failures. Marzi and Martin (1990) reported the design of a neural network that which analyzed the gradual failures represented by changes in the transient response at the outlet of the pump of a machine tool coolant system. Lee and Kramer (1993) proposed a methodology using neural networks to monitor machine tool behavior. A pattern discrimination model is used to measure the performance degradation quantitatively. Lee (1995) reviewed machine tool condition monitoring and fault diagnosis methods. Drake and Pan (1996) presented a method for diagnosing multiple failures and the levels of severity of individual faults in the flood coolant system of a CNC vertical milling machine tool. The method employed a neural network for pattern recognition with features extracted from the transient response of the coolant pressure on shut down. Ye and Zhao (1996) developed a highly integrated system, integrating neural networks with a procedural decision-making algorithm, to implement hypothesistest cycles in a manufacturing system diagnosis of tested failure events. Zeng and Wang (1991) described an experimental study to investigate the feasibility of employing fuzzy set theory in an integrated failure diagnostic system. The main monitored signal was assumed to be acceleration transformed into frequency spectra. Comparisons between the operating machine patterns and those in the failure dictionary were made to define the machine operating system by the use of the fuzzy fault assignment technique. Holloway and Krogh (1990) had proposed a behavioral model approach for failure detection and analysis in automated manufacturing systems. Their model provided the basis for on-line failure detection by generating expected system response signals that were compared with the actual

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sensor signals from the system. Failure analysis was accomplished by maintaining a current set of operational assumptions that identify the system components possibly causing deviations from the expected behavior. Isermann (1991) described mathematical model based techniques for the detection of gradual failures in machine tools. The diagnosis techniques were described based upon the measurement of the variation of parameters, concluding with a description of a knowledge-based diagnosis system. Martin (1994) discussed model-based failure detection techniques covering the fields of modeling, parameter estimation, state estimation, use of observers, and parity space approaches. Alexander et al. (1993) developed a model for the diagnosis of CIM equipment. Poltavets (1994) presented fault diagnostic parameters (temperature, movement accuracy, vibration, and acoustics) and suggested wide use of highly effective computer equipment, mathematical modeling, and intensive development of sophisticated system investigation methods. Rao (1997) reviewed key developments in the area of metal cutting machine tool design from a very practical perspective. Defining the drivers of machine tool design as higher productivity and higher accuracy, the author examined advances in design stemming from the needs of these two drivers. Kwon and Burdekin (1998) presented an adjustment technique for controller setting values in CNC machine tools by measurement of servo-induced feed drive errors. For measurement of the servo-induced errors, an experimental technique which incorporated two linear displacement sensors and a steel cube was developed, and servo feed drive errors were evaluated along a square corner test path. Based on evaluations of servo feed drive errors, different combinations of parameters in the machine control system and optimum setting parameters were found. Hu et al. (1999) proposed a systematic approach for the failure diagnosis of flexible manufacturing systems that integrates condition monitoring, failure diagnosis and maintenance planning. Two diagnostic models for PLC-controlled flexible manufacturing systems were presented. In another work, Hu et al. (2000) designed an intelligent integrated fault-diagnosis system with a modular, and reconfigurable structure. The implementation of the integrated diagnosis was presented in detail. The system could monitor conditions, and diagnose the major failures of a flexible manufacturing system, and give corresponding maintenance planning as well. Huang and Liao (2000) developed a maintenance schedule and fault diagnosis system that integrates an artificial neural network and an expert system for a wire EDM setup. The faults considered were: wire breaking and unsatisfactory accuracy. Suggestions were made to eliminate/reduce these faults. Rao and Gandhi (2002) presented digraph and matrix methods for failure cause analysis of machine tools. Das et al. (2007) discussed reliability aspects of the design and analysis of cellular manufacturing systems. Luis et al. (2006) presented details of a sensor-less tool failure monitoring system for drilling machines. Most of the techniques or approaches described above have drawbacks. In the case of systems such as pattern recognition techniques (using neural networks, fuzzy logic), and expert systems, a great deal of research is necessary in order to apply these types of systems to machine tool failure diagnosis. Significant amounts of data and time are required to define the normal healthy behavior of a machine tool. For example, pattern recognition techniques generally rely upon the use of

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failure dictionary stored information on the reaction of the system to certain failures. Because of the complexity of a machine tool, it will be possible to deal only with a limited number of failures and therefore, the necessity to define the most important failures. If a decision can be made regarding the significant failures, there still remains the decision as to which parameter will be sensitive to the failure. In certain cases, the parameter is easily definable, and the more complex cases will need research in themselves. In the laboratory, it is necessary to stimulate faults for which neither the time nor the resources are available to run the machine tools until failures occur. Even if this is done, most automatic data acquisition systems (DASs) generate excessive amounts of data, and the problem lies in data storage and analysis. In the case of mathematical modeling techniques, measurements have to be made on healthy systems to define the mathematical model, and to store the healthy response. These measurements will probably be different for what are normally the same machine tool type, and thus a separate machine needs its own measurement; it is not possible to take a measure of one machine and assume that this will apply to another. As explained above, fault diagnosis and maintenance are knowledge-intensive, experimental tasks that may go beyond the capabilities of the practicing maintenance engineer. Moreover, ad hoc replacements further aggravate the problems at the operational stage, which not only culminates in loss of production and increase in machine downtime, but can also lead to human loss and injuries. This problem can be minimized to a large extent if failure cause analysis is considered. Its implementation at the design stage will lead to the design of failurefree reliable machine tool systems. It will also help in minimizing downtime, and avoiding ad hoc replacements. The structure of a machine tool is highly important to understand and model its failure. The structure may be physical or abstract. In the system's structure, the components of the system/subsystem, the properties relevant to the problem are identified and their characteristic interdependence and interactions determined. The importance of a system's structure has been emphasized by many researchers (Czichos, 1978, 1980; Yoshikawa, 1982; Kokowa and Shingai, 1982; Kokowa et al., 1983; Ishida et al., 1985; Sethi and Agrawal, 1993; Gandhi and Agrawal, 1994, 1996; Clark and Paasch, 1997). The subsystems/components of a machine tool are expected to perform appropriate function(s) to attain a desired output. The output of a given machine tool depends upon how well individual subsystems/components perform. The malfunctioning of a machine tool system is attributed to improper functional interaction between its components and subsystems. This means a function specifies intended behavior of an individual component or subsystem. Moreover, the structure of a machine tool system is important for understanding the connectivity of its components and subsystems. Therefore, both function and structure are key entities in failure consideration as a whole. However, to analyze the failure causes of machine tools, it is indispensable to consider the functional and structural interaction of the machine tool system especially at the design stage. This exercise, which aims to minimize the operational failures, can be implemented at the design stage, if appropriate procedures based on this approach are made available to the designer. Fault tree analysis (Fussell, 1975, 1976) has been

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extensively used in chemical and process industries for root cause analysis. However, this does not take into account the structure of the system explicitly. Hence there is a need for an appropriate procedure to analyze the failure causes of a machine tool. This aspect is considered in the present work using graph theory and the matrix approach. Graph theory is useful to represent the system structure and in conjunction with the matrix approach enables analysis of the problem in a more convenient way. Rao and Gandhi (2002) demonstrated this approach for machine tool failure cause analysis with the identification of failure contributing events and their interaction for a machine tool failure cause. Failure cause of a machine tool is analyzed considering the contributing events and their interactions, and is demonstrated in the following sections.

12.2 Identifying Contributing Events of a Failure Cause
The contributing events of a failure cause of a machine tool are identified by examining various aspects such as affected system structure, mating components, cutting process, cutting conditions, and the tool and work piece. To illustrate this, an example of vibrations of machine tools is considered and the events of this failure cause (i.e., vibrations) are considered by examining the following aspects: Machine tool: The machine tool structure deflects due to cutting forces and the weight of the moving subassemblies. The stiffness of the structure must be high with high damping characteristics to minimize the influence of dynamic loads. If this is not so, the frequency of vibration may coincide easily with the natural frequency of any mode of the machine tool, resulting in complete or partial destruction of the machine tool. Besides, vibration decreases the life of the machine tool. It is commonly experienced that, in any machine shop floor, if anywhere dynamic force through vibration is transmitted to the ground, then the machine shop floor will vibrate. This vibration may be transmitted to the machine tool through its foundation, and cause vibrations in the machine tool and damage the job surface. Incorrect machine tool leveling will also cause vibrations in the machine tool. The disturbances in the machine tool drives also lead to vibrations in the machine tool. These disturbances are generated due to many reasons. Some of the reasons are: Rotating unbalanced masses: The effect of rotating unbalanced masses becomes more prominent when rotating bodies, or parts, are supported on the top of slender parts. Faulty arrangement of drives: Faulty arrangement of drives also produces vibrations. If the driving gears have eccentricities, pitch errors, profiles errors, damaged portions, etc., then they will produce non-uniform rotation which may contribute to machine tool vibrations. In the case of belt drives, if the section of the belt used is non-uniform then the effective pulley radius will change periodically causing a periodic variation of belt

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tension. Belts that are too tight or too slack will also cause machine tool vibrations. Fault in the supporting bearings: If the bearings supporting the rotating members of the machine tool are faulty, the rotating members will not be fixed in position and will change position periodically depending on the nature of the fault. Moreover, if the frequency of the system is of the same order, then an appreciable vibration may be generated. Radial and axial play in the spindle may lead to vibrations. Reciprocating disturbances: The disturbance in the elements of machine tool executing rectilinear motion can also cause vibrations. This type of vibration may be due to reciprocating imbalance, or to stick-slip motion. Type of cutting and cutting conditions: Sometimes, when the cutting process itself is intermittent (e.g., milling), or periodically discontinuous (e.g., cutting with discontinuous chip formation), then cutting force fluctuates with a definite period. Due to this fluctuating or dynamic cutting force, which is transmitted to the machine tool via the cutting tool and the job, it is quite likely that a forced vibration will be generated due to the elastic nature of the system. If the frequency of force fluctuation falls in the range of natural frequency of the machine tool, then the vibrations will be severe. In addition, incorrect cutting conditions, e.g., cutting speed, feed, and depth of cut, cause vibrations. The machine tool can vibrate due to the cutting process itself under particular conditions. In these cases, the active force is not from an outside element, but is due to the cutting process itself. These types of vibrations are self-induced, and commonly known as machine tool chatter. A slight disturbance in the cutting process caused by varying chip thickness, varying rate of penetration of the tool into the job, or variation in the angular speed of the job may cause such vibration. Work piece: If any inhomogeneity is present in the work material, an impulsive force will be generated due to a sudden increment in the hardness of the work material. As an effect of this impulse, a free vibration is set up in the cutting tool, and also in the machine tool body. Not-so-rigid work piece holding and its balancing, and slenderness of the work material also lead to vibrations. Cutting tool: Tool overhanging contributes to machine tool vibrations. Proper setting is required. A wrong geometry of the tool, or blunt tool lead to vibrations. Vibrations decrease the cutting tool life. Built-up edge on the cutting tool, formed due to the wrong cutting conditions, has an effect on vibrations similar to that of inhomogeneities in the work material. If the machine tool system is not dynamically stable, then the effect is considerable. Sudden impact load on the cutting tool sets up vibrations in the cutting tool and also in the machine tool body. It may be added that the contributing events for other failure causes of a machine tool mentioned earlier can be identified in a similar way as that described above. The contributing events identified above are considered for modeling the machine tool failure cause using graph theory and the matrix approach, and this is discussed in the next section.

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12.3 Machine Tool Failure Causality Digraph (MTFCD) and its Matrix Representation
The machine tool failure causality digraph (MTFCD) models a failure cause of a machine tool system, subsystem, or component, considering the failure contributing events and their interaction in terms of cause-effect relationship (i.e., causality). A node Vi represents the i-th failure contributing event, and a directed edge eij from node i to node j represents the causality relation between i and j events. For example, if event i is the cause event, and j is the affected event, then a directed edge eij is drawn from node i to node j. If no causality relation exists between two events, then no edge is drawn between these nodes, i.e., eij = 0. Sometimes it is possible that two events may be cause and effect events to one another. In such a case, two directed edges, eij and eji, are drawn, i.e., one from node i to node j, and the other from node j to node i. If an event i is the cause and effect event to itself, then it shall be represented by a self-loop at that node. For a considered failure cause, all the contributing events are to be identified first, and also their causality relations. Therefore, every care needs to be taken in identifying all the failure contributing events for a failure cause. It is suggested that this exercise be carried out by a team consisting of designers, and operating and maintenance personnel. To develop the machine tool failure causality digraph, a machine tool failure cause, i.e., vibrations of the machine tool, is considered, and has been described in the previous section. However, for illustration six most important vibration contributing events are selected, and these events are listed below: 1. Machine tool leveling 2. Type of cutting and the cutting conditions 3. Inhomogeneities in the work material 4. Disturbance in machine tool drives 5. Cutting process 6. Tool setting and job holding These six events are represented in the machine tool failure causality digraph shown in Figure 12.1 by six nodes. The directed edges are drawn keeping in mind the discussion presented earlier in this section. For example, machine tool leveling affects the disturbance in machine tool drives. So, a directed edge is drawn from node 1 to node 4 in the digraph. Similarly, other directed edges are drawn and the digraph is developed as shown in Figure 12.1. It is likely that there may be more causality relations between these events (i.e., six events) and other events not shown (of other failure causes of machine tool), and these are represented as dashed directed edges. This is, however, for illustration only and is not considered further in the analysis.

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Figure 12.1. Machine tool failure causality digraph (from Rao and Gandhi 2002; reprinted with permission from Elsevier)

The machine tool failure causality digraph represents the graphical relationship among thee contributing events for a failure cause. If there are a large number of contributing events, then due to this large number of nodes and the directed edges, the digraph becomes complex. Visual appraisal also may not be easy. For instance, in the above example, if there were more than six contributing events, then obviously the related digraph would become complicated due to these events and their causality relations. So, to handle the machine tool failure causality digraph conveniently using a computer, a matrix approach is adapted. From this matrix form, an expression that becomes characteristic of the machine tool failure cause can be developed. This matrix is named the ‘machine tool failure severity and causality matrix’. The machine tool failure severity and causality matrix for the failure cause ‘vibrations’ is written as matrix D.

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Events 1 2 D= 3 4 5 6

1 S1 0 0 0 0 0

2 0 S2 c32 c42 c52 c62

3 0 0 S3 0 0 0

4 c14 c24 c34 S4 c54 c64

5 0 c25 c35 c45 S5 c65

6 c16 0 0 c46 0 S6

The diagonal element Si represents a variable of severity of the i-th failure contributing event. Off-diagonal element cij represents the causality relation (of some degree) between the i-th and j-th events. It may be noted that this matrix considers both the severity of the failure contributing events and their causality relations for the considered machine tool failure cause ‘vibrations’. The permanent of the machine tool failure severity and causality matrix i.e., per (D) is named ‘machine tool failure causality function (MTFCF)’. For matrix D, MTFCF is written as: per (D) = S1 S2 S3 S4 S5 S6+ (c24 c42 S1 S3 S5 S6 + c25 c52 S1 S3 S4 S6 + c45 c54 S1 S2 S3 S6 + c46 c64 S1 S2 S3 S5 ) + [(c24 c45 c52 S1 S3 S6 + c 25 c54 c42 S1 S3 S6 ) + c24 c46 c62 S1 S3 S5 + c46 c65 c54 S1 S2 S3] + [((c25 c52 ) (c46 c64 ) S1 S3 ) + (c24 c46 c65 c52 S1 S3 + c25 c54 c46 c62 S1 S3)] (12.1) MTFCF helps to analyze the failure cause from combinatorial consideration. This is desirable to give proper physical meaning to the events and their causality relations. Moreover, the permanent function does not contain negative sign, and thus no information is lost. The reasons for adapting the permanent function, rather than characteristic and other such functions, are explained in Chapter 2. Equation 12.1, i.e., machine tool failure causality function, is the characteristic of the failure cause as it contains a number of terms that are its structure invariants. These are arranged in groupings. The first grouping represents the severity of six events (i.e., S1 S2 S3 S4 S5 S6). The second group is absent, as an event can not become cause and effect to itself. The third grouping contains four terms. Each term represents a 2-event causality loop (i.e., c24 c42, c25 c52, c45 c54, c46 c64), and the severity of four events (i.e., S1 S3 S5 S6, S1 S3 S4 S6, S1 S2 S3 S6, S1 S2 S3 S5). Similarly, the other terms of MTFCF can be explained. It may be noted that Equation 12.1 is characteristic for the considered failure cause of the machine tools, i.e., vibrations in this case.

12.4 General Machine Tool Failure Causality Function
The machine tool failure causality digraph (MTFCD) represents a machine tool failure cause, no matter how complicated it is. For a given machine tool failure cause, all the contributing events need to be identified first, and the causality relations of these identified events are to be determined for the failure cause. MTFCD is the key to the proposed machine tool failure causality analysis. The causality relations between the machine tool failure cause events must be thoroughly understood before assigning some value to these. If the causality

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relation between two failure cause events is wrongly understood as 0, then this 0 will cause many terms of the MTFCF to become 0, thereby leading to the loss of much information useful during the machine tool failure cause analysis. Hence it is desirable that one should interact with as many engineers as possible, preferably of different fields (design, operation, maintenance, etc.), to reproduce an exact machine tool failure cause representation. It must be emphasized that the process of constructing such a MTFCD would need the information and experience acquired to date, and if these aspects are taken care of in the digraph representation, this will substantially reduce the danger of failing to recognize the possible events and their causality relations. Keeping in mind these aspects, a general form of machine tool failure causality matrix is described in this section. In general, if there are M number of failure contributing events and the causality relations exist among all the failure contributing events, then the failure severity and causality matrix, P, for the considered MTFCD is written as Equation 12.2, which is similar to Equation 2.10. Events 1 2 P= 3 M 1 S1 c21 c31 cM1 2 c12 S2 c32 cM2 3 c13 c23 S3 cM3 M c1M c2M c3M SM

(12.2) The MTFCF for this matrix P contains factorial M (M!) number of terms. In sigma form, this is written as Equation 12.3, which is similar to Equation 2.11.
M M-1 M M

per (P) = i =1

Si + i=1 j=i+1

………
M=t+1

(cij cji )Sk Sl Sm Sn So …..St SM
... , M pus

M-2

M-1

M

M

+ i=1 j=i+1 k=j+1

.......... l=1 M=t+1

(cij cjk cki + cik ckj cji ) Sl Sm Sn So …..St SM k, … , M pus

M- 3

M

M-1

M

M

+[ i=1 j=i+1 k=i+1 l=i+2

………
M=t+1

(cij cji) (ckl clk ) Sm Sn So …..St SM k,l, … , M pus

M-3

M-1

M

M

M

+ i=1 j=i+1

……… (cijcjk ckl cli +cil clk ckj cji) Sm Sn So …..St SM] k=i+1 l=j+1 M=t+1 k,l, ... , M M-2 M-1 M M-1 M M pus

+[ i=1 j=i+1

……… (cijcjk cki+cik ckj cji)( clm cml)Sn So …..St SM k=j+1 l=1 m=l+1 M=t+1 k,l,m , ... , M pus

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M-4 M-1

M

M

M

M

+ i=1 .......... (cijcjkckl clm cmi+cim cmlclk ckj cji)Sn So…..StSM] j=i+1 k=i+1 l=i+1 m=j+1 M=t+1 k,l,m, ... , M M-3 M-1 M M M-1 M M pus

+ [(

……… (cijcjkcklcli+cilclk ckj cji)(cmn cnm)So…..St SM
M=t+1 k,l,m,n, ... , M pus

i=1 j=i+1 k=i+1 l=j+1 m=1 n=m+1

M-5 M-1 M M-2 M-1 M

M

+

….… (cijcjkcki+cikckjcji)(clmcmncnl+clncnmcml)So..St SM
M=t+1 k,l,m,n, ... , M pus

i=1 j=i+1 k=j+1 l=1 m=l+1 n=m+1

M-5 M

M- 3 M

M-1

M

M

+ i=1 j=i+1 k=i+1

......... (cij cji) (ckl clk ) (cmn cnm ) So …..St SM l=i+2 m=k+1 n=k+2 M=t+1 pus k,l,m,n, ... , M

M-5 M-1 M

M

M

M

M

+

….. (cijcjkcklclmcmncni+cincnmcmlclkckjcji)So…..St SM] k,l,m,n, ... , M pus

i=1 j=i+1 k=i+1 l=i+1 m=i+1 n=j+1 M=t+1

+ ----------

(12.3)

‘pus’ stands for ‘previously used subscripts’ i.e., in Equation 12.3, k, l, m, n, …, and M take those subscripts that are other than previously used subscripts. The MTFCF contains terms arranged in (M +1) groups and these groups represent the severity measures of failure contributing events and the causality relation loops. The first group represents the measures of M events. The second group is absent, as there is no self-loop in the digraph. The third group contains 2-event causality relation loops and measures of (M-2) events. Each term of the fourth group represents a set of a 3-event causality relation loop, or its pair, and measures of (M3) events. The fifth group contains two sub-groups. The terms of the first subgroup is a set of two 2-event causality relation loops and the measures of (M-4) events. Each term of the second sub-group is a set of a 4-event causality relation loop, or its pair, and the measures of (M-4) events. The sixth group contains two sub-groups. The terms of the first sub-group is a set of 3-event causality relation loop, or its pair, and a 2-event causality relation loop, and the measures of (M-5) events. Each term of the second sub-group is a set of a 5-event causality relation loop, or its pair, and the measures of (M-5) events. Similarly other terms of the equation are defined. Thus, the MTFCF fully characterizes the considered machine tool failure cause, as it contains all possible events and their causality relations.

12.5 Machine Tool Failure Cause Evaluation
It is desirable to evaluate the machine tool failure cause subjectively or objectively, and in terms of index/measure to ascertain the severity of the machine tool failure

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cause. The numerical value of the MTFCF is called the machine tool failure causality index (MTFCI). This index gives a measure of the severity of failure cause. To evaluate MTFCF, the values of Si and cij are required. It is preferable to have these values based on shop-floor data or experience of the shop-floor personnel. If such objective value is not available, then a ranked value judgement on a fuzzy conversion scale may be adapted (e.g., Tables 4.1 or 4.3). It is possible, for a failure cause, that some of the Si values may be subjective, and the others objective. It is desirable to normalize the objective value of Si on the same scale as the subjective value. The causality relation, i.e., cij, is also assigned on a scale. If the causality relation is strong between two events, then a value of 3 is assigned. If no causality relation exists between two events, then a value of 0 is assigned. This is suggested in Table 12.1.
Table 12.1. Quantification of causality relation between two events, cij __________________________________________________________________ Causality relation between two events Assigned value, cij __________________________________________________________________ None 0 Weak 1 Medium 2 Strong 3 __________________________________________________________________

However, if one wishes a fuzzy assignment for the causality relation also, this can be done by following appropriate fuzzy conversion scale suggested by Chen and Hwang (1992), and modifying it suitably. It may be mentioned that one can choose any scale for Si or cij. However, a lower value for these is desirable to obtain manageable values of the MTFCI. It is possible that plant data pertaining to Si and cij are not available. In such cases, these are assigned subjective values based on Tables 4.1 (or 4.3) and 12.1. With the help of Tables 4.1 (or 4.3) and 12.1 and Equation 12.3, the numerical value of the MTFCF i.e., MTFCI is calculated. This index gives a measure of the severity of failure cause. A higher value of MTFCI indicates that the considered failure cause is a serious one. A lower value of MTFCI indicates that the considered failure cause is not serious, and is therefore, desired. Using MTFCI, two failure causes of a machine tool can be compared. The failure cause having higher value of MTFCI needs to be considered and efforts should be made to reduce the value of the index by taking appropriate failure minimization steps. Thus, different failure causes of a machine tool can be analyzed and arranged in decreasing order of the machine tool failure causality indices. The failure analyst can take suitable actions for their prevention in order of their severity as understood from the values of MTFCI.

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12.6 Machine Tool Failure Cause Analysis
The machine tool failure causality function is a useful expression for the failure cause analysis of machine tools, as it represents the severity of the events and the causality relations. The analysis is carried out term by term. (i) The first term represents the severity of M failure contributing events, and is given as: / S1 / S2 / S3 / ………./SM / The slash represents a separation mark between the severity of two events. The analysis is to be carried out event-wise and turn by turn. A designer or practicing engineer needs to consider each and every event in detail. If the severity of an event is higher then more attention should be paid to this event, and to finding ways and means to minimize the severity of this event. For example, if the analysis is carried out for the failure cause ‘vibrations’ of a machine tool, the first term is S1 / S2 / S3 / S4 / S5 / S6 /. If the event 4 (i.e., disturbances in machine tool drives) has more severity then in-depth study may reveal that this can be attributed to: rotating unbalanced masses, faulty arrangement of drives, faults in the supporting bearings, damaged gears, worn out belts, spindle play, manufacturing faults in the drive elements, etc. By the application of appropriate techniques, the severity of this event can be reduced. On the same lines, the severity of other events is considered. (ii) When self-loops do not exist in the digraph, then this grouping will be absent. (iii) When self-loops are absent, each term of the third grouping represents a set of 2-event causality loops and the severity of (M-2) events. This is given as: / (cij cji ) / Sk / Sl /………./SM / The entity to be analyzed first is cij cji. This is a 2-event causality loop and represents the resultant causality relation between i and j. If the analysis indicates that this value is comparatively high, then in-depth study is needed to reduce this entity to a lower value. For the present failure cause ‘vibrations’ of a machine tool, the third grouping is: / c24 c42 / S1 / S3 / S5 / S6 / + ….. The first entity to be analyzed in the first term is c24 c42. This means that the effect of type of cutting and cutting conditions on disturbances in machine tool drives, and the effect of disturbances in machine tool drives on type of cutting and cutting conditions are to be studied. These two events are cause and effect to each other, and c24 c42 represents the resultant causality relation between these two events. Along with this resultant causality between the first two events, the severity of events 3, 5, and 6 is to be considered. Similarly, the other terms of the grouping can be analyzed. (iv) When self-loops are absent, the fourth grouping contains the terms, each is a set of a 3-event causality loop, or its pair, and the severity of (M-3) events. This is given as: / (cij cjk cki + cik ckj cji ) / Sl / Sm /………./SM / The first entity to be analyzed is the 3-event causality loop cij cjk cki, and its pair cik ckj cji. If analysis indicates the entity’s value comparatively higher, then

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efforts should be made to reduce its value. For the present failure cause ‘vibrations’ of a machine tool, the fourth grouping is: / (c24 c45 c52 + c25 c54 c42 ) / S1 / S3 / S6 / + …… The first entity in the first term to be analyzed is c24 c45 c52. This is the resultant causality relation between events 2, 4, and 5. This means that in the considered failure cause ‘vibrations’, the causality relations between the type of cutting and the cutting conditions and disturbance in machine tool drives, and between disturbance in machine tool drives and the cutting process, and between the cutting process and type of cutting and cutting conditions are to be studied in detail, and this is expected to minimize this entity. Along with the resultant causality relation among these events, the severity of events 1, 3 and 6 is to be considered. In the same manner, c25 c54 c42 is to be studied. Similarly, other entities of the other terms of this grouping can be critically analyzed. Ways and means to reduce the value of the entities can be suggested. Finally, this leads to the minimization of failure. Proceeding as described above, other groupings of the MTFCF can be assessed. The above procedure analyzes the failure causes of the machine tools by identifying the failure-contributing events and their causality relations. Each and every entity in different groupings are analyzed, along with how they are contributing to the machine tool failure cause. The analysis, when carried out as described above, helps to identify the areas where improvements can be made, and leads to minimization of failures in machine tools. For the considered failure cause, ‘vibrations’, of a machine tool, these may be in terms of proper machine leveling along with proper vibration isolation arrangements, improving the stiffness and the damping characteristics of the machine tool, balancing of the rotating and nonrotating drives, correct arrangement of the drives, proper tool setting and job holding procedures, selection of right tool and work materials, right cutting conditions, maintaining proper belt tension, removing the spindle play, choosing right quality bearings, gears, etc. Thus, it would be possible to minimize vibrations, a common failure cause in machine tools. The above procedure is applicable not only at the design stage of the machine tools but also at the operating stage. The designer or the practicing engineer needs to list the likely or observed failure causes in order of their probability of occurrence. Then the failure cause with the highest probability is attempted first in the above-described procedure. Similarly, other failure causes of the machine tool are analyzed. Comparison of two failure causes can be done by calculating the value of coefficient of similarity/dissimilarity based on the numerical value of the terms of the MTFCF. The procedure is similar to that described in Section 2.5.2.

12.7 Methodology
The methodology for the proposed failure cause analysis of machine tools using graph theory and the matrix approach is given below:

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1. Identify all failure causes attributed to a machine tool under consideration. This should be based on shop-floor data on machine tools, and the experience of persons involved in its operation, maintenance, and design. 2. Consider the first failure cause, and identify its contributing events and their interrelations. If any event is a cause and effect event to itself, consider that aspect also. Assign severity to the events (i.e., Si), and to the causality relations (i.e., cij). 3. Develop the machine tool failure causality digraph considering the identified failure contributing events and their interrelations (i.e., causality relations) in step 2. This digraph consists of nodes and directed edges. The number of nodes shall be equal to the number of failure-contributing events (i.e., M). If an event is cause and effect to itself, then a self-loop is to be drawn at the node representing that event. 4. Develop the machine tool failure causality matrix for the machine tool failure causality digraph. This will be an M x M matrix with diagonal elements representing the severity of the failure contributing events (plus the causality relations for self-loops, if any, in the digraph) and off-diagonal elements representing the causality relations among the failure contributing events. 5. Obtain the machine tool failure causality function for the machine tool failure causality matrix, on the lines of Equation 12.3. Substitute the values of the severity of the failure contributing events and their causality relations obtained in step 2 into the machine tool failure causality function, and calculate the value of the machine tool failure causality index i.e., MTFCI. 6. Carry out the failure cause analysis by critically examining each and every term of different groupings of the machine tool failure causality function. Suggest the ways and means to minimize the severity of the failure cause. 7. Repeat the steps 1 to 6 for all the other failure causes of the machine tool. 8. Arrange the MTFCI values for different failure causes in decreasing order. This gives an idea of the severity of the failure causes. 9. Evaluate the coefficients of similarity and dissimilarity for all the failure causes. List the values for all combinations. Compile the analysis, and document the failure causes for future analysis.

12.8 Summary
A methodology is presented in this chapter that is applied to a machine tool failure cause analysis, with the identification of failure-contributing events and their interaction for a machine tool failure cause. The procedure is useful for designers of reliable machine tools, and practicing engineers involved in failure minimization of the operating machine tool, leading to improved productivity and cost minimization. The proposed methodology helps in identifying areas of improvement, and minimizing the severity of failure causes, thereby leading to the development of a machine tool of increased reliability. The procedure is useful not only for the failure cause analysis of machine tools, but also for the failure cause analysis of any type of systems. Further, the procedure is useful for comparison and evaluation of failure causes.

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References
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Ishida Y, Adachi N, Tokumaru H (1985) A topological approach to failure diagnosis of large scale system. IEEE Transactions on Systems, Man, and Cybernetics 20:129–141. Johansson KE (1981) Field monitoring of NC machines - a systems approach. In: Innovation for Maintenance Technology Improvements, MFPG 3rd Meeting, National Bureau of Standards, New York Kegg RL (1984) On line process diagnostics. CIRP Annals 33:469–473 Keller AZ, Perera VD (1981) Reliability analysis of CNC machine tools. In: Proc. 3rd National Conference on Reliability, Macclesfield Kilmartin BR, Hannan RG (1981) An in-company study of NC machine utilization and its improvement by a systems approach. International Journal of Production Research 19:289–300 Kokowa M, Miyazaki S, Shingai S (1983) Fault location using digraph and inverse direction search with application. Automatica 19:729–735 Kokowa M, Shingai S (1982) Failure propagating simulation and non-failure path search in network systems. Automatica 18:335–341 Kwon HD, Burdekin M (1998) Adjustment of CNC machine tool controller setting values by an experimental method. International Journal of Machine Tools & Manufacture 38:1045–1065 Lee J (1995) Machine performance monitoring and proactive maintenance in computer integrated manufacturing: review and perspective. International Journal of Computer 1ntegratedManufacturing 8:370–380 Lee J, Kramer BM (1993) Analysis of machine degradation using a neural network approach. Journal of Manufacturing Systems 12:379–387 Luis AFG, Gilberto HR, Rocio PV, Rene DJRT, Wbaldo LT (2006) Sensorless tool failure monitoring system for drilling machines. International Journal of Machine Tools and Manufacture 46:381–386 Majstorovic V, Milacic V (1990) Expert system for diagnosis and maintenance. Maintenance 5:19–22 Marczewsky R (1988) An expert system for machine tool diagnosis. In: Proc. of 2nd Engineering Society of Detroit Conference on Expert Systems, Detroit Martin KF (1994) A review by discussion of condition monitoring and fault diagnosis in machine tools. International Journal of Machine Tools & Manufacture 34:527–551 Martin KF, Hoh SM, Thorpe P (1990) Fault diagnosis of hard faults. In: International Conference on Manufacturing Systems and Environment, Japan Society of Mechanical Engineers, Tokyo Marzi MH, Martin KF (1990) Artificial neural network condition monitoring and fault diagnosis. In: Proc. ASME International Conference on Neural Networks, San Diego, CA NCSR (1988) CNC machining center. AMTA Reliability Publications, Risley Poltavets OF (1994) Diagnostics in the machine tool: purpose, state, and prospects. Russian Engineering Research 14:6–8 Puetz RD, Eichhorn S (1987) Expert systems for fault diagnosis of CNC machines. In: Sviram D, Adey RD (eds) Knowledge-based expert systems for engineering. Computational Mechanics Publications, London .

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Robot Selection for a Given Industrial Application

13.1 Introduction
The word robot was coined in 1920 by the Czech author K. Capek in his play Rossum’s Universal Robots; it is derived from the Czech word robota, meaning ‘worker’. An industrial robot is commonly defined as a reprogrammable multifunctional manipulator, designed to move materials, parts, tools, or other devices by means of variable programmed motions, and to perform a variety of other tasks. In a broader context, the term robot also includes manipulators that are activated directly by an operator. Recent developments in information technology and engineering sciences have been the main reason for the increased utilization of robots in a variety of advanced manufacturing facilities. Robots with vastly different capabilities and specifications are available for a wide range of applications. The selection of robots to suit a particular application and production environment from among the large number available in the market has become a difficult task. Various aspects such as product design, production system, and economics, need to be considered before a suitable robot can be selected. The selection problem is particularly relevant in view of the likely lack of experience of prospective users in employing a robot. Indeed, robots are still a new concept in industry as a whole, and so it is not unusual for an industry to be a first-time robot purchaser. Many precision-based methods for robot selection have been developed to date. Knott and Getto (1982) suggested a model to evaluate different robotic systems under uncertainty, and different alternatives were evaluated by computing the total net present values of cash flows of investment, labor components, and overheads. Offodile et al. (1987) developed a coding and classification system that was used to store robot characteristics in a database, and then selected a robot using economic modeling. While the attempt provides a valuable aid at the stage of final selection, such an exercise will be prohibitive at the initial selection stage when the number of potential robots is large, and many other considerations have to be taken into account. Imang and Schlesinger (1989) presented decision models for robot selection, and compared ordinary least squares and linear goal programming

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methods. Agrawal et al. (1991) employed the TOPSIS method for robot selection. However, the authors had not considered the subjective attributes. Boubekri et al. (1991) developed an expert system for industrial robot selection considering functional, organizational, and economical attributes in the selection process. Wang et al. (1991) presented a decision support system that applies a fuzzy set method for robot selection. The objective attributes were evaluated via marginal value functions while the subjective attributes were evaluated via fuzzy set membership function. Data from both evaluations were finally processed such that a fuzzy set decision vector was obtained. However, the fuzzy method presented is a complicated one, and requires more computation. Booth et al. (1992) proposed a decision model for the robot selection problem using both Mahalanobis distance analysis, i.e., a multivariate distance measure, and principal-components analysis. Liang and Wang (1993) proposed a robot selection algorithm by combing the concepts of fuzzy set theory and hierarchical structure analysis. The algorithm was used to aggregate decision makers’ fuzzy assessments about robot selection attributes weightings, and to obtain fuzzy suitability indices. The suitability ratings were then ranked to select the most suitable robot. Khouja and Offodile (1994) reviewed the literature on industrial robots selection problems and provided directions for future research. Khouja (1995) presented a two-phase robot selection model that involved the application of data envelopment analysis (DEA) in the first phase, and a multi-attribute decision-making model in the second phase. Zhao and Yashuhiro (1996) introduced a genetic algorithm (GA) for an optimal selection and work station assignment problem for a computer-integrated manufacturing (CIM) system. Goh et al. (1996) proposed a revised weighted sum decision model that took into account both objective and subjective attributes of the robots under consideration. The model incorporated values assigned by a group of experts on different attributes in selecting the robots. Goh (1997) employed the analytic hierarchy process (AHP) method for robot selection. Parkan and Wu (1999) presented decision-making and performance measurement models with applications to robot selection. Particular emphasis was placed on a performance measurement procedure called operational competitiveness rating (OCRA) and a multiple attribute decision-making method, TOPSIS. The final selection was made on the basis of rankings obtained by averaging the results of OCRA, TOPSIS, and a utility model. However, the models had not considered the subjective attributes, and no explanation was given on how to assign the weightings to different robot selection attributes. Khouja and Kumar (1999) used options theory and an investment evaluation procedure for selection of robots. Braglia and Petroni (1999) carried out investment evaluation using DEA for robot selection. Layek and Resare (2000) developed a decision support system (DSS) based on analytical algorithms to select machining centers and robots concurrently from the market milien. Chu and Lin (2003) pointed out the limitations of the Liang and Wang (1993) method, and proposed a fuzzy TOPSIS method for robot selection. However, the authors had converted the available objective values of the robot selection attributes into fuzzy values, which violates the basic rule of fuzzy logic, i.e., the available objective values need not be fuzzified. Further, only a 5-point scale was adapted for the rating of robots under

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subjective attributes. Also, the fuzzy method was complicated, and requires more computation. Bhangale et al. (2004) listed a large number of robot selection attributes, and ranked the robots using TOPSIS and graphical methods, comparing the rankings given by these methods. However, the weights assigned by the authors to the attributes were not consistent. Karsak and Ahiska (2005) introduced a practical common weight MCDM methodology using the DEA method with an improved discriminating power for technology selection. Rao and Padmanabhan (2006) proposed a methodology based on digraph and matrix methods for evaluation of alternative industrial robots. A robot selection index was proposed that evaluates and ranks robots for a given industrial application. The index was obtained from a robot selection attributes function, in turn obtained from the robot selection attributes digraph. The digraph was developed based on robot selection attributes and their relative importance for the application considered. A step by step procedure for evaluation of a robot selection index was suggested. The objective of a robot selection procedure is to identify the robot selection attributes, and obtain the most appropriate combination of the attributes in conjunction with the real requirements of the industrial application. A robot selection attribute is defined as a factor that influences the selection of a robot for a given industrial application. These attributes include: cost, configuration, load capacity, weight and size of the robot, type and number of end effectors, type of control, velocity of movements, type of programming, programming flexibility, reliability, repeatability, positioning accuracy, resolution, number of degrees of freedom, number of joints, their sequence and orientation, motion transformation characteristics, ease of operation, work volume, drive system, man-machine interface, vendor’s service contract, training, delivery period, maintainability, ease of assembly, ease of disassembly, types and number of sensors used, availability or assured supply, management constraints, etc. Efforts need to be extended to determine attributes that influence robot selection for a given industrial application, using a logical approach to eliminate unsuitable robots, and for selection of a proper robot to strengthen the existing robot selection procedure. Pertinent attributes and the alternative robots involved are to be identified. Values of the attributes and their relative importance are to be obtained. An objective or subjective value, or its range, may be assigned to each identified attribute as a limiting value, or threshold value, for its acceptance for the considered robot selection problem. An alternative robot with each of its selection attributes, meeting the acceptance value, may be short-listed. After short-listing the alternative robots, the main task to choose the alternative robot is to see how it serves the attributes considered. The next section presents applications of the GTMA and fuzzy MADM methods for robot selection for a given industrial application.

13.2 Examples
Now, to demonstrate and validate the application of decision-making methods, two examples are considered.

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13.2.1 Example 1 An example is considered to demonstrate the application of the GTMA and fuzzy MADM methods. This example problem considers five robot selection attributes, and three alternative robots. The objective and subjective information of the attributes is given in Table 13.1. Man–machine interface (MI) and programming flexibility (PF) are expressed subjectively in linguistic terms, and these attributes are assigned objective values with the help of Table 4.3. The objective data of the attributes are given in Table 13.2.
Table 13.1. Robot selection attributes information of example 13.2.1 ______________________________________________________________ Robot PC ($1,000) LC (kg) RE (mm) MI PF ______________________________________________________________ Robot 1 73 48 0.15 A H Robot 2 71 46 0.18 AA VH Robot 3 75 51 0.14 BA H ______________________________________________________________ PC: Purchasing cost LC: Load carrying capacity R: Repeatability error MI: Man-machine interface PF: Programming flexibility A: Average; AA: Above average; BA: Below average; H: High; VH: Very high Table 13.2. Objective data of the robot selection attributes of example 13.2.1 ______________________________________________________________ Robot PC ($1,000) LC (kg) RE (mm) MI PF ______________________________________________________________ Robot 1 73 48 0.15 0.5 0.665 Robot 2 71 46 0.18 0.59 0.745 Robot 3 75 51 0.14 0.41 0.665 ______________________________________________________________

13.2.1.1 Application of GTMA In the present work, the attributes considered are PC, LC, R, MI, and PF. The objective values of the robot selection attributes, which are given in Table 13.2, are to be normalized. LC, MI, and PF are beneficial attributes, and higher values are desirable. Values of these attributes are normalized, as explained in Section 2.4, and are given in Table 13.3 in the respective columns. PC and R are non-beneficial attributes, and lower values are desirable. The values of these attributes for different robots are normalized, and given in Table 13.3 in the respective columns.

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Table 13.3. Normalized data of the robot selection attributes of example 13.2.1 ______________________________________________________________ Robot PC LC RE MI PF ______________________________________________________________ Robot 1 0.9726 0.9412 0.9333 0.8475 0.8926 Robot 2 1.0000 0.9020 0.7777 1.0000 1.0000 Robot 3 0.9467 1.0000 1.0000 0.6949 0.8926 ______________________________________________________________

Let the decision maker prepare the assignments: PC LC RE MI PC --0.745 0.5 0.865 LC 0.255 --0.255 0.59 RE 0.5 0.745 --0.865 MI 0.135 0.41 0.135 --PF 0.255 0.5 0.255 0.59

following relative importance PF 0.745 0.5 0.745 0.41 ---

The robot attributes digraph, robot attributes matrix of the digraph, and robot function for the matrix can be prepared. The value of the robot selection index is calculated using the values of Ai and aij for each robot. The robot selection index values of different robots are given below in descending order: Robot 2 6.1701 Robot 1 5.9386 Robot 3 5.7184 From the above values of the robot selection index, robot 2 is considered as the best choice among the robots considered for the given industrial application. The second choice is robot 1, and the third choice is robot 3. 13.2.1.2 SAW Method Let the decision maker assign the following weights of importance to the attributes: WPC = 0.40, WLC = 0.08, WR = 0.40, WMI = 0.05, and WPF = 0.08 Using these weights, and the normalized data of the attributes for different robots, the robot selection index values are calculated, and are arranged in descending order of the index. Robot 3 0.9579 Robot 1 0.9429 Robot 2 0.9032 As mentioned above, the ranking depends upon the weights of importance assigned to the attributes. 13.2.1.3 WPM Application of WPM leads to the following ranking: Robot 3 0.9554 Robot 1 0.9424 Robot 2 0.8969

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13.2.1.4 AHP and its Versions If the same weights as those selected for the SAW method are used in this method, then the ranking of robots obtained by using the relative as well as ideal mode AHP methods will be the same. The multiplicative AHP method also leads to the same ranking. However, rather than the above, let the decision maker decide to use the AHP method to determine the weights (wj) of the attributes, and prepare the following matrix: PC LC R MI PF PC 1 5 1 7 5 LC 1/5 1 1/5 2 1 R 1 5 1 7 5 MI 1/7 1/2 1/7 1 1/2 PF 1/5 1 1/5 2 1 Purchasing cost (PC) is considered as strongly more important than the load carrying capacity (LC) in this example. So, a relative importance value of 5 is assigned to PC over LC (i.e., a12 = 5), and a relative importance value of 1/5 is assigned to LC over PC (i.e., a21 = 1/5). PC and R are considered as equally important in this example. So, a relative importance value of 1 is assigned to PC over R, and a relative importance value of 1 is assigned to R over PC. Similarly, the relative importance among other attributes can be explained. The normalized weights of each attribute are calculated and these are: WPC = 0.3916, WLC = 0.084, WR = 0.3916, WMI = 0.0485, and WPF = 0.0841. The value of max is 5.0204 and CR = 0.00455, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. The value of the robot selection index is now calculated, and the robots are arranged in descending order of the robot selection index. Robot 3 0.9551 Robot 1 0.9416 Robot 2 0.9045 From the above values of the robot selection index, robot 3 is considered as the best choice among the robots considered for the given industrial application. For the above weights of importance of attributes, multiplicative AHP also leads to the same ranking order of 3-1-2. 13.2.1.5 TOPSIS Method The quantitative values of the robot selection attributes, which are given in Table 13.5, are normalized as explained in Section 3.2.6. Relative importance of attributes (aij) is assigned using the AHP method as explained in Section 13.2.2.4, and these are WPC = 0.3916, WLC = 0.084, WR = 0.3916, WMI = 0.0485, and WPF = 0.0841. The weighted normalized matrix is calculated, and is shown below:

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0.2259 0.2323 0.2199

0.0482 0.0462 0.0512

0.2323 0.0277 0.0466 0.1936 0.0327 0.0522 0.2489 0.0227 0.0466

Ideal (best) and negative ideal (worst) solutions are calculated, and these are given as: VPC+ = 0.2199 VPC- = 0.2323 + VLC- = 0.0462 VLC = 0.0512 + VR- = 0.2489 VR = 0.1936 + VMI = 0.0327 VMI- = 0.0227 + VPF- = 0.0446 VPF = 0.0522 Separation measures are calculated, and these are: S1+ = 0.0400 S1- = 0.0186 + S2- = 0.0565 S2 = 0.0134 + S3- = 0.0134 S3 = 0.0565 The relative closeness of a particular alternative to the ideal solution is calculated, and these are: P1 = 0.3169, P2 = 0.8088, and P3 = 0.1912 This relative closeness to the ideal solution can be named as the ‘robot selection index’ in the present work. The alternative robots are arranged in descending order of their robot selection index. This can be arranged as 2-1-3. 13.2.1.6 Modified TOPSIS Method The positive ideal solution (R+) and the negative ideal solution (R-) are calculated, and are given below: RPC+ = 0.5614 RPC= 0.5930 + RLC = 0.6087 RLC= 0.5489 RR+ = 0.5129 RR= 0.6595 RMI+ = 0.6740 RMI= 0.4684 + RPF = 0.6209 RPF= 0.5543 The weighted Euclidean distances are calculated as D1+ = 0.0402 D1= 0.0734 + D2 = 0.0933 D2= 0.0531 D3+ = 0.0531 D3= 0.0933 The relative closeness of a particular alternative to the ideal solution is calculated (i.e., robot selection index), and these are: P1-mod = 0.6460 P2-mod = 0.3625 P3-mod = 0.6375 The alternative robots are arranged in descending order of their robot selection index, as 1-3-2. From this, it appears that the ranking presented by using the modified TOPSIS method is not appropriate for the example problem considered.

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13.2.2 Example 2 Bhangale et al. (2004) listed a large number of robot selection attributes, and ranked the robots using TOPSIS and graphical methods, comparing the rankings given by these methods. The example problem considering five attributes and seven alternative robots is shown in Table 13.4.
Table 13.4. Objective data of the robot selection attributes of example 13.2.2 (from Bhangale et al. 2004; reprinted with permission from Elsevier) _____________________________________________________________ Robot LC RE MS MC MR _____________________________________________________________ Robot 1 60 0.4 2,540 500 990 Robot 2 6.35 0.15 1,016 3,000 1,041 Robot 3 6.8 0.1 1,727.2 1,500 1,676 Robot 4 10 0.2 1,000 2,000 965 Robot 5 2.5 0.1 560 500 915 Robot 6 4.5 0.08 1,016 350 508 Robot 7 3 0.1 1,778 1,000 920 _____________________________________________________________ LC: Load capacity (kg) RE: Repeatability error (mm) MS: Maximum tip speed (mm/s) MC: Memory capacity in points or steps MR: Manipulator reach (mm)

13.2.2.1 Application of GTMA Now, to demonstrate the proposed procedure of robot selection through GTMA, various steps of the methodology, given in Section 2.6, are carried out as described below: In the present work, the attributes considered are LC, RE, MS, MC and MR. The objective values of the robot selection attributes, which are given in Table 13.4, are to be normalized. LC, MS, MC, and MR are beneficial attributes, and higher values are desirable. Values of these attributes are normalized, and are given in Table 13.5 in the respective columns. RE is a non-beneficial attribute, and lower values are desirable. The values of this attribute for different robots are normalized, and given in Table 13.5 in the respective columns.
Table 13.5. Normalized data of the robot selection attributes of example 13.2.2 _______________________________________________________________ Robot LC RE MS MC MR _______________________________________________________________ Robot 1 1 0.2 1 0.1667 0.5907 Robot 2 0.1058 0.53333 0.4 1 0.6211 Robot 3 0.1133 0.8 0.68 0.5 1 Robot 4 0.1667 0.4 0.3937 0.6667 0.5758 Robot 5 0.0417 0.8 0.2205 0.1667 0.5459 Robot 6 0.075 1 0.4 0.1167 0.3031 Robot 7 0.05 0.8 0.7 0.3333 0.5489 _______________________________________________________________

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Relative importance of attributes (aij) is assigned values as explained in Section 2.4. Let the decision maker select the following assignments using the AHP procedure: LC 6 7 7 5 RE 1/6 2 2 1/2 MS 1/7 1/2 1 1/3 MC 1/7 1/2 1 1/3 MR 1/5 2 3 3 -

LC RE MS MC MR

The value of max for this matrix is 5.0874 and CR = 0.0197, and, thus there is good consistency in the judgements made (of relative importance of attributes). The value of the robot selection index is now calculated, and the robots are arranged in the descending order of the robot selection index. Robot 3 92.004 Robot 1 88.074 Robot 2 84.929 Robot 7 81.391 Robot 4 77.954 Robot 6 72.986 Robot 5 71.296 From the above values of the robot selection index, robot 3 is considered as the best choice among the robots considered for the given industrial application. The second choice is Robot 1 and the last choice is robot 5. However, Bhangale et al. (2004) gave a ranking order of: robot 4 - robot 1 - robot 3 - robot 7 - robot 2 robot 6 - robot 5. However, the relative importance matrix prepared by Bhangale et al. (2004) was completely inconsistent, and it is not possible to justify how the authors had calculated the weights of the relative importance of the attributes based on such a highly inconsistent judgement matrix. Thus, the ranking presented here for the proposed GTMA method is more genuine. It may be mentioned that the ranking depends upon the judgements made by the user. The above ranking may change if the user assigns different relative importance values to the attributes. 13.2.2.2 AHP and its Versions Let the decision maker prepares the following relative importance matrix: LC 6 7 7 5 RE 1/6 2 2 1/2 MS 1/7 1/2 1 1/3 MC 1/7 1/2 1 1/3 MR 1/5 2 3 3 -

LC RE MS MC MR

The normalized weights of each attribute are calculated following the procedure presented in Section 3.2.3, and these are: WLC = 0.036, WRE = 0.192,

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WMS = 0.326, WMC = 0.326, and WMR = 0.120. The value of max for this matrix is 5.0874 and CR = 0.0195, and, thus there is good consistency in the judgements made. The value of the robot selection index is now calculated using the above weights, and the normalized data of the attributes given in Table 13.2. The alternative robots are arranged in descending order of the robot selection index. Robot 3 0.6623 Robot 2 0.6371 Robot 7 0.5581 Robot 1 0.5256 Robot 4 0.4976 Robot 6 0.4000 Robot 5 0.3468 From the above values of the robot selection index, it is clear that the robot, designated as 3 is the best choice among the robots considered for the given industrial application. For the above weights of importance of attributes, multiplicative AHP leads to the same ranking order of 3-2-7-4-1-6-5.

References
Agrawal VP, Kohli V, Gupta S (1991) Computer aided robot selection: the ‘multiple attribute decision making’ approach. International Journal of Production Research 29:1629–1644 Bhangale PP, Agrawal VP, Saha SK (2004) Attribute based specification, comparison and selection of a robot. Mechanism & Machine Theory 39:1345– 1366 Booth DE, Khouja M, Hu M (1992) A robust multivariate statistical procedure for evaluation and selection of industrial robots. International Journal of Operations & Production Management 12:15–24 Boubekri N, Sahoui M, Lakrib C (1991) Development of an expert system for industrial robot selection. Computers & Industrial Engineering 20:119–127 Bragilia M, Petroni A (1999) Evaluating and selecting investments in industrial robots. International Journal of Production Research 37:4157–4178 Chu TC, Lin YC (2003) A fuzzy TOPSIS method for robot selection. International Journal of Advanced Manufacturing Technology 21:284–290 Goh CH (1997) Analytic hierarchy process for robot selection. Journal of Manufacturing Systems 16:381–386. Goh CH, Tung YCA, Cheng CH (1996) A revised weighted sum decision model for robot selection. Computers & Industrial Engineering 30:193–198 Imang MM, Schlesinger RJ (1989) Decision models for robot selection: a comparison of ordinary least squares and linear goal programming method. Decision Sciences 20:40–53 Karsak EE, Ahiska SS (2005) Practical common weight multi-criteria decisionmaking approach with an improved discriminating power for technology selection. International Journal of Production Research 43:1537–1554

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Khouja M (1995) The use of data envelopment analysis for technology selection. Computers & Industrial Engineering 28:123–132 Khouja MJ, Kumar RL (1999) An options view of robot performance parameters in a dynamic environment. International Journal of Production Research 37:1243–1257 Khouja M, Offodile OF (1994) The industrial robots selection problem: a literature review and directions for future research. IIE Transactions 26:50–61 Knott K, Getto RD (1982) A model for evaluating alternative robot systems under uncertainty. International Journal of Production Research 20:155–165 Layek AM, Resare LJ (2000) Algorithm based decision support system for the concerted selection of equipment in machining/assembly cells. International Journal of Production Research 38:323–339 Liang GH, Wang MJ (1993) A fuzzy multi-criteria decision-making approach for robot selection. Robotics and Computer Aided Manufacturing 10:267–274 Offodile OF, Lambert PK, Dudek RA (1987) Development of a computer aided robot selection procedure (CARSP). International Journal of Production Research 25:1109–1112 Parkan C, Wu ML (1999) Decision-making and performance measurement models with applications to robot selection. Computers & Industrial Engineering 36:503–523 Rao RV, Padmanabhan KK (2006) Selection, identification and comparison of industrial robots using digraph and matrix methods Robotics and Computer Integrated Manufacturing 22:373–383 Wang MJ, Singh HP, Huang WV (1991) A decision support system for robot selection. Decision Support Systems 7:273–283 Zhao L, Yashuhiro T (1996) Genetic algorithm for robot selection and work station assignment problem. Computers & Industrial Engineering 31:599–602

14
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Selection of an Automated Inspection System

14.1 Introduction
As automation increases in all aspects of manufacturing processes and operations, the need for automated inspection has become obvious. Flexible manufacturing systems and manufacturing cells have led to the adoption of advanced measuring techniques and systems. In fact, installation and utilization of these systems is now necessary and essential in manufacturing. In the past, a batch of parts was manufactured and sent to be measured in a separate quality control room; if this batch passed measurement inspection, it was put into inventory. Automated inspection, however, is based on various on-line sensor systems that monitor the dimensions of the parts while they are being made, and if necessary use these measurements as input to correct the process (Kalpakjian and Schmid, 2000). Automated inspection techniques can be divided into two broad categories: (1) contact inspection and (2) non-contact inspection. In contact inspection, physical contact is made between the object and the measuring or gaging instrument, whereas in non-contact inspection no physical contact is made. The principal contact inspection technologies are: Conventional measuring and gaging instruments, manual and automated Coordinate measuring machines (CMMs) and related techniques Stylus type surface texture measuring machines Conventional measuring and gaging techniques and CMMs measure dimensions and related specifications. Surface texture measuring machines measure surface characteristics such as roughness and waviness. Non-contact inspection methods utilize a sensor located at a certain distance from the object to measure or gage the desired features (Groover, 2001). The noncontact inspection technologies can be classified into two categories: (1) optical and (2) non-optical. Optical inspection technologies make use of light to accomplish the measurement or gaging cycle. The most important optical technology is machine vision; however, other optical techniques are important in certain industries. Non-optical inspection technologies utilize energy forms other

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than light to perform the inspection; these other energies include various electrical fields, radiation and ultrasonics. The characteristics and quality of measuring instruments or gages are generally described by various specific attributes such as accuracy, repeatability, sensitivity, amplification, calibration, stability, linearity, drift, precision, resolution, speed of response, volumetric performance, maintainability, reliability, initial cost, operation cost, throughput rate, environmental factor requirement (temperature, humidity, dust and so on), flexibility in software interface, size and type of parts to be measured, operator skills required, etc. The selection of an automated inspection system requires consideration of various attributes as mentioned above. Very limited research work was done on this selection aspect. Elshennaway (1989) presented a methodology for the performance evaluation of CMMs. Golomski (1990) had discussed the selection of automated inspection device from accounting point of view. The author had shown that using automated inspection equipment can reduce the indirect cost of inspection but increase the depreciation cost as well as the maintenance cost. Pandey and Kengpol (1995) presented a methodology for selecting the best possible automated inspection device for use in FMSs. The problem had been modeled as that of multicriterion decision making and solved using Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE). The study had demonstrated the effectiveness of multicriterion decision making approach. Now, to demonstrate and validate the application of proposed decision making methods, an example is considered. First GTMA is applied and subsequently few MADM methods are applied to rank and select the automated inspection systems.

14.2 Example
Pandey and Kengpol (1995) presented a methodology for selecting the best possible automated inspection device for use in FMSs. The authors had surveyed the Thailand industries and considered 11 attributes and 4 alternative automated inspection systems. The eleven attributes considered were accuracy, volumetric performance, repeatability, resolution, maintainability, reliability, initial cost, operation cost, throughput rate, environmental factor requirement and flexibility in software interface. The four alternative automated inspection systems considered were CMM1(USA), CMM2(Japan), AVI(USA), LASER SCAN (Japan).The corresponding data is presented in Table 14.1. 14.2.1 Application of Graph Theory and Matrix Approach (GTMA) Various steps of the methodology, proposed in Section 2.6, are carried out as described below: Step 1: In the present work, the attributes considered are the same as of those Pandey and Kengpol (1995), and these are: accuracy (A), volumetric performance (V), repeatability (R), resolution (S), maintainability (M), reliability (L), initial cost

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(I), operation cost (O), throughput rate (T), environmental factor requirement (E), and flexibility in software interface (F).
Table 14.1. Data of the automated inspection system selection attributes (from Pandey and Kengpol 1995; reprinted with permission from Elsevier) ______________________________________________________________ Attributes A B C D ______________________________________________________________ Accuracy 90 80 60 75 Volumetric performance 80 70 50 70 80 80 50 70 Repeatability Resolution 70 70 80 60 Maintainability 60 60 80 70 Reliability 85 80 70 70 Initial cost 40 30 20 25 Operation cost 2 7 1 4 Throughput rate 70 70 80 80 Environmental factor requirement 80 80 60 70 Flexibility in software interface 80 60 60 70 ______________________________________________________________ A: CMM1 (USA); B: CMM2 (Japan); C: AVI (USA); D: LASER SCAN (Japan)

The quantitative values of the automated inspection system selection attributes, which are given in Table 14.1, are to be normalized. A, V, R, S, M, L, T, and F are beneficial attributes, and higher values are desirable. Values of these attributes are normalized, and are given in Table 14.2 in the respective columns. I, O and E are non-beneficial attributes, and lower values are desirable. The values of these attributes for different alternative automated inspection systems are normalized, and given in Table 14.2 in the respective columns.
Table 14.2. Normalized data of the automated inspection system selection attributes _________________________________________________________________ A B C D Attributes _________________________________________________________________ Accuracy 1 0.8889 0.6667 0.8333 Volumetric performance 1 0.875 0.625 0.875 Repeatability 1 1 0.625 0.875 0.875 0.875 1 0.75 Resolution Maintainability 0.75 0.75 1 0.875 Reliability 1 0.9412 0.8235 0.8235 Initial cost 0.5 0.6667 1 0.8 0.5 0.1428 1 0.25 Operation cost Throughput rate 0.875 0.875 1 1 Environmental factor requirement 0.75 0.75 1 0.8571 Flexibility in software interface 1 0.75 0.75 0.875 _________________________________________________________________

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Let the decision maker (i.e., user organization) prepare the following relative importance assignments: A V A - 0.590 V 0.41 R 0.50 0.59 S 0.335 0.41 M 0.335 0.41 L 0.335 0.41 I 0.41 0.5 O 0.335 0.41 T 0.5 0.59 E 0.255 0.335 F 0.41 0.5 R 0.500 0.410 0.335 0.335 0.335 0.41 0.335 0.5 0.255 0.41 S 0.665 0.590 0.665 0.5 0.5 0.59 0.5 0.665 0.335 0.59 M 0.665 0.590 0.665 0.5 0.5 0.59 0.5 0.665 0.5 0.59 L 0.665 0.590 0.665 0.5 0.5 0.59 0.5 0.59 0.41 0.59 I 0.590 0.500 0.590 0.41 0.41 0.5 0.41 0.5 0.335 0.5 O 0.665 0.590 0.665 0.5 0.5 0.5 0.59 0.665 0.5 0.59 T E F 0.5 0.745 0.59 0.41 0.665 0.50 0.5 0.745 0.59 0.335 0.665 0.41 0.335 0.500 0.41 0.41 0.59 0.5 0.41 0.665 0.5 0.335 0.5 0.41 - 0.745 0.59 0.255 0.335 0.41 0.665 -

Step 2: 1. The automated inspection system selection attributes digraph, showing the presence as well as relative importance of the above attributes, is similar to Figure 2.2, but 11 attributes is drawn. This is not shown here due to obvious reasons. 2. The automated inspection system selection attributes matrix of this digraph is written based on Equation 2.10. However, it is not shown here. 3. The automated inspection system selection attributes function is written. However, it may be added that as a computer program is developed for calculating the permanent function value of a matrix, this step can be skipped. 4 & 5. The automated inspection system selection index (AIS-SI) is calculated using the values of Ai and aij for each alternative automated inspection system. The AIS-SI values of different automated inspection systems are given below in descending order: AVI (USA): 31158.7734 CMM (USA): 29780.7563 LASER SCAN (Japan): 27462.2604 CMM (Japan): 25897.6459 From the above values of AVS-SI, it is understood that the automated inspection system AVI (USA) is the right choice for the given inspection application under the given conditions. The next choice is CMM (USA), and the last choice is CMM (Japan). However, Pandey and Kengpol (1995) suggested CMM (USA) as the first choice, LASER SCAN (Japan) as the second choice, AVI (USA) as the third choice, and CMM (Japan) as the last choice.

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14.2.2 AHP and its Versions Let the decision maker prepare the following matrix: A 1 1/3 1 1/4 1/5 1/4 1/3 1/5 1/2 1/6 1/3 V 3 1 3 1/2 1/3 1/2 1 1/3 2 1/4 1 R 1 1/3 1 1/4 1/5 1/4 1/3 1/5 1/2 1/6 1/3 S 4 2 4 1 1/2 1 2 1/2 3 1/3 2 M 5 3 5 2 1 2 3 1 4 1/2 3 L 4 2 4 1 1/2 1 2 1/2 3 1/3 2 I 3 1 3 1/2 1/3 1/2 1 1/3 2 1/4 1 O T 5 2 3 1/2 5 2 2 1/3 1 1/4 2 1/3 3 1/2 1 1/4 4 1 1/2 1/5 3 1/2 E 6 4 6 3 2 3 4 2 5 1 4 F 3 1 3 1/2 1/3 1/2 1 1/3 2 1/4 1

A V R S M L I O T E F

In the above matrix, accuracy (A) and repeatability (R) are considered more important than the remaining attributes. The normalized weights of each attribute are calculated following the procedure presented in Section 3.2.3, and these are: WA = 0.2071, WV = 0.0858, WR = 0.2071, WS = 0.0518, WM = 0.0325, WL = 0.0518, WI = 0.0858, WO = 0.0325, WT = 0.1376, WE = 0.0219, and WF = 0.0858. The value of max is 11.1958 and CR = 0.01332, which is much less than the allowed CR value of 0.1. Thus, there is good consistency in the judgements made. The value of AIS-SI is now calculated using the above weights and the normalized data of the attributes given in Table 14.2. This leads to the ranking given by the revised AHP or ideal mode of AHP method. The alternative automated inspection systems are arranged in descending order of the AIS-SI: CMM (USA): 0.9050 CMM (Japan): 0.8493 LASER SCAN (Japan): 0.8487 AVI (USA): 0.7925 It may be noted that the ranking depends upon the judgements of relative importance of attributes made by the decision maker. For the above weights of importance of attributes, multiplicative AHP leads to the following ranking order: CMM (USA): 0.8837 LASER SCAN (Japan): 0.8301 CMM (Japan): 0.8154 AVI (USA): 0.7738

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14.2.3 TOPSIS Method Following the steps of the methodology given in Section 3.2.6, the TOPSIS method gives the ranking order shown below: CMM (USA): 0.6811 CMM (Japan): 0.6074 LASER SCAN (Japan): 0.5977 AVI (USA): 0.3813 It may be observed that the ranking given by the TOPSIS method is same as that given by the ideal AHP method. 14.2.4 Modified TOPSIS Method This methods leads to the following ranking order: CMM (USA): 0.6308 LASER SCAN (Japan): 0.5724 AVI (USA): 0.5280 CMM (Japan): 0.4572 The ranking suggested by this method is same as that proposed by Pandey and Kengpol (1995) using the PROMETHEE method. In this particular example of automated inspection system selection, proposing CMM (USA) as the first right choice seems to be more logical and objective. AVI (USA) is better than the other alternative inspection systems with respect to six of 11 attributes. However, the weights of importance assigned to the attributes play an important role in the selection process.

References
Elshennaway AK (1989) The role of inspection in automated manufacturing. Computers & Industrial Engineering 17:327–333 Golomski WA (1990) Justification Methods for Computer Integrated Manufacturing Systems. In: Accounting Aspects of Automated Inspection Systems, Elsevier, Amsterdam Groover MP (2001) Automation, production systems and computer integrated manufacturing. Prentice Hall of India, New Delhi Kalpakjian S, Schmid SR (2000) Manufacturing engineering and technology. Addison Wesley Longman (Singapore), Indian branch, Delhi Pandey PC, Kengpol A (1995) Selection of an automated inspection system using multiattribute decision analysis. International Journal of Production Economics 39:289–298

15
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Selection of Material Handling Equipment

15.1 Introduction
Material handling equipment selection is an important function in the design of a material handling system, and thus a crucial step for facilities planning. Using proper material handling equipment can enhance the production process, provide effective utilization of manpower, increase production, and improve system flexibility. The importance of material handling equipment selection cannot be overlooked. However, with the wide range of material handling equipment available today, determination of the best equipment alternative for a given production scenario is not an easy task (Chan et al., 2001). Material handling accounts for 30-75% of the total cost of a product, and efficient material handling can be responsible for reducing the manufacturing system operations cost by 15-30% (Sule, 1994). These values underscore the importance of material handling costs as an element in improving the cost structure of a product. The determination of a material handling system involves both the selection of suitable material handling equipment, and the assignment of material handling operations to each individual piece of equipment. Hence, material handling system selection can be defined as the selection of material handling equipment to perform material handling operations within a given working area considering all aspects of the products to be handled (Sujono and Lashkari, 2007). The material handling system (MHS) plays a crucial role in flexible manufacturing systems. When inadequately designed, the MHS can indeed interfere severely with the overall performance of the system, and lead to substantial losses in productivity and competitiveness, and to unacceptably long lead times. Thus, to avoid such pitfalls, MHS selection is considered as an important issue in manufacturing industries. Material handling equipment has been classified into the following main groups of industrial trucks, conveyors, automated guided vehicles (AGVs), cranes, storage/retrieval systems and industrial robots (Sule, 1994; Kulak, 2005). This module includes examples of 40 move equipment types, and six storage equipment with their performance attributes. Table 15.1 presents the material handling

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equipment types, and Table 15.2 presents the material handling equipment selection attributes for manufacturing systems.
Table 15.1. Types of material handling equipment (from Kulak 2005; reprinted with permission from Elsevier) __________________________________________________________________________ (1) Industrial trucks: Handcart, tier platform truck, handlift truck, power-driven handtruck, powerdriven platform truck, forklift truck, narrow-aisle trucks, material lift, tractortrailer train, drum truck, drum lifter (2) Conveyors: Belt conveyor, roller conveyor, chute conveyor, slat conveyor, screw conveyor, chain conveyor, plain chain conveyor, trolley conveyor, wheel conveyor, tow conveyor, bucket conveyor, cart-on-track conveyor, pneumatic tube conveyor, overhead monorail conveyor (3) Automated guided vehicles (AGV): Manual load/unload AGV, low-lift AGV, high-lift AGV, tugged AGV, roller deck AGV, stationary deck AGV, lift deck AGV (4) Cranes: Stacker crane, tower crane, gantry crane, jib crane (5) Storage/retrieval systems: Unit load AS/RS, man-on-board AS/RS, shelf storage system, pallet rack system, block stocking on floor, block stocking in rack (6) Robots: Pneumatic robot, electric robot, hydraulic robot, mechanized manipulator __________________________________________________________________________

In the literature, there are various studies focusing on the solution of the complicated problem of material handling equipment selection. Malmborg et al. (1987) developed a prototype expert system considering 17 equipment attributes and 47 devices for industrial truck type selection. Velury and Kennedy (1992) studied the selection of relevant factors that need to be considered in the design of a bulk material handling system, and the selection of equipment once these factors had been considered. A model was presented that took into account economics, characteristics of the equipment, environmental characteristics, and compatibilities between equipment types. Swaminathan et al. (1992) developed EXCITE, the expert consultant for inplant transportation equipment, addressing 35 equipment types, and 28 material, move, and method attributes. Chu et al. (1995) developed a computer-aided material handling equipment selection system called ADVISOR. Park (1996) developed an intelligent consultant system for material handling equipment selection, including 50 equipment types and 29 attributes, i.e., move attributes, material characteristics, operation requirements, and area constraints. Kim and Eom (1997) introduced a material handling selection expert system. Fisher et al. (1998) introduced MATHES, the ‘material handling equipment selection expert systems’, for the selection of material handling equipment from 16 possible choices. MATHES including 172 rules dealing with path, volume of flow, sizes of unit, and distance between departments as parameters. MATHES II had been

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provided with the same procedure as MATHES. However, MATHES II had a larger working scope, and greater consultation functions.
Table 15.2. Material handling equipment selection attributes for manufacturing systems (from Kulak 2005; reprinted with permission from Elsevier) _________________________________________________________________ Material: Material type: individual unit, pallet unit, loose, bulk, packed, bar-stock, etc. Material weight: light, medium, heavy Bottom surface: flat, non-flat Material nature: fragile, sturdy Material size: small, medium, large Annual demands of the material:…...