SOME ISSUES IN CELLULAR
MANUFACTURING SYSTEMS DESIGN WITH VAGUE INFORMATION
By
RAVI SHANKER
Department of Mechanical Engineering
Submitted in fulfillment of the requirements of the degree of
DOCTOR OF PHILO6OPHY
to the
INDIAN INSTITUTE OF TECHNOLOGY, DELHI
August 1998
CERTIFICATE
This is to certify that the thesis entitled "Some Issues in Cellular Manufacturing Systems Design with Vague Information" being submitted by Ravi Shanker to the Indian Institute of Technology Delhi for the award of the degree of Doctor of Philosophy is a record of original bonafide research work carried out by him. He has worked under my guidance and supervision and has fulfilled the requirement for the submission of this thesis, which has reached the requisite standaid.4l izic
fP*44,
The results contained in this thesis have not boiligseittedoirf part or full, to any other University or Institute for the award of any degree or diploma.
(Dr. Prem Vrat)
Professor, Mechanical Engineering Department, Indian Institute of Technology Delhi,
New Delhi 110 016 (INDIA).
Dedicated to
My mother
ACKNOWLEDGEMENT
I am immensely grateful to my supervisor Prof. Prem Vrat for his stimulated guidance, unwavering support and encouragement. This thesis could not have attained its present form, both in content and presentation without his active interest, direction and help. His unmatched-excellence in the subject, bountiful energy, and personal care has been the source of great inspiration.
I sincerely thank Mrs. Vrat for her kind concern and affectionate co-operation during my research work.
I am grateful from the core of my heart to Dr. S.G. Deshmukh, Associate Professor, Mechanical Engineering Department, IIT Delhi for constructive criticism, moral support, and help throughout this work. It is impossible to account for his ever-ready genius- supports, and ever-smiling appreciation; both acted as the much-needed stimuli for this endeavour.
I express my gratitude to Prof. Arun Kanda, Chairman of my Student Research Committee (SRC) at IIT Delhi for providing valuable suggestions and words of encouragement. I am also thankful to Prof. D.K. Banwet and Dr. S. Wadhwa, who as members of my SRC have provided invaluable suggestions.
I am thankful to Prof. R.S. Agarwal and Prof. A.D. Gupta of Mechanical Engineering Department, IIT Delhi; Prof. K.N. Singh of IIM Lucknow and Dr. Sushil of NITIE Mumbai for their just and timely help and encouragement during this research.
iii
I also thank my ex-colleagues at
Rn
Jamshedpur; who were very considerate and helpful to me in this endeavour. In this connection, I sincerely thank Dr. S.S. Mishra, Prof. B.Sahay, Dr. B. Kumar, Prof. K.K. Srivastava, Prof. S.K. Mukherjee, Prof. A. Mishra, Dr.
Arun K. Singh, Dr. R.V. Sharma and Dr. Shalendra Kumar. I also thank Mr. Sarosh S.
Gandhi, and Late Er. B.B Prasad for timely help.
I extend my sincerest thanks to Prof. N. Singh (Wayne State University, USA) and Prof.
A. Subash Babu (IIT Bombay) for the fruitful discussions, help and encouragement.
I sincerely thank Mr. Ashutosh, Mr. Rajat Bhagwat and Mr. Majid Ali at IIT Delhi; Dr.
R.K. Srivastava, Mr. Rakesh Narain and Mr. Sanjeev Sinha at REC Allahabad for their help. I am also thankful to Mr. M.K. Bhatnagar and Mrs. Leela Bharti for their help in utilising the lab and computational facilities. I thank Mr. Rajeev Gupta for his help in typesetting the report.
I specially thank my wife, Dr. Poonam and children, Pratyush and Megha for their hearty support, patience and loving participation in accomplishing this task, which would not have been possible otherwise. Last but not the least, I thank all my relatives, well wishers and specially my parents, in-laws and brothers Devesh and Dhiraj for their support in completing my research work.
VP/
RAVI SHANKER
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ABSTRACT
Cellular Manufacturing System (CMS) is based on the principle of Group Technology (GT). It exploits the potential benefits in the similarity of design and manufacturing. CMS allows small batch production to give economic advantages similar to that of mass-production with additional advantages of flexibility, normally associated with job-shop production systems. One of the most important issues in designing the CMS is to decompose the manufacturing system into cells. In this research three aspects of CMS design are considered:
(i) Clustering of pans and machines into part family and machine cells,
(ii) Selection of strategy for exceptional elements (EE) and bottleneck machines (BM), and
(iii) Evaluation of CMS designs.
For the clustering of parts and machines into part family and machine cells, a sequence dependent incidence matrix is considered. An improved decomposition-recombination algorithm is proposed for cell formation. A recombination index is proposed, which accounts for the backtracking of parts in the cellular arrangement. The algorithm generates alternate cellular layouts.
Some information related to the situational parameters of a manufacturing system design, such as part demand, budget for machine acquisition, etc may not be available with precision at the cell design stage. This is mainly because of time gap between design and implementation, and high cost in acquiring the value of these parameters with precision. In the present research the issue of informational vagueness is tackled by modeling CMS through chance constrained programming, range objective programming and fuzzy programming approaches. Chance constrained programming is used for handling information of probabilistic nature. An in grid is proposed to facilitate decision making under various combinations of management attitude towards risk and informational attribute related to vagueness. Range objective model is attempted to tackle vague cost information, which is
available in a range rather than a point estimate. A quantitative estimate of risk by gain ratio is proposed to understand the model behaviour, and to facilitate the selections of appropriate strategy for EEIBM. In the fuzzy programming model, informational vagueness of linguistic nature is modeled. Results of all the models are compared with deterministic models, available in literature. The fuzzy programming model of the present research is extended to a multi objective formulation and results are compared with the goal programming formulation.
For the evaluation of CMS designs, an AHP-based evaluation framework is proposed. It has the potential to incorporate quantitative as well as subjective criteria in the design evaluation.
The major contributions made by this research are as follows:
1. Incorporating the consideration for uncertainty and vague design information,
2. Application of chance constrained programming, range objective programming and fuzzy programming to the CMS design problem,
3. Development of an AHP-based evaluation framework for handling a more comprehensive set of design objectives, which include quantitative, subjective and semi judgmental criteria,
4. Considerations for sequence of machining operations in conventional part-machine incidence matrix for accounting the effect of backtracking in a clustering problem, and 5. Demonstrating the use of fuzzy programming fora multi objective, CMS design problem
at the post-clustering stage.
The present research thus focuses on some of the most relevant issues in CMS design. It is expected that the focus on informational vagueness, which is considered in this research, will take CMS design closer to reality.
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TABLE OF CONTENTS
Page No.
CERTIFICATE
DEDICATION ii
ACKNOWLEDGEMENT iii
ABSTRACT
TABLE OF CONTENTS vii
LIST OF ABBREVIATIONS xii
LIST OF SYMBOLS AND NOTATIONS xiv
LIST OF FIGURES xvii
LIST OF TABLES xix
CHAPTER 1: INTRODUCTION 1-20
1.1 MANUFACTURING SYSTEMS 1
1.1.1 Types of Manufacturing Systems 1 1.2 CELLULAR MANUFACTURING SYSTEMS 3
1.2.1 Advantages of CMS 4
1.2.2 Limitations of CMS 6
1.2.3 Suitability of CMS 7
1.3 PART-MACHINE INCIDENCE MATRIX 9
1.4 CORE ISSUES IN CMS 9
1.4.1 Design Related Issues 9 1.4.2 Assumptions in CMS Design Problems 10 1.4.3 Operational Issues 11 1.5 SOME ASPECTS OF CMS DESIGN CONSIDERED IN THIS
THESIS 12
1.5.1 Vagueness in CMS Design Parameters 12 1.5.2 Strategy Selection for EE/BM 12 1.5.3 Sequence of Operations in Incidence Matrix 15 1.6 OBJECTIVE OF THE RESEARCH WORK 16 1.7 ORGANIZATION OF THIS REPORT 17
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CHAPTER 2: DESIGN OF CMS AND RELATED ISSUES: A
LITERATURE REVIEW 21-74
2.1 INTRODUCTION 21
2.2 EARLY DEVELOPMENTS IN CELLULAR
MANUFACTURING AREA 21
2.3 CODING AND CLASSIFICATION SYSTEMS 24 2.4 SIMILARITY COEFFICIENT-BASED METHODS 26 2.5 INCIDENCE MATRIX-BASED METHODS 30 2.6 INCIDENCE MATRIX DECOMPOSITION AND
SYNTHESIS -BASED METHODS 33 2.7 NON-HIERARCHICAL CLUSTERING APPROACH 35
2.8 HEURISTIC METHODS 35
2.9 GRAPH / NETWORK-BASED METHODS 38 2.10 MATHEMATICAL PROGRAMMING-BASED MODELS 39 2.11 MULTI OBJECTIVES/MULTI CRITERIA-BASED MODELS 44 2.12 GENETIC ALGORITHM-BASED METHODS 46 2.13 METHODS INVOLVING COMBINATORIAL AND OTHER
APPROACHES 46
2.14 NEURAL NETWORK-BASED METHODS 50 2.15 FUZZY MATHEMATICS-BASED METHODS 51 2.16 KNOWLEDGE-BASED AND EXPERT SYSTEM-BASED
METHODS 54
2.17 SIMULATION-BASED METHODS 54 2.18 UNCERTAINTY-BASED METHODS 56 2.19 MODELS DEALING WITH EFJBM 58 2.20 STATE OF ART AND SURVEY PAPERS 60 2.21 EVALUATION OF CMS DESIGNS 63 2.22 INDUSTRIAL APPLICATIONS OF CMS 67
2.23 GENERAL OBSERVATIONS 69
2.24 MOTIVATION FOR THE PRESENT RESEARCH 73
2.25 SUMMARY 74
CHAPTER 3: DESIGN OF CMS: AN IMPROVED ALGORITHM 75-91
3.1 INTRODUCTION 75
3.2 NOTATION 76
3.2.1 The Algorithm (RI Algorithm) 78 3.2.2 Recombination Index (Spq) 80 3.2.3 Summary of Procedure for RI Algorithm 81
3.3 NUMERICAL ILLUSTRATION 82
3.4 DISCUSSIONS 89
3.5. CONCLUSIONS 90
VIII
CHAPTER 4: DESIGN OF CMS: A CHANCE CONSTRAINED
PROGRAMMING APPROACH 92-116
4.1 INTRODUCTION 92
4.2 ISSUE OF INFORMATIONAL VAGUENESS IN CMS
DESIGN PARAMETERS 93
4.3 MODELING CMS. WITH CHANCE CONSTRAINED
PROGRAMMING APPROACH 95
4.3.1 Model Formulation 96
4.3.2 Conversion of a Chance Constrained Formulation into
the Deterministic Equivalent 98
4.4 ILLUSTRATIVE EXAMPLES 99
4.4.1 Problem 4.1 102
4.4.2 Problem 4.2 103
4.5 RESULTS 103
4.5.1 Results of Problem 4.1 103 4.5.2 Results of Problem 4.2 107
4.6 DISCUSSIONS 111
4.7 CONCLUSIONS 116
CHAPTER 5: DESIGN OF CMS: A RANGE OBJECTIVE FUNCTION
APPROACH 117-139
5.1 INTRODUCTION 117
5.2 INTERVAL OBJECTIVE FUNCTION 119 5.2.1 Interval Nomenclature 120 5.2.2 Order Relation for Minimization Problem 121 5.2.3 Minimisation of Interval Objective Function 122 5.3 RISK BY GAIN RATIO (0) IN THE ANALYSIS OF
UNCERTAINTY IN RANGE ESTIMATE 123 5.4 MODELING CMS WITH INTERVAL OBJECTIVE
FUNCTION 123
5.4.1 Model Formulation 124
5.4.2 The Model 125
5.4.3 Conversion of Interval Objective Function into Multi
Objective Model 126
5.5 ILLUSTRATIVE EXAMPLE 127
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5.6 RESULTS AND DISCUSSIONS 128
5.7 CONCLUSIONS 139
CHAPTER 6: DESIGN OF CMS: A FUZZY PROGRAMMING
APPROACH 140-160
6.1 INTRODUCTION 140
6.2 MODELLING CMS WITH FUZZY PARAMETERS 140 6.2.1 Membership Function 142 6.2.2 Crisp LP Formulation 143 6.3 APPLICATION OF [f-LP1] FOR CMS MODELLING 143 6.3.1 Application of Model [f-LP3] to CMS Modelling 145 6.3.2 Illustrative Example of [f-LP3] 146 6.4 EXTENSION OF [f-LP3] TO MULTI OBJECTIVE CMS
MODELLING 149
6.4.1 Illustration of [f-MOLP1] 153 6.4.1.1 Solution Methodology 153 6.5 COMPARISON WITH GOAL-PROGRAMMING
FORMULATION 155
6.6 DISCUSSIONS ON FUZZY MODELS 156 6.6.1 Discussions on Model [f-LPI] 157 6.6.2 Discussions on Model [f-MOLP1] 157 6.6.3 General Discussions on Two Fuzzy Models 158
6.7 CONCLUSIONS 160
CHAPTER 7: EVALUATION OF CMS DESIGN: AN AHP FRAMEWORK 161-181
7.1 INTRODUCTION 161
7.2 ISSUE RELATED TO EVALUATION OF OUTPUT OF A
PATTERN GENERATING ALGORITHM 167 7.3 ISSUES RELATED TO OPERATIONAL EFFECTIVENESS
OF DESIGN 169
7.4 ISSUES RELATED TO SUBJECTIVE CRITERIA 169 7.5 ISSUES RELATED TO MULTI CRITERIA EVALUATION
FRAMEWORK 170
7.6 THE EVALUATION FRAMEWORK 170
7.6.1 Analytic Hierarchy Process (AHP) Approach 172
7.6.2 Steps in AHP 174
7.7 APPLICATION OF AHP IN EVALUATION OF CMS DESIGN
7.7.1 Selection of Weights 7.7.2 Consistency Ratio (CR) 7.8 RESULTS AND DISCUSSION 7.9 CONCLUSIONS
174 175 177 179 181
CHAPTER 8: CONCLUSIONS, LIMITATIONS AND SCOPE FOR
FUTURE WORK 182-192
8.1 INTRODUCTION 182
8.2 SUMMARY OF THE FINDINGS 182
8.3 LIMITATIONS OF THE RESEARCH WORK 185 8.4 MAJOR CONTRIBUTIONS OF THIS RESEARCH 190
8.5 SCOPE FOR FUTURE WORK 191
REFERENCES 193-227
APPENDICES 228-231
Al ROC ALGORITHM (King and Nakomchai, 1982) 228 A2 MODROC ALGORITHM (Chandrasekharan and Rajagopalan,
1986 a) 229
A3 SI ALGORITHM (Wu and Chang, 1990) 230 A4 LINEARISATION SCHEME (Glover and Woolsey, 1973) 231
LIST OF PUBLICATIONS FROM RESEARCH 232
BIOGRAPHICAL PROFILE OF RESEARCHER 233
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