v
Contents
Preface.......................................................................................................................xi
Biographical Note .................................................................................................. xiii
Chapter 1 Introduction ..........................................................................................1
1.1 Prole of Multiple Criterion Decision Making .........................1
1.2 Historical Development of Multiple Attribute Decision
Making ......................................................................................3
1.3 Historical Development of Multiple Objective Decision
Making ......................................................................................6
1.4 Introduction to Fuzzy Sets .........................................................8
1.4.1 Basic Concepts .............................................................8
1.4.2 Fuzzy Arithmetic Operations .....................................10
1.4.2.1 Extension Principle .....................................10
1.4.2.2 α-Cut Arithmetic ........................................ 11
1.4.3 Ranking Fuzzy Numbers ........................................... 11
1.5 Outline of the Book ................................................................. 12
SECTION I Concepts and Theory of Multi-
Objective Decision Making
Chapter 2 Multi-Objective Evolutionary Algorithms ......................................... 17
2.1 Concepts of Genetic Algorithms ............................................. 17
2.2 GA Procedures ........................................................................ 18
2.2.1 String Representation ................................................. 18
2.2.2 Population Initialization ............................................. 18
2.2.3 Fitness Computation ................................................... 19
2.2.4 Genetic Operators....................................................... 19
2.2.4.1 Selection ...................................................... 19
2.2.4.2 Crossover ....................................................20
2.2.4.3 Mutation ......................................................20
2.3 Multi-Objective Evolutionary Algorithms (MOEAs) .............. 21
2.3.1 Numerical Example ....................................................22
Chapter 3 Goal Programming .............................................................................25
3.1 Goal Setting ............................................................................. 25
3.2 Weighted Goal Programming .................................................26
3.3 Lexicography Goal Programming ...........................................28
vi Contents
3.4 Min–Max (Tchebycheff) Goal Programming ......................... 30
3.5 Fuzzy Goal Programming ....................................................... 31
Chapter 4 Compromise Solution and TOPSIS ....................................................37
4.1 Compromise Solution .............................................................. 37
4.2 TOPSIS for MODM .................................................................40
4.3 Fuzzy Compromise Solution and TOPSIS ..............................42
Chapter 5 De Novo Programming and Changeable Parameters ........................47
5.1 De Novo Programming ........................................................... 47
5.2 De Novo Programming by Genetic Algorithms ...................... 51
5.3 De Novo Programming by Compromise Solution ..................52
5.4 Extensions of De Novo Programming .....................................54
5.5 MOP with Changeable Parameters ..........................................56
Model 5.1: MOP with Changeable Budgets ............................57
Model 5.2: MOP with Changeable Objective Coefcients .....59
Model 5.3: MOP with Changeable Technological
Coefcients............................................................60
Chapter 6 Multi-Stage Programming .................................................................65
6.1 Dynamic Programming ...........................................................65
6.2 Application of Multi-Stage Problem: Competence Sets ..........68
6.3 Fuzzy Multi-Stage Multi-Objective Competence Sets ............70
Appendix ............................................................................................ 74
Chapter 7 Multi-Level Multi-Objective Programming ....................................... 75
7.1 Bi-Level Programming ............................................................75
7.2 Multiple Level Programming ..................................................77
7.3 Fuzzy Programming for Multi-Level Multi-Objective
Programming ...........................................................................78
Chapter 8 Data Envelopment Analysis ...............................................................83
8.1 Traditional DEA ......................................................................83
8.2 Network DEA ..........................................................................87
8.2.1 Input-Oriented Efciency ...........................................89
8.2.2 Output-Oriented Efciency ........................................90
8.2.3 Non-Oriented Efciency ............................................90
8.3 Fuzzy Multi-Objective Programming (FMOP) to DEA .........94
8.3.1 Model 1 .......................................................................94
8.3.2 Model 2 .......................................................................96
viiContents
SECTION II Applications of Multi-Objective
Decision Making
Chapter 9 Motivation and Resource Allocation for Strategic Alliances
through the De Novo Perspective ..................................................... 101
9.1 Motivations for Strategic Alliances ....................................... 102
9.1.1 Transaction Cost Theory .......................................... 102
9.1.2 Resource-Based View .............................................. 103
9.2 Problems of Resource Allocation .......................................... 103
9.3 De Novo Perspective of Strategic Alliances ..........................105
9.4 Numerical Example ............................................................... 106
9.5 Discussion ..............................................................................109
9.6 Conclusions ............................................................................ 110
Chapter 10 Choosing Best Alliance Partners and Allocating Optimal
Alliance Resources Using Fuzzy Multi-Objective Dummy
Programming Model ........................................................................ 113
10.1 Review of Strategic Alliances ............................................... 114
10.2 Fuzzy Multiple Objective Dummy Programming ................. 116
10.2.1 Joint Venture Model ................................................. 118
10.2.2 M&A Model ............................................................. 119
10.3 Numerical Example ............................................................... 120
10.4 Discussion ..............................................................................123
10.5 Conclusions ............................................................................124
Chapter 11 Multiple-Objective Planning for Supply Chain Production and
Distribution Model: Bicycle Manufacturer ......................................125
11.1 Literature on Supply Chain and Multi-Objective
Programming for Production and Distribution .....................126
11.1.1 Relevant Supply Chain Literature ............................ 126
11.1.2 Multi-Objective and Fuzzy Multi-Objective
Programming ...........................................................127
11.1.2.1 Multi-Objective Compromise
Programming ............................................127
11.1.2.2 Weighted Multi-Objective Programming ... 128
11.1.2.3 Fuzzy Multi-Objective Programming ...... 129
11.1.2.4 Weighted Fuzzy Multi-Objective
Programming ............................................129
11.1.2.5 Two-Phase Fuzzy Multi-Objective
Programming ............................................130
11.2 Establishing Model for Bicycle Supply Chain .......................130
viii Contents
11.2.1 Basic Assumptions, Denitions, and
Establishment of Model............................................130
11.2.2 Model Construction .................................................. 131
11.2.2.1 Objective 1: Maximize Total Prot and
Competitiveness ........................................ 131
11.2.2.2 Objective 2: Maximize Level of
Customer Service Quality per Period ....... 133
11.2.3 Model Constraints .................................................... 133
11.2.3.1 Raw Material Constraint .......................... 133
11.2.3.2 Productivity Constraint .............................134
11.2.3.3 Inventory Constraint ................................. 134
11.2.3.4 Relationship of Product Distribution
and Demand .............................................. 135
11.2.3.5 Non-Negative Constraint .......................... 135
11.3 Real Empirical Case of a Bicycle Manufacturer ................... 135
11.3.1 Problem Description and Denitions ....................... 135
11.3.2 Results and Analysis ................................................136
11.3.3 Sensitivity Analyses and Discussions ...................... 139
11.4 Conclusions and Recommendations ...................................... 140
Appendix A: Max–Min Operation ................................................... 142
A.1 Determination of Ceiling and Bottom Limits of
Objectives and Constraint Equations ....................... 142
A.2 Establishment of Membership Function .................. 142
A.3 Setting Membership Function for Decision
Making Set μ
D
(x) ...................................................... 142
A.4 Turning Multiple Objectives into Single
Objective for Resolution ........................................... 143
Appendix B: Concept of Weighted Fuzzy Multi-Objective
Programming ................................................................................... 143
Chapter 12 Fuzzy Interdependent Multi-Objective Programming ..................... 145
12.1 Interdependence with Objectives........................................... 146
12.2 Fuzzy Interdependent Multi-Objective Programming .......... 148
12.3 Numerical Example ............................................................... 155
12.4 Discussion .............................................................................. 157
12.5 Conclusions ............................................................................158
Appendix .......................................................................................... 159
Chapter 13 Novel Algorithm for Uncertain Portfolio Selection ......................... 161
13.1 Possibilistic Regression ......................................................... 162
13.2 Mellin Transformation ........................................................... 163
13.3 Numerical Example ............................................................... 165
13.4 Discussion .............................................................................. 167
13.5 Conclusions ............................................................................ 170
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