Multi-level Decision Making-Models Methods and Applications-BOOK


Part I Bi-level Decision Making
1 Decision Making and Decision Support Systems. . . . . . . . . . . . . . 3
1.1 Organizational Decision Making . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Classification for Decision Problems and Techniques . . . . . . . 4
1.2.1 Decision Problem Classification . . . . . . . . . . . . . . . . 4
1.2.2 Decision Support Technique Classification . . . . . . . . . 5
1.3 Main Decision Support Techniques . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Mathematical Programming . . . . . . . . . . . . . . . . . . . 7
1.3.2 Multi-criteria Decision Making . . . . . . . . . . . . . . . . . 8
1.3.3 Case-Based Reasoning. . . . . . . . . . . . . . . . . . . . . . . 10
1.3.4 Data Warehouse and Data Mining. . . . . . . . . . . . . . . 11
1.3.5 Decision Tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.6 Fuzzy Sets and Systems. . . . . . . . . . . . . . . . . . . . . . 13
1.4 Decision Support Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.1 Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.2 Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.3 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5 DSS Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5.1 Model-Driven DSS . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5.2 Data-Driven DSS . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5.3 Knowledge-Driven DSS or Intelligent DSS . . . . . . . . 18
1.5.4 Group DSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.5 Web-Based DSS. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 DSS Software Illustration. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.6.1 Case 1: Decider . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.6.2 Case 2: A DSS for Ore Blending Cost Optimization
of Blast Furnaces . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
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2 Optimization Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1 Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 Non-linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1 Varieties of Non-linear Programming . . . . . . . . . . . . 29
2.3.2 Theories and Optimality Conditions
of Non-linear Programming . . . . . . . . . . . . . . . . . . . 30
2.3.3 Methods for Solving Non-linear Programming
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Multi-objective Programming . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1 Multi-objective Programming Model . . . . . . . . . . . . . 32
2.4.2 Multi-objective Linear Programming Methods . . . . . . 34
2.4.3 A Case-Based Example . . . . . . . . . . . . . . . . . . . . . . 36
2.5 Goal Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 Stackelberg Game Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.6.1 Stackelberg Game and Bi-level Programming . . . . . . . 42
2.6.2 Stackelberg Game and Nash Game . . . . . . . . . . . . . . 43
2.6.3 Applications of Stackelberg Games . . . . . . . . . . . . . . 43
2.7 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . 44
2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3 Bi-level Programming Models and Algorithms . . . . . . . . . . . . . . . 47
3.1 Bi-level Programming Model . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Solution Theories for Linear Bi-level Programming. . . . . . . . . 49
3.3 Kth-Best Algorithm for Linear Bi-level Programming . . . . . . . 53
3.4 Kuhn-Tucker Approach for Linear Bi-level Programming . . . . 55
3.5 Branch-and-Bound Algorithm for Linear Bi-level
Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6 Penalty Function Method for Linear Bi-level Programming . . . 59
3.7 Multi-level Programming Model . . . . . . . . . . . . . . . . . . . . . . 61
3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Part II Multi-level Multi-follower Decision Making
4 Bi-level Multi-follower Decision Making. . . . . . . . . . . . . . . . . . . . 65
4.1 Problem Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Framework for Bi-level Multi-follower Decision Making . . . . . 66
4.3 Bi-level Multi-follower Decision Models . . . . . . . . . . . . . . . . 68
4.3.1 BLMF Decision Entity-Relationship Diagram . . . . . . . 68
4.3.2 Linear BLMF Decision Models . . . . . . . . . . . . . . . . 68
4.4 Uncooperative Bi-level Multi-follower Decision Making . . . . . 76
4.4.1 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.2 Theoretical Properties . . . . . . . . . . . . . . . . . . . . . . . 77
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4.4.3 Uncooperative BLMF Kth-Best Algorithm . . . . . . . . . 79
4.4.4 Uncooperative BLMF Kuhn-Tucker Approach . . . . . . 83
4.5 Semi-cooperative Bi-level Multi-follower Decision Making . . . 85
4.5.1 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5.2 Theoretical Properties . . . . . . . . . . . . . . . . . . . . . . . 87
4.5.3 Semi-cooperative BLMF Kth-Best Algorithm . . . . . . . 87
4.5.4 Semi-cooperative BLMF Kuhn-Tucker Approach . . . . 89
4.6 Reference-Uncooperative Bi-level Multi-follower Decision
Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6.1 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6.2 Theoretical Properties . . . . . . . . . . . . . . . . . . . . . . . 93
4.6.3 Reference-Uncooperative BLMF Kth-Best
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6.4 Reference-Uncooperative BLMF Kuhn-Tucker
Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Bi-level Multi-leader Decision Making . . . . . . . . . . . . . . . . . . . . . 105
5.1 Problem Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2 Framework for Bi-level Multi-leader Decision Making . . . . . . 106
5.3 Linear Bi-level Multi-leader Decision Models. . . . . . . . . . . . . 107
5.4 Concepts and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5 Generalized Nash Equilibrium Solution . . . . . . . . . . . . . . . . . 114
5.6 BLML Particle Swarm Optimization Algorithm . . . . . . . . . . . 115
5.7 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6 Tri-level Multi-follower Decision Making . . . . . . . . . . . . . . . . . . . 121
6.1 Problem Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.2 Basic Tri-level Decision Models . . . . . . . . . . . . . . . . . . . . . . 123
6.3 Tri-level Multi-follower Decision Framework . . . . . . . . . . . . . 125
6.3.1 TLMF Decision Concepts . . . . . . . . . . . . . . . . . . . . 125
6.3.2 TLMF Decision Problem Classification . . . . . . . . . . . 126
6.3.3 TLMF Decision Framework . . . . . . . . . . . . . . . . . . . 127
6.3.4 TLMF Decision Entity-Relationship Diagrams . . . . . . 127
6.4 Tri-level Multi-follower Decision Models. . . . . . . . . . . . . . . . 133
6.4.1 General Model for TLMF Decision . . . . . . . . . . . . . . 133
6.4.2 Typical Standard Models for TLMF Decision. . . . . . . 134
6.4.3 Hybrid TLMF Decision Models . . . . . . . . . . . . . . . . 142
6.5 Case Studies for TLMF Decision Modeling . . . . . . . . . . . . . . 144
6.5.1 Case 1: S28 Model . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.5.2 Case 2: S27 Model . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.5.3 Case 3: S54 Model . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.5.4 Case 4: Hybrid of S41, S45 and S48 Models . . . . . . . 150
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6.6 Tri-level Decision Solution Methods . . . . . . . . . . . . . . . . . . . 151
6.6.1 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.6.2 Theoretical Properties . . . . . . . . . . . . . . . . . . . . . . . 153
6.6.3 Tri-level Kth-Best Algorithm . . . . . . . . . . . . . . . . . . 155
6.6.4 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . 157
6.7 Tri-level Multi-follower Decision Solution Methods . . . . . . . . 159
6.7.1 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.7.2 Theoretical Properties . . . . . . . . . . . . . . . . . . . . . . . 162
6.7.3 TLMF Kth-Best Algorithm. . . . . . . . . . . . . . . . . . . . 165
6.7.4 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . 167
6.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Part III Fuzzy Multi-level Decision Making
7 Fuzzy Bi-level Decision Making . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.1 Problem Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.2 Fuzzy Sets and Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.2.1 Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
7.2.2 Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.3 Fuzzy Bi-level Decision Models . . . . . . . . . . . . . . . . . . . . . . 183
7.4 Fuzzy Approximation Kth-Best Algorithm . . . . . . . . . . . . . . . 188
7.4.1 Property and Algorithm . . . . . . . . . . . . . . . . . . . . . . 188
7.4.2 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . 197
7.5 Fuzzy Multi-Follower Approximation Kth-Best Algorithm . . . . 201
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8 Fuzzy Multi-objective Bi-level Decision Making . . . . . . . . . . . . . . 207
8.1 Problem Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
8.2 Fuzzy Multi-objective Bi-level Decision Model . . . . . . . . . . . 208
8.3 Fuzzy Approximation Kuhn-Tucker Approach . . . . . . . . . . . . 219
8.3.1 Fuzzy Approximation Kuhn-Tucker Approach . . . . . . 220
8.3.2 A Case-Based Example . . . . . . . . . . . . . . . . . . . . . . 220
8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
9 Fuzzy Multi-objective Bi-level Goal Programming . . . . . . . . . . . . 229
9.1 Problem Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
9.2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
9.3 Fuzzy Bi-level Goal-Programming Algorithm . . . . . . . . . . . . . 241
9.4 A Numerical Example and Experiments. . . . . . . . . . . . . . . . . 242
9.4.1 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . 242
9.4.2 Experiments and Evaluation . . . . . . . . . . . . . . . . . . . 246
9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
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Part IV Rule-set-based Bi-level Decision Making
10 Rule-Set-Based Bi-level Decision Making . . . . . . . . . . . . . . . . . . . 251
10.1 Problem Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
10.2 Information Tables and Rule-Sets . . . . . . . . . . . . . . . . . . . . . 252
10.2.1 Information Tables . . . . . . . . . . . . . . . . . . . . . . . . . 252
10.2.2 Formulas and Rules . . . . . . . . . . . . . . . . . . . . . . . . 253
10.2.3 Decision Rule Set Function . . . . . . . . . . . . . . . . . . . 255
10.2.4 Rule Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
10.2.5 Rules Comparison. . . . . . . . . . . . . . . . . . . . . . . . . . 258
10.3 Rule-Set-Based Bi-level Decision Model . . . . . . . . . . . . . . . . 260
10.3.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
10.3.2 Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
10.3.3 Rule-Set-Based Bi-level Decision Model . . . . . . . . . . 261
10.4 Rule-Set-Based Bi-level Decision Modeling Approach. . . . . . . 262
10.5 Rule-Set-Based Bi-level Decision Solution Algorithms . . . . . . 264
10.5.1 Concepts and Properties. . . . . . . . . . . . . . . . . . . . . . 264
10.5.2 Rule-Based-Based Solution Algorithm. . . . . . . . . . . . 265
10.5.3 Transformation-Based Solution Algorithm . . . . . . . . . 268
10.6 A Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
10.6.1 Problem Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 273
10.6.2 Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
10.7 Experiments and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 283
10.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

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Abbreviations
AHP