New Developments in Multiple Objective and Goal Programming (eBook)

Preface 5
Contents 7
List of Contributors 9
Multi-Objective Stochastic Programming Approaches for Supply Chain Management 11
1 Introduction 11
2 Problem Description 13
3 Multi-Objective Techniques 15
3.1 Goal Attainment Technique 16
3.2 STEM Method 17
3.3 Surrogate Worth Trade-Off (SWT) Method 19
4 Numerical Experiments 20
5 Conclusion 23
References 23
A Review of Goal Programming for Portfolio Selection 25
1 Introduction 25
2 The Use of Multi-Criteria Decision Analysis in Portfolio Selection and the Importance of Goal Programming 26
3 Portfolio Selection Using Goal Programming: Theoretical and Practical Developments 29
4 Goal Programming Variants for Portfolio Selection 32
4.1 Weighted Goal Programming in Portfolio Selection Models 32
4.2 Lexicographic Goal Programming in Portfolio Selection Models 32
4.3 MINMAX (Chebyshev) Goal Programming in Portfolio Selection Models 33
4.4 Fuzzy Goal Programming in Portfolio Selection Models 33
5 Performance Measurement for Portfolios 35
6 Goal Programming and Portfolio Analysis: Other Issues 35
6.1 Issues Concerning Multi-Period Returns 36
6.2 Issues Concerning Extended Factors 37
6.3 Issues Concerning the Measurement of Risk 38
7 Conclusions 40
References 40
A Hypervolume-Based Optimizer for High-Dimensional Objective Spaces 44
1 Motivation 44
2 Related Work 46
3 HypE: Hypervolume Estimation Algorithm for Multiobjective Optimization 47
3.1 Algorithm 48
3.2 Basic Scheme for Mating Selection 49
3.3 Extended Scheme for Environmental Selection 51
3.4 Estimating the Fitness Values Using Monte Carlo Sampling 54
4 Experiments 55
4.1 Experimental Setup 55
4.2 Results 56
5 Conclusion 60
References 61
Minimizing Vector Risk Measures 64
1 Introduction 64
2 Dealing with Vector Risk Functions 66
3 Saddle Point Optimality Conditions 69
4 Applications 75
4.1 Portfolio Choice 75
4.2 Optimal Reinsurance 75
5 Conclusions 76
References 77
Multicriteria Programming Approach to Development Project Design with an Output Goal and a Sustainability Goal 79
1 Introduction 79
2 Methodology 80
2.1 First Objective: Output Maximization 81
2.2 Second Objective: Sustainability 82
2.3 Compromise Solution 82
2.4 Feedback 83
3 An Illustrative Example 83
3.1 First Objective: Output Maximization (Unrelatedto the Pattern) 84
3.2 Second Objective: Sustainability (Related to the Pattern) 84
3.3 Compromise Solution and Final Solution on the Frontier 85
3.4 Comparison of Results 86
4 Concluding Remarks 86
References 87
Automated Aggregation and Omission of Objectives for Tackling Many-Objective Problems 88
1 Introduction 88
2 Objective Reduction by Aggregating Objectives 89
3 A Greedy Heuristic for Finding the Best Aggregation 93
3.1 Main Procedure 93
3.2 Optimally Aggregating Two Objectives 93
4 Experimental Validation 97
4.1 The Influence of Different Weight Choices Within the Optimal Interval 98
4.2 Comparison Between Aggregation and Omission 99
4.3 Objective Reduction During Search 101
5 Application to a Real-World Problem 106
6 Conclusions 107
References 108
Trade-Off Analysis in Discrete Decision Making Problems Under Risk 110
1 Introduction 110
2 Formulation of the Problem 112
3 Point-to-Point Trade-Offs 113
4 The Procedure 115
5 Numerical Example 118
6 Conclusions 121
References 122
Interactive Multiobjective Optimization for 3D HDR Brachytherapy Applying IND-NIMBUS 123
1 Introduction 123
2 Methods 125
2.1 Dose Calculation 125
2.2 Objective Function Formulation 126
2.3 Multiobjective Optimization 127
2.3.1 Multiobjective Optimization Problem 127
2.3.2 The Interactive Multiobjective Optimization Method NIMBUS 128
3 Results 129
3.1 Problem Settings 129
3.2 Fletcher–Suit Applicator Example 130
3.2.1 Interactive Solution Process 130
3.2.2 Comparison and Discussion 133
4 Conclusions 135
References 136
Multicriteria Ranking Using Weights Which Minimizethe Score Range 138
1 Introduction 138
2 Geometric Representation 139
3 Can the Maximin Approach Produce a SingleWinning Alternative? 143
4 Criteria Can be Completely Ignored 143
5 Conclusion 143
References 144
In Search of a European Paper Industry Ranking in Terms of Sustainability by Using Binary Goal Programming 146
1 Introduction 146
2 Sustainability Indicators 147
3 Methodology 150
4 Results and Conclusions 152
References 153
Nurse Scheduling by Fuzzy Goal Programming 155
1 Introduction 155
2 Problem Statement: The Case Study 156
2.1 Legal and Policy Restrictions 157
2.2 Nurses' Preferences 157
3 Fuzzy Goal Programming 158
4 The Fuzzy Goal Programming Model for Scheduling Model 160
4.1 Hard Constraints 160
4.2 Fuzzy Goals 163
5 Results and Discussion 165
6 Concluding Remarks 166
References 167