Practical Goal Programming (eBook)

Preface 8
Contents 12
1 History and Philosophy of Goal Programming 15
1.1 Terminology 16
1.2 Underlying Philosophies 20
1.2.1 Satisficing 20
1.2.2 Optimising 21
1.2.3 Ordering or Ranking 21
1.2.4 Balancing 22
2 Goal Programming Variants 24
2.1 Generic Goal Programme 24
2.2 Distance Metric Based Variants 26
2.2.1 Lexicographic Goal Programming 26
2.2.2 Weighted Goal Programming 28
2.2.3 Chebyshev Goal Programming 28
2.3 Decision Variable and Goal-Based Variants 29
2.3.1 Fuzzy Goal Programming 30
2.3.2 Integer and Binary Goal Programming 33
2.3.3 Fractional Goal Programming 35
3 Formulating Goal Programmes 36
3.1 Formulating Goals and Setting Target Levels 36
3.1.1 Example 37
3.1.2 Resumption of Example 39
3.2 Variant Choice 40
3.3 Lexicographic Variant 41
3.3.1 Good Modelling Practice for the Lexicographic Variant 45
3.4 Weighted Variant 47
3.5 Normalisation 47
3.5.1 Percentage Normalisation 47
3.5.2 Zero--One Normalisation 49
3.5.3 Euclidean Normalisation 51
3.6 Preferential Weight Choice 51
3.7 Chebyshev Variant 54
3.8 Summary Ten Rules for Avoiding Pitfalls in Goal Programming Formulations 54
3.9 Exercises 55
Example 1 -- Conversion from Linear to Goal Programming 55
Example 2 -- On-line Retailer 55
Example 3 -- Production Planning 57
Example 4 -- Employee Scheduling 58
Example 5 -- Diet Planning 58
Example 6 -- Travelling Salesperson 60
Example 7 -- Downstream Oil Industry 60
Example 8 -- Macro Economics 60
Example 9 -- Budget Planning 60
Example 10 -- Healthcare Planning 60
4 Advanced Topics in Goal Programming Formulation 65
4.1 Axioms 65
4.2 Non-standard Preference Function Modelling 66
Type 1: Increase in Per Unit Penalty (Penalty Function) 67
Type 2: Decrease in Per Unit Penalty (Reverse Penalty Function) 70
Type 3: Single Increase in Penalty (Discontinuity in Preference) 71
Type 4: Non-linearity 74
Model Growth 74
Objective Bounds 74
4.2.1 Interval Goal Programming 75
4.2.2 Other Paradigms for Modelling Non-standard Preferences 75
4.3 Extended Lexicographic Goal Programming 76
4.4 Meta-goal Programming 78
Example 79
4.5 Weight Space Analysis 82
4.6 Exercises 84
5 Solving and Analysing Goal Programming Models 88
5.1 Computerised Solution of Weighted Goal Programming Example 88
5.1.1 Solution via Excel Solver 88
5.1.2 Solution via LINGO 89
5.2 Computerised Solution of Chebyshev Goal Programming Example 89
5.2.1 Solution via Excel Solver 90
5.2.2 Solution via LINGO 91
5.3 Computerised Solution of Lexicographic Goal Programming Examples 92
5.3.1 Theory of Solving Lexicographic Goal Programmes 92
5.3.2 Solution via Excel Solver 94
5.3.3 Solution via LINGO 96
5.4 Solution of Other Goal Programming Variants 98
5.4.1 Fuzzy Goal Programmes 98
5.4.2 Integer and Binary Goal Programmes 98
5.4.3 Non-linear Goal Programmes 99
5.4.4 Meta and Extended Lexicographic Goal Programmes 99
5.5 Analysis of Goal Programming Results 99
5.6 Specialist Goal Programming Packages Past and Future 101
5.7 Exercises 101
6 Detection and Restoration of Pareto Inefficiency 106
6.1 Pareto Definitions 108
6.2 Pareto Inefficiency Detection 109
6.2.1 Continuous Weighted and Lexicographic Variants 109
6.2.2 Integer and Binary Variants 111
6.3 Restoration of Pareto Efficiency 113
6.4 Detection and Restoration of Chebyshev Goal Programmes 117
6.5 Detection and Restoration of Non-linear Goal Programmes 120
6.6 Conclusion 121
6.7 Exercises 121
7 Trend of Integration and Combination of Goal Programming 124
7.1 Goal Programming as a Statistical Tool 124
7.2 Goal Programming as a Multi-criteria Decision Analysis Tool 125
7.2.1 Goal Programming and Other Distance Metric Based Approaches 126
7.2.2 Goal Programming and Pairwise Comparison Techniques 127
7.2.2.1 Using the AHP to Determine Goal Programming Preferential Weights 128
7.2.2.2 Using Goal Programming as a Technique to Derive the Weighting Vector in AHP 128
7.2.3 Goal Programming and Other MCDM/A Techniques 130
7.2.3.1 Goal Programming and Interactive Methods 130
7.2.3.2 Goal Programming and A Posteriori Techniques 131
7.2.3.3 Goal Programming and Discrete Choice/Outranking Methods 132
7.3 Goal Programming and Artificial Intelligence/Soft Computing 132
7.3.1 Goal Programming and Pattern Recognition 132
7.3.2 Goal Programming and Fuzzy Logic 134
7.3.3 Goal Programming and Meta-heuristic Methods 135
7.3.3.1 Multi-objective Evolutionary Algorithms 136
7.4 Goal Programming and Other Operational Research Techniques 136
7.4.1 Goal Programming and Data Envelopment Analysis 137
7.4.2 Goal Programming and Simulation 137
8 Case Study: Application of Goal Programming in Health Care 140
8.1 Context of Application Area 140
8.2 Initial Goal Programming Models 141
8.2.1 Data Collection 141
8.2.2 Model Description 142
8.2.2.1 Assumptions 142
8.2.2.2 Decision Variables 143
8.2.2.3 Achievement Function 144
8.2.2.4 Goals 144
8.2.2.5 Constraints 146
8.2.2.6 Sign Restrictions 148
8.2.3 Solution and Analysis 148
8.3 Combined Simulation and Goal Programming Model 149
8.3.1 Further Data collection for the Simulation Model 150
8.3.2 Simulation Model Description 151
8.3.3 Model Refinement, Verification, and Validation 154
8.3.4 What/If Scenario Investigation 154
8.3.4.1 Second Consultant Post-Take Ward Round 156
8.3.5 Post-goal Programme 157
8.3.5.1 Decision Variables 158
8.3.5.2 Data 158
8.3.5.3 Algebraic Goal Programming Model 158
8.4 Conclusions 160
9 Case Study: Application of Goal Programming in Portfolio Selection 161
9.1 Overview of Issues and Objectives in Multi-objective Portfolio Selection 161
9.1.1 Lexicographic Goal Programming in Portfolio Selection Models 163
9.1.2 Chebyshev Goal Programming in Portfolio Selection Models 163
9.1.3 Fuzzy Goal Programming in Portfolio Selection Models 164
9.2 Multi-phase Portfolio Models 164
9.2.1 The Two-Phase Model of Tamiz et al. 165
Phase 1 165
Phase 2 166
9.2.2 The Three-Phase Model of Perez et al. 168
Phase 1 169
Phase 2 169
Phase 3 169
9.3 Summary 169
References 171
Index 179