Practical Goal Programming / Edition 1

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Practical Goal Programming is intended to allow academics and practitioners to be able to build effective goal programming models, to detail the current state of the art, and to lay the foundation for its future development and continued application to new and varied fields. Suitable as both a text and reference, its nine chapters first provide a brief history, fundamental definitions, and underlying philosophies, and then detail the goal programming variants and define them algebraically. Chapter 3 details the step-by-step formulation of the basic goal programming model, and Chapter 4 explores more advanced modeling issues and highlights some recently proposed extensions.

Chapter 5 then details the solution methodologies of goal programming, concentrating on computerized solution by the Excel Solver and LINGO packages for each of the three main variants, and includes a discussion of the viability of the use of specialized goal programming packages. Chapter 6 discusses the linkages between Pareto Efficiency and goal programming. Chapters 3 to 6 are supported by a set often exercises, and an Excel spreadsheet giving the basic solution of each example is available at an accompanying website.

Chapter 7 details the current state of the art in terms of the integration of goal programming with other techniques, and the text concludes with two case studies which were chosen to demonstrate the application of goal programming in practice and to illustrate the principles developed in Chapters 1 to 7. Chapter 8 details an application in healthcare, and Chapter 9 describes applications in portfolio selection.

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Table of Contents

1 History and Philosophy of Goal Programming 1

1.1 Terminology 2

1.2 Underlying Philosophies 6

1.2.1 Satisficing 6

1.2.2 Optimising 7

1.2.3 Ordering or Ranking 7

1.2.4 Balancing 8

2 Goal Programming Variants 11

2.1 Generic Goal Programme 11

2.2 Distance Metric Based Variants 13

2.2.1 Lexicographic Goal Programming 13

2.2.2 Weighted Goal Programming 15

2.2.3 Chebyshev Goal Programming 15

2.3 Decision Variable and Goal-Based Variants 16

2.3.1 Fuzzy Goal Programming 17

2.3.2 Integer and Binary Goal Programming 20

2.3.3 Fractional Goal Programming 22

3 Formulating Goal Programmes 23

3.1 Formulating Goals and Setting Target Levels 23

3.1.1 Example 24

3.1.2 Resumption of Example 26

3.2 Variant Choice 28

3.3 Lexicographic Variant 28

3.3.1 Good Modelling Practice for the Lexicographic Variant 32

3.4 Weighted Variant 34

3.5 Normalisation 34

3.5.1 Percentage Normalisation 34

3.5.2 Zero-One Normalisation 36

3.5.3 Euclidean Normalisation 38

3.6 Preferential Weight Choice 39

3.7 Chebyshev Variant 41

3.8 Summary – Ten Rules for Avoiding Pitfalls in Goal Programming Formulations 42

3.9 Exercises 42

4 Advanced Topics in Goal Programming Formulation 53

4.1 Axioms 53

4.2 Non-standard Preference Function Modelling 54

4.2.1 Interval Goal Programming 63

4.2.2 Other Paradigms for Modelling Non-standard Preferences 63

4.3 Extended Lexicographic Goal Programming 64

4.4 Meta-goal Programming 66

4.5 Weight Space Analysis 70

4.6 Exercises 72

5 Solving and Analysing Goal Programming Models 77

5.1 Computerised Solution of Weighted Goal Programming Example 77

5.1.1 Solution via Excel Solver 77

5.1.2 Solution via LINGO 78

5.2 Computerised Solution of Chebyshev Goal Programming Example 79

5.2.1 Solution via Excel Solver 79

5.2.2 Solution via LINGO 80

5.3 Computerised Solution of Lexicographic Goal Programming Examples 81

5.3.1 Theory of Solving Lexicographic Goal Programmes 81

5.3.2 Solution via Excel Solver 83

5.3.3 Solution via LINGO 85

5.4 Solution of Other Goal Programming Variants 87

5.4.1 Fuzzy Goal Programmes 87

5.4.2 Integer and Binary Goal Programmes 87

5.4.3 Non-linear Goal Programmes 88

5.4.4 Meta and Extended Lexicographic Goal Programmes 88

5.5 Analysis of Goal Programming Results 89

5.6 Specialist Goal Programming Packages – Past and Future 90

5.7 Exercises 91

6 Detection and Restoration of Pareto Inefficiency 95

6.1 Pareto Definitions 97

6.2 Pareto Inefficiency Detection 98

6.2.1 Continuous Weighted and Lexicographic Variants 98

6.2.2 Integer and Binary Variants 100

6.3 Restoration of Pareto Efficiency 102

6.4 Detection and Restoration of Chebyshev Goal Programmes 106

6.5 Detection and Restoration of Non-linear Goal Programmes 109

6.6 Conclusion 110

6.7 Exercises 110

7 Trend of Integration and Combination of Goal Programming 113

7.1 Goal Programming as a Statistical Tool 113

7.2 Goal Programming as a Multi-criteria Decision Analysis Tool 114

7.2.1 Goal Programming and Other Distance Metric Based Approaches 115

7.2.2 Goal Programming and Pairwise Comparison Techniques 116

7.2.3 Goal Programming and Other MCDM/A Techniques 119

7.3 Goal Programming and Artificial Intelligence/Soft Computing 121

7.3.1 Goal Programming and Pattern Recognition 121

7.3.2 Goal Programming and Fuzzy Logic 123

7.3.3 Goal Programming and Meta-heuristic Methods 124

7.4 Goal Programming and Other Operational Research Techniques 125

7.4.1 Goal Programming and Data Envelopment Analysis 126

7.4.2 Goal Programming and Simulation 126

8 Case Study: Application of Goal Programming in Health Care 129

8.1 Context of Application Area 129

8.2 Initial Goal Programming Models 130

8.2.1 Data Collection 130

8.2.2 Model Description 131

8.2.3 Solution and Analysis 137

8.3 Combined Simulation and Goal Programming Model 138

8.3.1 Further Data collection for the Simulation Model 139

8.3.2 Simulation Model Description 140

8.3.3 Model Refinement, Verification, and Validation 143

8.3.4 What/If Scenario Investigation 143

8.3.5 Post-goal Programme 146

8.4 Conclusions 149

9 Case Study: Application of Goal Programming in Portfolio Selection 151

9.1 Overview of Issues and Objectives in Multi-objective Portfolio Selection 151

9.1.1 Lexicographic Goal Programming in Portfolio Selection Models 153

9.1.2 Chebyshev Goal Programming in Portfolio Selection Models 153

9.1.3 Fuzzy Goal Programming in Portfolio Selection Models 154

9.2 Multi-phase Portfolio Models 155

9.2.1 The Two-Phase Model of Tamiz et al. 155

9.2.2 The Three-Phase Model of Perez et al. 158

9.3 Summary 160

References 161

Index 169

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