The Doctor Rostering Problem - Asser Fahrenholz

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Contents Preface i Abstract ii Resumé iii Acknowledgements iv List of Figures viii List of Tables ix List of Algorithms x 1 Introduction 1 1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 The Doctor Rostering Problem 3 2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 The staff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Shift types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Rolling Days Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 A mathematical model for the DRP 8 3.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Hard constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Soft constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4 The objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4.1 Problem size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4 Solving the DRP 15 4.1 DRP complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Exact methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.3 Heuristics for the DRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 v
Contents vi 4.3.1 A construction heuristic . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3.2 Neighborhoods and Local Search . . . . . . . . . . . . . . . . . . . 20 4.3.3 The GRASP metaheuristic . . . . . . . . . . . . . . . . . . . . . . 23 4.3.4 The Simulated Annealing metaheuristic . . . . . . . . . . . . . . . 25 4.3.5 Heuristic bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.4 Heuristic implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.4.1 The data structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.4.2 A partial enumeration . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4.3 Construction heuristic . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.4.4 Metaheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.4.5 Implementation optimisations . . . . . . . . . . . . . . . . . . . . . 30 5 Optimal solution 31 5.1 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6 The DRP Program 34 6.1 The user . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6.2 The Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . 35 6.2.1 Measuring the quality of the solution . . . . . . . . . . . . . . . . . 40 6.3 End user feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6.4 From prototype to release candidate . . . . . . . . . . . . . . . . . . . . . 41 7 Metaheuristic tests 42 7.1 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 7.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 7.2.1 Instance parameter effects . . . . . . . . . . . . . . . . . . . . . . . 44 7.2.2 Metaheuristic parameter effects . . . . . . . . . . . . . . . . . . . . 46 7.2.3 Metaheuristic performance . . . . . . . . . . . . . . . . . . . . . . 48 7.3 Test conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 8 Future considerations 53 8.1 User-added rules - relation/logic of shifts . . . . . . . . . . . . . . . . . . . 53 8.2 Neighborhood delta function and feasibility . . . . . . . . . . . . . . . . . 54 8.3 GRASP learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 8.3.1 GRASP stop criterion . . . . . . . . . . . . . . . . . . . . . . . . . 55 8.4 SA extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 9 Conclusion 57 A Implementation 59 A.1 Neighborhoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 A.1.1 Inversion neighborhood . . . . . . . . . . . . . . . . . . . . . . . . 59 A.1.2 Rotation neighborhood . . . . . . . . . . . . . . . . . . . . . . . . 60 A.2 Construction heuristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 A.3 GRASP metaheuristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 A.4 Simulated Annealing metaheuristic . . . . . . . . . . . . . . . . . . . . . . 67 A.5 Choosing the assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Page 1 and 2: TECHNICAL UNIVERSITY OF DENMARK The
Page 3 and 4: TECHNICAL UNIVERSITY OF DENMARK Abs
Page 5: Acknowledgements Foremost, I would
Page 9 and 10: List of Figures 4.1 The transformat
Page 11 and 12: List of Algorithms 4.1 Adaptive gre
Page 13 and 14: Chapter 1. Introduction and problem
Page 15 and 16: Chapter 2. The Doctor Rostering Pro
Page 17 and 18: Chapter 2. The Doctor Rostering Pro
Page 19 and 20: Chapter 3 A mathematical model for
Page 21 and 22: Chapter 3. The model and design 10
Page 27 and 28: Chapter 4. Solving the DRP 16 it in
Page 29 and 30: Chapter 4. Solving the DRP 18 4.3.1
Page 31 and 32: Chapter 4. Solving the DRP 20 Given
Page 33 and 34: Chapter 4. Solving the DRP 22 Since
Page 35 and 36: Chapter 4. Solving the DRP 24 1. Co
Page 37 and 38: Chapter 4. Solving the DRP 26 decre
Page 39 and 40: Chapter 4. Solving the DRP 28 This
Page 41 and 42: Chapter 4. Solving the DRP 30 Simul
Page 43 and 44: Chapter 5. Optimal solution 32 The
Page 45 and 46: Chapter 6 The DRP Program Through t
Page 47 and 48: Chapter 6. The DRP Program 36 Figur
Page 49 and 50: Chapter 6. The DRP Program 38 of th
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Page 53 and 54: Chapter 7 Metaheuristic tests This
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Chapter 7. Tests, results and discu
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Chapter 8. Future considerations 54
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Chapter 8. Future considerations 56
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Chapter 9. Conclusion 58 The three
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Appendix A. Implementation 60 27 //
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2 Appendix A. Implementation 62 3 i
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Appendix A. Implementation 64 A.3 G
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Appendix A. Implementation 66 97 wh
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Appendix A. Implementation 68 27 su
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Appendix A. Implementation 70 119 P
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Appendix A. Implementation 72 64 br
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Appendix A. Implementation 74 28 Ch
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Appendix B GAMS Model This chapter
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Appendix B. GAMS Model 78 46 c(day
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Appendix B. GAMS Model 80 109 B1( f
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Appendix B. GAMS Model 82 **** REPO
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Appendix B. GAMS Model 84 B.3 The s
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Appendix B. GAMS Model 86 B.3.3 The
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Appendix C. Tests 88 C.1.1 Instance
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Appendix C. Tests 94 JST PZH HP SDA
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Appendix C. Tests 96 JST PZH HP SDA
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Appendix C. Tests 100 Cons 12 Imps
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Appendix C. Tests 102 Test 3 RCL 1
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Appendix C. Tests 116 160 140 120 1
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Bibliography 118 [10] Michael R. Ga
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