The Doctor Rostering Problem - Asser Fahrenholz

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Contents vii A.5.1 Shift assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 A.5.2 Permutations of size k chosen from N elements . . . . . . . . . . . 72 A.5.3 Day assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 B GAMS Model 76 B.1 The night, evening and wishes . . . . . . . . . . . . . . . . . . . . . . . . . 76 B.2 The GAMS model and report . . . . . . . . . . . . . . . . . . . . . . . . . 76 B.3 The solved model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 B.3.1 GAMS solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 B.3.2 The best greedy solution . . . . . . . . . . . . . . . . . . . . . . . . 85 B.3.3 The best GRASP solution . . . . . . . . . . . . . . . . . . . . . . . 86 C Tests 87 C.1 Test instances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 C.1.1 Instance 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 C.1.2 Instance 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 C.1.3 Instance 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 C.1.4 Instance 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 C.1.5 Instance 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 C.1.6 Instance 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 C.1.7 Instance 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 C.1.8 Instance 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 C.1.9 Instance 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 C.1.10 Instance 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 C.2 Summarized results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 C.2.1 RCL performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 C.2.2 Enum effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 C.2.3 Weights effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 C.2.4 Iterations effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 C.2.5 Highlighted results . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Bibliography 117
List of Figures 4.1 The transformation chain from SAT to Timetable Design . . . . . . . . . 16 4.2 Various types of RCL parameters . . . . . . . . . . . . . . . . . . . . . . . 19 4.3 Local and global optima . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.4 The rotation principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.5 The inversion principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.6 The implementation of the schedule . . . . . . . . . . . . . . . . . . . . . 27 4.7 Heuristics inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.1 Comparison of heuristic performances for the GAMS problem . . . . . . . 33 6.1 The main window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 6.2 The file menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6.3 Microsoft Excel workbook containing the night and evening shifts . . . . . 36 6.4 The main window w. imported shifts . . . . . . . . . . . . . . . . . . . . . 37 6.5 The settings menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.6 The weights window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6.7 The codes window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.8 RDO enabled and disabled . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.9 The main window w. generated schedule . . . . . . . . . . . . . . . . . . . 40 7.1 GRASP performance: Test 0 . . . . . . . . . . . . . . . . . . . . . . . . . 49 7.2 SA performance: Test 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 7.3 GRASP performance: Test 5 . . . . . . . . . . . . . . . . . . . . . . . . . 50 7.4 GRASP performance: Test 6 . . . . . . . . . . . . . . . . . . . . . . . . . 51 7.5 SA performance: Test 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 7.6 SA performance: Test 2 and 5 . . . . . . . . . . . . . . . . . . . . . . . . . 52 C.1 Optimal solution for test 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 C.2 Example of the decreasing temperature . . . . . . . . . . . . . . . . . . . 116 viii
Page 1 and 2: TECHNICAL UNIVERSITY OF DENMARK The
Page 3 and 4: TECHNICAL UNIVERSITY OF DENMARK Abs
Page 5 and 6: Acknowledgements Foremost, I would
Page 7: Contents vi 4.3.1 A construction he
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
Page 51 and 52: Chapter 6. The DRP Program 40 Figur
Page 53 and 54: Chapter 7 Metaheuristic tests This
Page 55 and 56: Chapter 7. Tests, results and discu
Page 57 and 58: Chapter 7. Tests, results and discu
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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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The Doctor Rostering Problem - Asser Fahrenholz

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