The Doctor Rostering Problem - Asser Fahrenholz

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Chapter 3. The model and design 11 ⎧ ⎪⎨ 1 if rule o is violated on yiko = ⎪⎩ 0 day i for doctor k otherwise ⎧ ⎪⎨ 1 if rule 3 is violated on day i yijk3 = ⎪⎩ 0 shift j for doctor k otherwise ⎧ ⎪⎨ 1 if the LHS of rule o is zero, tiko = ⎪⎩ 0 allows yiko to remain zero too otherwise ⎧ ⎪⎨ 1 if the LHS of rule 3 is zero, tijk3 = ⎪⎩ 0 allows yijk3 to remain zero too otherwise The y-variables are used as counting variables, indicating how many violations of a soft constraint the doctor has. The t-variables are used for the specific case of the left hand side of the equation is zero. This variable, and the fact that we are dealing with a minimisation problem, allows the y-variable to remain zero. The following are the soft constraints that apply when constructing a model for the DRP: B0 No doctor should have both the Monday noon shift and the following Friday afternoon shift in the same week: min δB0 i yik0 ∀ k st. xi2k + x (i+4)3k = 1 + yik0 − tik0 ∀ k, i ∈ M (B0) B1 No doctor should have both the Friday afternoon shift and the following Monday noon shift: min δB1 i yik1 ∀ k st. xi3k + x (i+3)2k = 1 + yik1 − tik1 ∀ k, i ∈ F ∧ i < n − 3 (B1)
Chapter 3. The model and design 12 B2 All shifts assigned should be divided equally among all doctors. δB2 ⎛ ⎝max k i,j∈sa xijk − min k i,j∈sa xijk ⎞ ⎠ (B2) B3 No doctor should have two noon shifts nor two afternoon shifts two days in a row: ⎛ min δB3 ⎝ i,j yijk3 ⎞ ⎠ ∀ k st. xijk + x (i+1)jk = 1 + yijk3 − tijk3 ∀i = {1 . . . n − 1}, j ∈ sa, k B4 No doctor should have the afternoon shift the day after an evening shift: min δB4 i yik4 ∀ k st. bi4k + x (i+1)3k = 1 + yik4 − tik4 ∀i = {1 . . . n − 1}, k B5 No doctor should have the noon shift the same day as an evening shift: min δB5 i yik5 ∀ k st. bi4k + xi2k = 1 + yik5 − tik5 ∀i, k (B3) (B4) (B5) B6 No doctor should have the noon shift the day after an afternoon shift and vice verca: min δB6a i yik6a ∀ k st. xi3k + x (i+1)2k = 1 + yik6a − tik6a min δB6b ∀i = {1 . . . n − 1}, k i yik6b ∀ k st. xi2k + x (i+1)3k = 1 + yik6b − tik6b ∀i = {1 . . . n − 1}, k (B6a) (B6b)
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 and 8: Contents vi 4.3.1 A construction he
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: Chapter 3. The model and design 10
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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
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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 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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