The Doctor Rostering Problem - Asser Fahrenholz

Recommendations

Info

Chapter 3. The model and design 13 3.4 The objective function The constraints described in the two previous sections is the complete list of constraints as the medical practice has described them. The objective function value of a schedule s is the collective sum of the above described soft constraints and is denoted z(s): min z(s) = δB0 + δB2 i ⎛ yik0 ⎝max k ⎛ + δB3 ⎝ + δB5 + δB6b i,j i i + δB1 i,j∈sa i yik1 xijk − min k ⎞ ⎠ + δB4 yijk3 yik5 yik6b + δB6a i ∀k i i,j∈sa yik4 yik6a xijk ⎞ ⎠ (Z(S)) An objective function value of 0 means that we have found an optimal solution for any DRP problem. If the objective function value is positive, it can still be optimal, but under any circumstances means that one or more soft constraints are invalid. Leaving the weight, δ, of all the soft constraints equal to 1 means that we can derive from an objective function value of i.e. 4, that soft constraints are invalid in 4 cases. If we choose to alter the weights of the rules, the same still applies, but the transparency of the objective function value decreases. The objective function thus determines the value of solutions for the DRP and is used by optimal solvers such as GAMS (see chapter 5) and the heuristics in the next chapter, which will describe how solutions can be found for the DRP. 3.4.1 Problem size The amount of variables with 4 shifts per day, 6 doctors and 100 working days:
Chapter 3. The model and design 14 |V ars| = |Shifts| · |Doctors| · |Schedule| = 4 · m · n = 4 · 6 · 100 = 2400 Given 10 constraints, the total number of constraints for this problem becomes: |Equations| = |Shifts| · |Doctors| · |Schedule| · |Constraints| = 4 · m · n · 10 = 4 · 6 · 100 · 10 = 24000 Commonly, problems are big if they have more than 2500 variables and 10000 equations. This is not ruling out that any larger problems can not be solved, as techniques (i.e. Cutting-plane method, Branch and cut) exist that, using the constraints, can limit the search region of the problem. A topic not addressed in this project.
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 and 22: Chapter 3. The model and design 10
Page 23: Chapter 3. The model and design 12
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 65 and 66: Chapter 8. Future considerations 54
Page 67 and 68: Chapter 8. Future considerations 56
Page 69 and 70: Chapter 9. Conclusion 58 The three
Page 71 and 72: Appendix A. Implementation 60 27 //
Page 73 and 74: 2 Appendix A. Implementation 62 3 i
Page 75 and 76:
Appendix A. Implementation 64 A.3 G
Page 77 and 78:
Appendix A. Implementation 66 97 wh
Page 79 and 80:
Appendix A. Implementation 68 27 su
Page 81 and 82:
Appendix A. Implementation 70 119 P
Page 83 and 84:
Appendix A. Implementation 72 64 br
Page 85 and 86:
Appendix A. Implementation 74 28 Ch
Page 87 and 88:
Appendix B GAMS Model This chapter
Page 89 and 90:
Appendix B. GAMS Model 78 46 c(day
Page 91 and 92:
Appendix B. GAMS Model 80 109 B1( f
Page 93 and 94:
Appendix B. GAMS Model 82 **** REPO
Page 95 and 96:
Appendix B. GAMS Model 84 B.3 The s
Page 97 and 98:
Appendix B. GAMS Model 86 B.3.3 The
Page 99 and 100:
Appendix C. Tests 88 C.1.1 Instance
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Appendix C. Tests 94 JST PZH HP SDA
Page 107 and 108:
Appendix C. Tests 96 JST PZH HP SDA
Page 109 and 110:
Page 111 and 112:
Appendix C. Tests 100 Cons 12 Imps
Page 113 and 114:
Appendix C. Tests 102 Test 3 RCL 1
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Appendix C. Tests 116 160 140 120 1
Page 129 and 130:
Bibliography 118 [10] Michael R. Ga
show all

The Doctor Rostering Problem - Asser Fahrenholz

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?