Physician Rostering Optimization（PRO）問題被定義為在指定的計劃範圍內，考慮到某些規則，規則或約束，將許多醫生分配到不同的班次。在現實生活中解決這個問題通常非常具有挑戰性，特別是採用獨特的方法在這項研究中，提出了一種改進的變鄰域搜索（VNS）算法來開發一種求解PRO問題的方法。當前方法由兩個階段組成，I階段通過使用貪婪啟發式方法開發初始解決方案，該方法滿足問題的所有硬約束，此後方法的II階段開始，旨在改進採用可變鄰域下降（VND）算法的初始解決方案。然後，在VNS算法中固定的振動階段增強所生成的解決方案，以便檢查是否可以獲得更好的解決方案。為了確定當前解決方案的質量，當前的研究使用目標函數的可變性，可變性是由於未完全實現軟約束而產生的懲罰。基於實驗設計（DOE）確定適當的算法設置，25個實例的計算結果獲得了更好的結果，所提出的算法在大多數情況下都優於經典VNS和兩個修改現行方法。

The Physician Rostering Optimization (PRO) problem is defined as the assignation of a number of physicians to different shifts during a specified planning horizon, considering certain rules, regulations or constraints. This is often very challenging to solve in real life especially applying a unique approach. In this research, a Modified Variable Neighborhood Search (VNS) algorithm is proposed to develop a method to solver the PRO problem. the current method is composed by in two phases, the I phase to develop an initial solution through the use of a greedy heuristic method which meets all the hard constraints of the problem, after this the II phase of the method starts which aims to improve the initial solution employing a Variable Neighborhood Descent (VND) algorithm. Then the Shaking phase, which is fixed in the VNS algorithm boost the generated solution in order to check whether or not, is possible to obtain a better one. To determine the quality of the current solution the current research use the variability of the objective function, the variability is the penalty generated due to the not full achievement of the soft constraints. Based on the Design of Experiments (DOE) to determine the appropriate algorithm setting the computational result of 25 instances were obtained a better result with the proposed algorithm which outperforms in most of the instances when it was compared with a classic VNS and two modifications of the current method.

Contents
Abstract II
摘要 III
Acknowledgments IV
Contents V
List of Tables VII
List of Figures VII
Chapter 1 Introduction 8
1.1 Background and Motivation 8
1.2 Research Objective 9
1.3 Research Method 9
Chapter 2 Literature Review 10
2.1 Health Care Rostering Problem 10
2.2 Variable Neighborhood Search 19
2.3 Integer Programming Approach 20
Chapter 3 Problem Definition 21
3.1 Problem Statement 21
3.2 Mathematical Model 21
Chapter 4 Methodology 25
4.1 I Stage: Initial Solution 27
4.2 II Stage: VNS Algorithm 30
Chapter 5 Experiments and Results 36
5.1 Dataset information 37
5.2 Parameter settings determination 38
5.3 Generation of instances 43
5.4 Analysis of different types of VNS algorithms 45
Chapter 6 Conclusion 55
References 58
Appendices 60
Appendix A: Manual verification of hard constraints 60
Appendix B: Design of Experiments (DOE) sample of replicates results 62
Appendix C: Sample of Instances schedules results 69
Appendix D: Replicates for the 25 instances (3 replicates per instance) 87

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