近年國內關於勞工工作時間的相關法規不斷的修改，也造成企業在排班及輪班上需要及時的做出調整，若違反了法規除了業者需負擔不少的罰款外，不好的排班及輪班也會直接的影響到營運的安全，像是疲勞駕駛、過度加班等，這也會間接影響到顧客對企業的滿意度，另外人員排班及輪班的結果也會直接影響到營運人事成本，種種原因，使得人員輪班問題備受關注。因此，本研究主要針對國內實務上所考量之規定，建構出一套可行有效率的演算方式。
人員輪班問題被證明為NP-hard 問題，非常難以解決。且為了使輪班表在實務中可以使用，因此需將公平性和舒適性納入考量，這也使得其更加複雜。在本研究中，我們將鐵路運輸中的非循環人員輪班問題建構為整數規劃（IP）問題，並納入了有關人員公平性和舒適性的許多實際限制。為了解決複雜的限制，我們設計了一種將禁忌搜索和整數規劃相結合的數學方法，以有效地搜索可行區域和鄰域。數值結果表明，所提出的解決方案優於商用軟體，並且可擴展用於解決較大的問題實例。

Crew rostering problem (CRP) aims to construct a roster so that the duties in the planning horizon are adequately covered while satisfying the contractual or labor rules. CRP is shown to be a NP-hard problem and solving it is a challenging task. To make a roster usable in practice, fairness and comfortableness need to be addressed, which further compounds the task. In this research, we formulate the non-cyclic CRP in railway transportation as an integer programming (IP) problem and incorporate many practical constraints concerning fairness and comfortableness of staff member in a roster. To solve the complicated formulation, we devise a matheuristic that integrates the tabu search and integer program-based technique to effectively explore the feasible region and neighborhood of incumbent solution. Numerical results show that the proposed solution framework outperforms commercial optimization package and is scalable to solve larger problem instances.

摘 要 I
ABSTRACT II
TABLE OF CONTENTS III
LIST OF TABLES V
LIST OF FIGURES VI
1. INTRODUCTION 1
2. LITERATURE REVIEW 4
2.1. Exact Solution Approach 4
2.2. Heuristic-based Solution Approach 6
2.3. Hybrid Solution Approach 9
2.4. Summary 10
3. MATHEMATICAL FORMULATION 11
3.1. Definitions 11
3.2. Formulation Assumptions 12
3.3. Problem Statement 12
3.4. Mathematical Formulation 17
4. A MATHEURISTICS SOLUTION APPROACH 28
4.1. The greedy heuristic (GH) for initial solution 28
4.2. The Overall Solution Framework and Tabu Search Heuristics 31
4.3. Neighborhood Search 33
5. NUMERICAL EXPERIMENTS 40
5.1. Parameters Employed in the Tabu Search 40
5.2. Model Validation 41
5.3. Sensitivity Analysis 49
6. CONCLUDING REMARKS AND FUTURE RESEARCH 57
7. REFERENCES 59

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