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研究生： 周書平
Shu-Ping Chou
論文名稱： A Polynomial Time Approximation Scheme for Parallel Machine Scheduling with Machine Availability Constraints
指導教授： 葉英傑
Yin-Chieh Yeh
口試委員:
學位類別： 碩士
Master
系所名稱： 管理學院 - 工業管理研究所
Graduate Institute of Industrial Management
論文出版年： 2018
畢業學年度： 106
語文別： 英文
論文頁數： 47
中文關鍵詞： 多項式時間近似方案 、機器可用區間限制 、平行機台
外文關鍵詞： Polynomial time approximation scheme, Availability constraints, Parallel Machines
相關次數： 點閱：18  下載：0 
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    • 本研究討論不可分割工作的平行機台的最大完工時間最小化問題，其中機器具有任意的可用區間限制；假設至少有一台機器在整個規劃期間始終可用，這種設置契合在產業應用上和學術上的需求。例如，製造業中，這樣的限制來自於機器需要進行例行性維護。而在學術上，根據本研究的探討，過去沒有提出對輸入添加結構的多項式時間近似方案演算法（PTAS）。透過向輸入資料添加結構，本研究提供第一個多項式時間近似方案演算法（PTAS）。

    This study analyzes the makespan minimization problem of non-preemptively scheduling identical parallel machines where machines may be unavailable during arbitrary time intervals. Assuming at least one machine is always available throughout the planning horizon, this setting is relevant practically and academically. For example, the unavailability occurs when machines are under preventive maintenance. So far as this study is concerned, no polynomial-time approximation scheme (PTAS) via structuring the input data has been proposed. This study aims to provide the first polynomial-time approximation scheme (PTAS) by adding structure to the input.

    摘要 i Abstract ii Contents iii List of Figures v List of Tables vi Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.2 Research Objective 2 1.3 Research Methodology 2 1.3.1 Approximation Scheme 2 1.4 Research Methodology 3 1.4.1 Structuring the Input 3 Chapter 2 Literature Review 6 2.1 Hardness Results 6 2.2 Related Problems and Previous Results 7 2.2.1 Cases with Machine Release Times 7 2.2.2 General Cases and Other Special Cases 7 2.3 Methodology: Polynomial Time Approximation Schemes (PTAS) 9 Chapter 3 Polynomial Time Approximation Scheme 11 3.1 Problem Definition & Preliminaries 11 3.1.1 Problem Definition 11 3.1.2 Preliminaries 12 3.2 Polynomial Time Approximation Scheme 15 3.2.1 Introduction to the Algorithm 15 3.2.2 Phase I 16 3.2.3 Phase II 16 3.2.4 Phase III 18 3.2.5 Phase IV 19 3.3 Numerical Example 20 3.3.1 The Input 20 3.3.2 Phase I with Numerical Example 22 3.3.3 Phase II with Numerical Example 22 3.3.4 Phase III with Numerical Example 23 3.3.5 Phase IV with Numerical Example 24 3.4 The Algorithm 26 Chapter 4 Computational Analysis 30 4.1 Algorithm Verification 30 4.2 Evaluation: Maximum Size of Instance for Heuristic Results 31 4.2.1 Examples Maximum Size Exanimated and Results 32 4.3 Sensitivity Analysis on Precision Parameter 33 Chapter 5 Conclusion 34 5.1 Main Results 34 5.2 Research Limitation 34 5.3 Future Research Direction 35 References 37

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