本研究主要探討了平行機台下的生產排程問題，並考慮了換線時存在一段與前後兩種工作（即訂單）相關（即順序相依）的整備時間，以及與工作和機台兩者均相關的加工速率。每一個訂單均有一個生產時窗(為訂單可開始加工時間與交期之間的時間區段)，其生產活動希望在其生產時窗內完成，倘若不可實現，則會因提早生產或延遲交貨而產生額外的費用。如果一個訂單的生產開始時間晚於其可開始加工時間，則生產提前時間為零；否則，可開始加工時間減去生產開始時間所得即為此訂單之生產提前時間。類似的，如果一個訂單的完成時間早於其交期，則交貨延遲時間為零；否則，完成時間減去交期所得的時間即為此訂單之交貨延遲時間。此外，機台的可用性亦被考慮在內。換言之，對於某一工作，並非所有機台均可以被用來加工之。據知，目前並沒有文獻完整地探討此類平行機台排程問題。本研究提出三種方法以求解此類問題，包括強制限制條件下的混合整數規劃（hard-constraint mixed integer programming, HCMIP）、允許提早或延遲下的混合整數規劃（earliness-tardiness mixed integer programming, ETMIP）以及啟發式方法提供起始解的混合整數規劃（heuristics-initialized mixed integer programming, HIMIP），並使用了隨機產生的問題測試、比較此三種方法之性能。相比之下，HIMIP的求解效率較為突出。此外，受實驗結果之啟發，本研究亦提出一種基於以上三種方法的多階段優化（multi-stage optimization, MSO）方法。

This study addresses the scheduling problem of a number of orders on unrelated parallel machines with sequence-dependent setup times and machine-dependent and order-dependent processing rate. Each order has a time window delimited by its ready date and due date. The processing time of an order is expected to lie within its time window. If not, penalties for earliness or tardiness will occur. If the start time of an order can be scheduled later than its ready date, the earliness is zero. Otherwise, the earliness of an order is calculated by subtract the start time from the ready date. Whereas, if the completion time of an order can be scheduled before its due date, the tardiness is zero. Otherwise, the tardiness of an order is calculated by subtract the due date from the completion time. In addition, machine eligibility is also taken into consideration; that is, not all of the parallel machines can be assigned to process a particular job.
To the best of our knowledge, no existing literature has thoroughly addressed such a scheduling problem. Three solution methods, the hard-constraint mixed integer programming (HCMIP), the earliness-tardiness mixed integer programming (ETMIP), and the heuristics-initialized mixed integer programming (HIMIP), are proposed and tested by experiments. Generally speaking, HIMIP is most effective in solving the problem. Further, based on the experimental results, a multi-stage optimization (MSO) procedure is proposed.

TABLE OF CONTENTS
摘要 I
Abstract II
LIST OF FIGURES VI
LIST OF TABLES VII
1. Introduction 1
1.1. Supply Chain Environment 1
1.2. Parallel Machine Scheduling with Machine Eligibility 4
1.2.1. Order splitting 4
1.2.2. Processing Time 5
1.2.3. Setup Time 5
1.2.4. Machine Eligibility 6
1.3. Problems Statement and Research Approach 7
2. Literature Review 9
3. Solution Methods 13
3.1. Hard-Constraint Mixed Integer Programming (HCMIP) Method 13
3.2. Earliness-Tardiness Mixed Integer Programming (ETMIP) Method 17
3.3. Heuristics-Initialized Mixed Integer Programming (HIMIP) Method 20
3.3.1. Heuristics for Generating Initial Integer Solutions 21
3.3.2. Mixed Integer Programming with Initial Solution 25
4. Computational Experiments 27
4.1. Experimental Parameters 27
4.2. Problem Generation Procedure 28
4.3. Parameter Setting 30
4.4. HCMIP Method: Results and Analysis 31
4.4.1. The Performances of HCMIP 31
4.4.2. Factorial Analysis of HCMIP 32
4.5. ETMIP Method: Results and Analysis 35
4.5.1. The Performances of ETMIP 35
4.5.2. Factorial Analysis of ETMIP 36
4.6. HIMIP Method: Results and Analysis 41
4.6.1. The Performances of HIMIP 41
4.6.2. Factorial Analysis of HIMIP 42
4.7. Performance Comparison 47
5. A Proposed Solution Procedure 52
5.1. The Procedure of Multi-Stage Optimization 52
5.2. The Decision Making Rule 55
6. Conclusion and Future Research Prospect 59
Appendix A: Constraints 1.7 and 2.7 Descriptions 61
Appendix B: Solution Trend Normalization Procedure 63
Reference 66

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