在此篇研究裡，我們考慮一製造網絡內，需要與上下游成員溝通及協調某些參數，以利其生產排程（production scheduling）的決策問題，而製造網絡可以是一間工廠，亦可是一條供應鏈。具體來說，這些需要被協議的參數包括訂單最早可開始加工時間（ready date）以及訂單最晚需交貨時間（due date），是經由與上下游成員協調所訂定的。此篇研究的主要目標為使所有訂單能夠在生產時窗（訂單可開始加工時間及交期之間的時間區段）裡完成，假使沒有辦法達成此目標，則退而求其次，尋找出一種排程使得此排程產生的額外費用(需要上游提早交貨或延遲交貨給下游產生的額外成本)能夠降到最低。由於外部市場變化迅速，在協調的過程中需要頻繁的重新排程，因此本研究旨在改善混合整數規劃法（mixed integer programming, MIP）求解此類排程問題的效率。
本研究應用且測試兩種混合整數規劃方法，包括非緊鄰變數的混合整數規劃（parallel linear ordering mixed integer programming, PLOMIP）緊鄰變數的混合整數規劃（parallel immediate precedence mixed integer programming, PIPMIP），並使用許多改善的手法增進此兩種方法在求解問題時的效率。在此篇研究中，另外比較兩種不同起始解產生方式，第一種方法源自Hung et al. (2015)年提出的：根據派工法則，選擇四種啟發式方法中最佳的作為起始解（4H），另一種方法為：將前一個排程問題的最後解作為新排程問題的起始解（FS）。根據實驗結果，PLOMIP-FS的求解效率在此排程問題中最為傑出。

This study investigates the production scheduling problem motivated by the negotiations between two upstream and downstream nodes in a manufacturing network, which can either be a factory or a supply chain. Be specific, the earliest time a job can start processing (normally called the ready date) and the latest time a job should be completed (called the due date) are the parameters determined through the negotiations with upstream/downstream nodes. The primary goal in this study is finding a feasible schedule that all jobs can be processed within the time windows of their ready and due dates. If such schedule does not exist, then finding a schedule with minimum early and delay penalties becomes the objective. Due to rapid changes in an external market, re-scheduling is frequently conducted to re-optimize the scheduling problem. Therefore, this study attempts to improve the efficiency of MIP approach in solving this problem.
This study implements and tests two modeling techniques of mixed integer programming (MIP), including parallel linear ordering mixed integer programming (PLOMIP) and parallel immediately precedence mixed integer programming (PIPMIP). Several improvements are made to enhance the solution efficiency of these models. In addition, two different methods are used to generate initial solutions that can be fed into MIP. One of the methods is proposed by Hung et al. (2015), which selects the best initial solution from four heuristic methods (4H), and the other method adopts the final schedule of the previous problem as an initial solution (FS). The experiment results show that PLOMIP-FS is the most effective method in solving the problem.

摘要 I
Abstract II
致謝文 III
LIST OF FIGURES VI
LIST OF TABLES VIII
1. Introduction 1
1.1. Industry 4.0 1
1.2. Research Motivation 4
1.3. Decision support tool 6
2. Literature Review 8
2.1. Parallel machine scheduling with setup consideration 8
2.1.1. Sequence-independent setup 8
2.1.2. Sequence-dependent non-batch setup 8
2.1.3. Sequence-dependent batch setup 9
2.2. Machine eligibility 10
2.3. earliness/tardiness (ET) oriented criteria 10
3. Solution method 12
3.1. Problem assumptions 12
3.2. Parallel Linear Ordering Mixed Integer Programming 13
3.2.1. Original linear ordering model 13
3.2.2. Modified linear ordering model 15
3.2.3. Extension 1 of PLOMIP 18
3.2.4. Extension 2 of PLOMIP 20
3.2.5. Extension 3 of PLOMIP 21
3.2.6. Extension 4 of PLOMIP 23
3.3. Parallel Immediately Precedence Mixed Integer Programming 25
3.3.1. Extension 3 of PIPMIP 27
3.3.2. Extension 4 of PIPMIP 28
3.4. Mixed integer programming with initial solutions 29
3.4.1. Heuristics for generating initial solutions 29
3.4.2. Re-scheduling initial solutions 32
3.5. Numerical example 33
4. Computation Experimental 36
4.1. Experimental Parameters 36
4.2. Problem Generation Procedure 37
4.3. Parameter Setting 39
4.4. Extension approach for two models: Results and Analysis 40
4.4.1. PLOMIP– effectiveness comparison 41
4.4.2. PIPMIP– effectiveness comparison 42
4.4.3. PLOMIP versus PIPMIP 44
4.5. Effectiveness of two initial solutions: Results and Analysis 46
4.5.1. PLOMIP model with initial solutions 46
4.5.2. PIPMIP model with initial solutions 47
4.5.3. Comparison of four approaches 48
4.6. Factorial analysis of PLOMIP-FS 49
5. Conclusion and future research 55
Reference 57

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