本研究所探討的是在非相關平行機台排程問題(Unrelated parallel machine scheduling)之中考慮訂單可開始加工時間(Ready time)、機台可行性(Machine eligibility)以及順序相依的設置時間(Sequence-dependent setup time)等限制下，建構一個混整數規劃(MIP)模型並以最小化總設置時間(Setup time)及等候開始加工時間(Delay time)為目標進行求解。在單部機台排程問題之中考慮順序相依設置時間的排程問題已被證明為NP-hard，因此本研究使用基因演算法(Genetic Algorithm)進行求解，以提升求解效率。
然而在實際生產系統之中，訂單可能會由於機器狀態、生產環境等不確定因素造成訂單延遲抵達。因此可能會造成原先的排程不可行或是績效較差，為避免頻繁發生此情形而導致需要重排，所以該如何得到一個穩健的排程在訂單可開始加工時間具有變異性的情況下將成為一個重要的議題。因此本研究將在考慮訂單可開始加工時間具有不確定性的情況下，提出一個穩健最佳化(Robust Optimization)模型，來解決訂單可開始加工時間具有不確定性的問題。
本論文以半導體封裝廠瓶頸站排程為實例，並透過穩健最佳化的方式得到在最小化設置時間以及等候開始加工時間的同時，在各情境(Scenario)之下的可行性(Feasibility)也能夠被提升。換句話說，由於訂單可開始加工時間具有不確定性，本研究不僅希望提升瓶頸站利用率以及降低訂單週期時間(Cycle time)，並且期望當訂單可開始加工時間延遲時，求解的排程依舊可行(Feasible)。

This research considers an unrelated parallel machine scheduling problem with ready times, machine eligibility and sequence-dependent setup times. The objective of the problem is to minimize the weight sum of setup times and delay times. Accordingly, a mixed integer programming formulation is presented. Since the single machine scheduling problem with sequence-dependent setup times is known to be NP-hard, a genetic algorithm is then developed with neighborhood search operator to solve the deterministic scheduling problem, which is also NP-hard.
However, the ready time of each job is uncertain in real world. In this case, the optimal solution from deterministic model may become an infeasible or a bad solution. Therefore, the deterministic model may be unsuitable. A robust optimization model is then proposed for identifying a robust schedule across all possible scenarios.
In this research, a robust optimization model is developed to solve the unrelated parallel machine scheduling problem in Semiconductor Assembly Factory with consideration of the ready times uncertainty. Due to the ready times uncertainty, this research not only minimizes setup time and delay time but also remains feasible in all scenarios.

摘要 i
Abstract ii
誌謝 iii
目錄 iv
第一章 緒論 1
1.1研究背景 1
1.2研究動機 2
1.3研究目的 3
1.4研究步驟 4
第二章 文獻回顧 6
2.1平行機台排程相關文獻 6
2.1.1 平行機台排程(確定型) 6
2.1.2 平行機台排程(訂單可開始加工時間具有不確定性) 9
2.2基因演算法相關文獻 10
2.3穩健最佳化相關文獻 14
第三章 平行機台排程問題-以半導體封裝廠為例 17
3.1問題描述與定義 17
3.2數學模型 19
3.2.1 MIP 模型 19
3.2.2 MIP模型之計算複雜度 21
3.3求解方法 23
3.4封裝廠生產排程範例 26
3.4.1封裝廠生產流程與特性 27
3.4.2封裝廠面臨之問題 29
3.4.3實驗數據設計 32
3.5實驗結果與分析 34
第四章 穩健最佳化應用於半導體封裝廠 42
4.1封裝廠特性 42
4.2問題描述與定義 44
4.3穩健最佳化模型 45
4.4情境生成 50
4.5求解方法 51
4.6實驗結果與分析 53
第五章 結論與建議 59
5.1結論 59
5.2建議 60
參考文獻 62
附錄 66
附錄一 : 訂單可開始加工時間 66
附錄二 : 訂單於各機型之加工時間 67

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