由於機台選擇問題應用於現實生活中之範圍非常廣泛，像是製造業以及半導體業等等，而此問題屬於組合最佳化之問題，當組合數愈多，則其複雜度愈高。本研究探討在一定的成本限制下該如何選擇機台種類給每一個工作站，使得整個流程之完工時間最小，而每個工作站可供選擇之機台種類個數均不相同，且每個工作站只能選擇一台機台。若工作站數量很大時，其組合數愈多，要找到最佳機台選擇之方式則更加困難。
本研究發展一套以巢狀分割法(Nested Partitions Method)為基礎之模擬最佳化演算法以處理大型複雜之機台選擇問題，其概念是將巢狀分割法結合有效之因子篩選方法，以減少處理大規模問題時所需之龐大計算量，使其能在有限之資源下得到一個滿意的結果。在本研究的數值研究中也顯示在有限的電腦資源下，本研究之演算法能夠找出近似最佳解或最佳解，其效果與效率比起兩種現有的演算法來得更佳。

Machine selection problem, which is one of the most popular and important issues, has been widely studied due to its extensive applications in real world, such as manufacturing and semiconductor industry. In this study, we focus on how to select different types of machines to each workstation can the makespan be minimized under a limited cost. Besides, as the number of decision variables increases, it would become increasingly difficult to find the optimal solution.
In this study, we propose a simulation optimization method, which combines nested partitions and factor screening method to solve the large-scale machine selection problems. By adopting factor screening method, we can identify the ranking of the importance of different workstations; therefore, the process of optimization can follow this ranking to find the optimal solution. As a result, the required computations can be efficiently reduced. Based on experimental results, the proposed method is able to find the nearly optimal solution or optimal solution within a limited computational budget. Furthermore, the method proposed in this study significantly outperforms the two existing algorithms.

摘要 I
ABSTRACT II
誌謝 III
目錄 IV
圖目錄 VI
表目錄 VII
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 論文架構 2
第二章 文獻探討 4
2.1 機台選擇問題 4
2.2 模擬最佳化 5
2.3 因子篩選方法 7
第三章 數學模型 9
3.1 問題定義 9
3.2 符號定義 10
3.3 指派問題模型 10
第四章 求解方法 12
4.1 巢狀分割法(NESTED PARTITIONS METHOD) 12
4.2 修改式巢狀分割法(MODIFIED NESTED PARTITIONS METHOD) 16
4.2.1 因子篩選方法 17
4.2.2 拉丁超立方體抽樣(Latin Hypercube Sampling) 27
第五章 數值結果 29
5.1 因子篩選方法 29
5.1.1 主效用模型之建構 29
5.1.2 實驗方式 29
5.1.3 參數設定 30
5.1.4 Case 1 30
5.1.5 Case 2 31
5.2 簡單機台選擇問題 32
5.2.1 簡單機台選擇問題參數設定 33
5.2.2 簡單問題演算法參數設定 35
5.2.3 簡單問題數值分析 38
5.3 複雜機台選擇問題 46
5.3.1 複雜問題參數設定 47
5.3.2 複雜問題演算法參數設定 48
5.3.3 複雜問題數值結果 48
第六章 結論與未來研究 51
6.1 結論 51
6.2 未來研究 51
參考文獻 52

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