在現今的製造業及科技業中，購買製造流程所需的機台為公司往自動化前進的第一步驟，所以當在購買機台時，正確的運用資金是相當重要的。而在現在這個講求效率的製造業環境下，為了長久的生產目標，公司必須決策如何在有限成本下，為每一個工作站選擇合適的機台種類與個數，使得能夠順利完成訂單的機率最高，是我們所要探討的主要問題，在此問題下，決策變數取決於購買的機台數量及種類，限制為有限的資金及每個工作站所能夠容納的機台數量，而最後的輸出為完成所有訂單的機率，又機台選擇正是屬於組合最佳化的問題，此類之問題被歸類為NP-hard，當組合數越多時，其複雜度就越高，且本研究之問題考慮到生產之不確定性故選擇利用模擬最佳化，求解難度更勝NP-hard，找到最佳的機台選擇方式也就越困難。

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，其概念是利用巢狀分割結合Nelder-Mead演算法，因可行解區域非常大，故我們利用巢狀分割來有效的切割可行解區域以解決如此大規模的問題。在本研究的數值中顯示，在有限的電腦資源下，我們仍可得到一個近似最佳解或最佳解，並將其與現有常用的禁忌搜尋法及單純使用巢狀分割法做比較，計算出的效果及效率更佳。

Nowadays, for industries in manufacturing and technology, purchasing machines required in manufacturing processes is the first step toward automation. Therefore, the correct usage of funds is very important when we buy machines. In this study, we focus on how to choose the appropriate type and number of machines for each workstation under a limited cost constraint while maximizing the probability of achieving the required capacity. The machine selection problem is a type of combination optimization. When the number of combinations is higher, the complexity increases, and finding the optimal solution becomes more difficult.
This study develops a set of simulation optimization algorithms based on the Nested Partitions method to deal with large scale machine selection problems. The framework involves using the Nested Partitions method combined with Nelder-Mead method. In this way, we can greatly reduce the amount of computations needed to solve large scale problems. Besides, by using a variance reduction procedure in the simulation process, we can make the screening results more reasonable and correct. Based on experimental results, we can achieve an optimal solution or a solution which is closed to the optimum under a limited computational budget. Furthermore, we compare our methodology with two common existing methods (Taboo Search method and the simple Nested Partitions method), finding that the current framework outperforms both in terms of effectiveness and efficiency.

摘要 I
ABSTRACT II
目錄 III
圖目錄 V
表目錄 VI
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 3
第二章　文獻回顧 5
2.1機台選擇問題 5
2.2整數規劃問題 6
2.3 模擬最佳化 7
2.4 NELDER-MEAD搜尋法 9
第三章　問題定義 10
3.1問題詳述 10
3.2符號定義 11
3.3數學模型 11
第四章　求解方法 13
4.1 巢狀分割法(NESTED PARTITIONS METHOD) 13
4.2 NELDER-MEAD METHOD 15
4.3 修改式巢狀分割法 19
4.3.1切割可行解區域 20
4.3.2拉丁超立方體抽樣 22
第五章　數值結果 23
5.1小規模機台選擇問題 23
5.1.1小規模機台選擇問題參數設定 24
5.1.2小規模問題演算法參數設定 26
5.1.3小規模機台選擇問題數值分析 28
5.2大規模機台選擇問題 33
5.2.1大規模機台選擇問題參數設定 33
5.2.2大規模問題演算法參數設定 35
5.2.3大規模機台選擇問題數值分析 36
第六章　結論與未來研究 38
6.1結論 38
6.2未來研究 39
參考文獻 40

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