在隨機環境下，風險管理能極小化決策所造成之不利趨勢。分量(Quantile)為風險管理中重要的績效指標。本研究發展了一新的方法論Stochastic Nelder-Mead Simplex Method for Quantile Optimization (SNM-Q)用以處理在隨機環境下以分量為績效指標的最佳化問題。SNM-Q以penalty function method為基礎同樣能處理具限制式的問題。本研究證明了SNM-Q在一般性的條件下皆具有收斂性，一系列系統性的數值實驗顯示SNM-Q可有效的處理隨機環境下的分量最佳化問題，值得進一步研究。

Risk management aims to minimize the downside of decisions made in stochastic environments. Quantile is the most popular metrics used in risk management. In this paper, we present a newly-developed methodology, called Stochastic Nelder-Mead Simplex Method for Quantile Optimization (SNM-Q), that can handle quantile-based stochastic optimization problems. We also present SNM-Q based on penalty function method that can solve problems with constraints. An extensive numerical study shows that SNM-Q can efficiently and effectively solve the problem and thus is worth further investigation.

目錄
摘要 I
ABSTRACT II
誌謝 III
目錄 IV
圖目錄 VII
表目錄 VIII
一、 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 4
1.3 論文架構 4
二、 文獻探討 7
2.1 模擬最佳化(SIMULATION OPTIMIZATION) 7
2.2 分量研究 8
三、 問題定義 11
四、 SNM-Q演算法 12
4.1分量估計 13
4.2無限制式問題之架構 16
4.2.1 SNM-Q之主架構 16
4.2.2 分量之樣本抽樣計畫 17
4.2.3 搜尋架構 19
4.3具限制環境之架構 23
4.3.1 Penalty Function Method 24
五、 數值實驗 27
5.1 無限制式數值研究 27
5.1.1 測試函數 27
5.1.2 比較指標 29
5.1.3 數值結果 29
5.2 具限制式數值研究 34
5.2.1 測試問題 34
5.2.2 數值結果 38
六、 個案研究 40
6.1 送報生問題 40
6.2 多產品組裝問題 41
七、 結論與未來研究 44
參考文獻 45

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