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研究生:曾耀賢
研究生(外文):Yao-HsienTseng
論文名稱:運用單一變異縮減技術於等候與存貨系統之最佳化問題
論文名稱(外文):Using Single Variance Reduction Technique to select the best queueing and inventory systems
指導教授:蔡青志
指導教授(外文):Shing-Chih Tsai
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工業與資訊管理學系碩博士班
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:46
中文關鍵詞:排序和選擇程序控制變量共同隨機亂數條件期望估計法相關性導入技術
外文關鍵詞:Ranking and Selection ProceduresControl VariatesCommon Random NumbersConditional ExpectationCorrelation Induction
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系統模擬包含的應用領域十分廣泛,舉凡:統計推論、品管製程、財務金融、地質探勘等,均可以使用模擬來進行分析,而當面對離散事件模擬最佳化問題時,若面對的問題維度有限,則可使用系統模擬領域中發展相當成熟的技術---排序與選擇程序,目的是能夠在正確選擇系統的信心水準下,建議最佳或近似最佳的系統供決策者選用;然而,排序與選擇程序只適用系統個數較小的前提下,若系統之績效值變異程度大,將影響程序執行進度,造成抽樣成本以及時間成本的提高,有鑑於此 ,配合另一項成熟的工具---變異縮減技術,計算出替代估計量取代原本之樣本平均數,其樣本變異數將較原本估計量之變異數來得低,達到變異數縮減的效果,其中,可將之分為兩種類別:輸入型技術以及輸出型技術,前者是使用相關性的輸入變量,藉此產生具有正或負相關的輸出值;而後者是使用輔助變量試圖修正輸出值,使得變異數下降。而本研究著眼於將諸多種具有不同屬性的變異縮減技術應用到三種排序與選擇程序當中。

本研究使用四種單一變異縮減技術,並將推算所得之估計量以及變異數估計量應用於篩選程序、兩階段選擇程序與完全連續選擇程序,且推論其滿足信心水準的
條件下,進而分析程序的優劣,並將程序用於M/M/s/c等候系統以及(s,S)
訂購策略之存貨模型兩種不同架構的問題之實驗比較,並由結果可得以下結論,控制變量CV具有最佳的縮減效果,在兩種情境下均符合。

The applied field of simulation is very extensive, when we want to resolve the optimization of stochastic discrete event simulation models. If the problem is finite dimensional, then we can use Ranking and Selection to recommend the best or near best systems to the decision makers that are guarantee confidence level; However, Ranking and Selection only be available in the condition that the number of alternatives is finite, if the variance of performance measures of system is large, will affect the execution of procedure, and increase the cost of time and computation; for this reason, we apply the other statistical techniques to improve the efficiency of output, i.e Variance Reduction Technique(VRT). it replaces the origin estimator, sample mean, the sample variance of estimator is less than the origin one, to accomplish the propose of reducing the variance in output from simulation models. We classify the VRTs into two categories: Input techniques: they induce positive or negative correlations among output random variables in simulation runs; Output techniques: they employ auxiliary variables in an attempt to correct the output variables to make the variance smaller. In our research, we focus on applying the variety of VRTs to three kinds of Ranking and Selection procedure.

In our research, we use four kinds of single Variance Reduction Technique, and calculate estimator and the estimator of variance, and apply them to Screening Procedure, Two-stage Selection Procedure, and Fully Sequential Selection Procedure, by inference or proving that each procedure will guarantee confidence level, to analyse the pros and cons of procedures, through illustrative example, we use two different types of systems(M/M/s/c queueing system and (s,S)inventory control systems) and compare the VRTs under various experimental conditions. In the result of our research we conclude that, CV perform better than the other single Variance Reduction Technique, corresponding with the conclusion in two experimental conditions.


目錄

中 文 摘 要 i
英 文 摘 要 ii
誌 謝 iv
目 錄 v
圖 目 錄 vii
表 目 錄 viii

第一章 緒論 1
1.1 研究背景與動機 2
1.2 研究目的 4
1.3 研究流程 4

第二章 文獻回顧與基本模型介紹 6
2.1 變異縮減技術 6
2.1.1 相關性導入技術 7
2.1.2 共同隨機亂數 13
2.1.3 控制變量 14
2.1.4 條件期望估計法 17
2.2 單一變異縮減技術 18
2.3 運用單一變異縮減技術之排序與選擇程序 19
2.4 小結 21

第三章 研究方法 22
3.1 排序與選擇程序介紹 22
3.2 篩選程序 22
3.2.1 程序步驟 22
3.3 兩階段選擇程序 23
3.3.1 程序步驟 23
3.4 完全連續選擇程序 25
3.4.1 程序步驟 25
3.5 單一變異縮減技術運用於模型之實驗 27
3.5.1 M/M/s/c 等候系統 27
3.5.2 (s,S) 訂購策略之存貨模型 30

第四章 情境設計與分析 33
4.1 實例驗證 33

第五章 結論與未來研究方向 41
5.1 研究總結 41
5.1.1 篩選程序 41
5.1.2 兩階段選擇程序 41
5.1.3 完全連續選擇程序 42
5.2 未來研究方向 42

參考文獻 43
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