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研究生: 朱一豪
Chu, I-Hao
論文名稱: 以控制型多階段選擇程序解決與標準系統比較之問題
Controlled Multistage Procedure for Comparison with a Standard
指導教授: 蔡青志
Tsai, Shin-Chin
學位類別: 碩士
Master
系所名稱: 管理學院 - 工業與資訊管理學系
Department of Industrial and Information Management
論文出版年: 2010
畢業學年度: 98
語文別: 中文
論文頁數: 63
中文關鍵詞: 標準系統比較排序與選擇程序變異減免技術
外文關鍵詞: Comparison With a Standard, Ranking and Selection Procedures, Variance Reduction Technique
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  • 標準系統比較(Comparison With a Standard; CWS)一直是系統模擬領域中很重要的一環,從 Nelson and Goldsman (2001)、Kim (2005)、Chen (2006)以及 Tsai (2009) 等文獻當中,各國學者致力於此議題的研究可以看出其受重視的程度。 CWS係在每一個系統中透過有限樣本的隨機抽樣過程,與標準系統進行比較,目的為決定其他系統與標準系統的優劣。標準系統可以視為現行系統,要進行替換必須付出成本,因此,只有當其他系統能夠「明顯優於」標準系統且帶來的利益優於汰換系統所付出的成本時,決策者才會執行汰換標準系統的行動。

    排序與選擇程序 (Ranking and Selection Procedure; R&S) 可分成篩選程序 (screening procedure) 和選擇程序 (selection procedure)。R&S 發展初期,輸出值 (output) 之期望值和變異數是利用樣本平均數 (sample Mean) 與樣本變異數 (sample Variance) 來估計之,隨著變異減免技術 (Variance Reduction Technique; VRT) 的發展,可以將樣本平均數與樣本變異數,利用 VRT 的手法,產生新的估計量取代之,其樣本變異數將比原始估計量的樣本變異數更低,可以提升程序的效率。 因此,藉由篩選程序和選擇程序的結合,本研究發展一全新的多階段選擇程序(Multistage Selection Procedure; MSP),並且導入 VRT 以解決 CWS 之問題。另外,針對 Kim (2005) 為了解決 CWS 問題而所提出的連續階段式選擇程序(Fully Sequential Selection Procedure; FSSP),本研究亦將 VRT 導入於其中,並且與本研究新發展的程序進行比較,衡量成本、參數分析、信心水準以及各種實驗情況的優劣,以佐證本研究確實具有效率。

    Comparison with a standard (CWS) is a very important issue in Simulation. The destination of CWS is to decide which system is best system via random sample. Standard system can be said as a system we are using and we have to pay some cost if we replace the standard system. On the other word, if the benefit of substitution for standard system can be apparent better than the cost of replacing the standard system, we will immediately replace standard system with substitution for better performance.

    Ranking and Selection (R&S) is divided into two parts, screening procedure and selection procedure. In the early development, R&S use sample mean and sample variance to estimate mean and variance of output data. Following the development of variance reduction technique (VRT), we can create a new estimator to replace raw estimator and the variance of new estimator will be lower than the raw one, and that will be helpful to improve the efficiency of procedure. Hense, we can introduce VRT into R&S to rise efficiency of deciding the best system and down the cost.
    We develop three procedures, CSSP, FMSP and IMSP for CWS problem by combining screening procedure and selection procedure and also introduce VRT to our procedure. After empirical evaluation, our three procedures is really better than the procedure recorded in document nowadays and there are also can be shown to satisfy the statistical validity.

    中文摘要 i 英文摘要 ii 誌謝 iii 目錄 iv 表目錄 vi 第一章 緒論 1 1.1 研究背景 1 1.2 研究動機與目的 3 1.3 論文架構 5 第二章 文獻回顧 6 2.1 標準系統比較 6 2.1.1 以兩階段式選擇程序解決與標準系統比較之問題 6 2.1.2 以連續階段式選擇程序解決與標準系統比較之問題 8 2.1.3 以完全成對比較程序解決與標準系統比較之問題 11 2.2 控制變數 12 2.2.1 控制變數 13 2.2.2 控制總和 : 以應用於FSSP為說明 15 第三章 研究方法 18 3.1 運用CS之CSSP 18 3.1.1 CSSP簡介 18 3.1.2 The Generic Procedure of CSSP 19 3.1.3 CSSP 統計有效性之證明 21 3.2 運用CV之FMSP 21 3.2.1 FMSP簡介 21 3.2.2 The Generic Procedure of FMSP 22 3.2.3 FMSP 統計有效性之證明 25 3.3 運用CS之IMSP 25 3.3.1 IMSP簡介 25 3.3.2 The Generic Procedure of IMSP 26 3.3.3 IMSP 統計有效性之證明 28 第四章 實驗設計與分析 29 4.1 實驗評估 29 4.2 效率分析 38 4.3 實例驗證 43 第五章 結論與未來研究方向 46 5.1 論文總結與貢獻 46 5.2 未來研究方向 47 附錄 49 參考文獻 61

    Bechhofer, R.E. (1954) A single-sample multiple decision procedure
    for ranking means of normal populations with known variances.
    The Annals of Mathematical Statistics, 25, 16--39.

    Bechhofer, R. E. and Turnbull, B.L. (1978) Two (k+1)-decision
    selection procedures for comparing k normal means with a specified
    standard. Journal of the American Statistical Association,
    73, 385--392.

    Branke, J., Chick, S.E. and Schmidt, C. (2007) Selecting a
    selection procedure. Operations Research, 53,
    1916--1932.

    Chen, E. (2006) Comparisons with a standard via all-pairwise
    comparisons. Discrete Event Dynamic Systems, 16,
    385--403.

    Hong, L.J. and Nelson, B.L. (2005) The tradeoff between sampling
    and switching: New sequential procedures for indifference-zone
    selection. IIE Transactions}, 37, 623--634.

    Kim, S.-H. and Nelson, B.L. (2001) A fully sequential procedure
    for indifference-zone selection in simulation. ACM
    Transactions on Modeling and Computer Simulation, 11,
    251--273.

    Kim, S.-H. (2005) Comparison with a standard via fully sequential
    procedures. ACM Transactions on Modeling and Computer
    Simulation}, 15, 144--174.

    Kim, S.-H. and Nelson, B.L. (2006) On the asymptotic validity of
    fully sequential selection procedures for steady-state simulation.
    Operations Research, 54, 475--488.

    Lavenberg, S.S. and Welch, P.D. (1981) A perspective on the use of
    control variables to increase the efficiency of Monte Carlo
    simulations. Management Science, 27, 322--335.

    Lesnevski, V., Nelson, B.L. and Staum, J. (2007) Simulation of
    coherent risk measures based on generalized scenarios.
    Management Science, 53, 1756--1769.

    Nelson, B.L. and Hsu, J.C. (1993) Control-variate models of common
    random numbers for multiple comparisons with the best.
    Management Science}, 39, 989--1001.

    Nelson, B.L. and D. Goldsman. (2001) Comparisons with a standard
    in simulation experiments. Management Science, 47,
    449--463.

    Nelson, B.L., Swann, J., Goldsman, D., and Song, W. (2001) Simple
    procedures for selecting the best simulated system when the number
    of alternatives is large. Operations Research,
    49, 950--963.

    Nelson, B.L. and Staum, J. (2006) Control variates for
    screening, selection, and estimation of the best. ACM
    Transactions on Modeling and Computer Simulation, 16,
    52--75.

    Paulson, E. (1952) On the comparison of several experimental
    categories with a control. Annals of Mathematical
    Statistics, 23, 239--246.

    Rinott, Y. (1978) On two-stage selection procedures and related
    probability-inequalities. Communications in
    Statistics--Theory and Methods, A7, 799--811.

    Ripley, B.D. (1987) Stochastic Simulation. John Wiley &
    Sons, New York, NY.

    Tsai, S.C., Nelson, B.L. and Staum, J. (2009) Combined
    screening and selection of the best with control variates.
    Advancing the Frontiers of Simulation: A Festschrift in
    Honor of George S. Fishman, Kluwer, 263--289.

    Tsai, S.C. (2010) Control variate methods for comparison with a
    standard. Journal of Statistical Computation and Simulation,
    accepted.

    Tsai, S.C. and Nelson, B.L. (2010) Fully sequential selection
    procedures with control variates. IIE Transactions,
    42, 71--82.

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