新區隔自由配置階層排序法之建構與比較

A Study of Alternative Models for Discriminating Efficiency Units in Free Disposal Hull

胡信正(Shing-Cheng Hu)

指導教授 ： 鍾雲恭

元智大學/工程學院/工業工程與管理學系/博士(2011年)

https://doi.org/10.6838/YZU.2011.00071

摘要

自從「效率衡量」的觀念由學者Farell (1975)提出後，學者Charnes et al. (1978)與Deprin et al. (1984)將此觀念應用線性規劃技術，分別假定凸性與非凸性之前提下，各自發展出衡量決策單位(decision making unit, DMU)生產效率的線性規劃模型，前者稱Charnes, Cooper, Rhodes(CCR)模型，後者稱自由配置階層(Free Disposal Hul, FDH)模型。這兩種模型均採用「技術比例」計算被觀察DMU相對於全體DMU的生產效率，效率1為判定DMU是「有效率」的基準，所有有效率DMU會構成前緣線，包絡所有無效率DMU，因此發展「資料包絡分析」(data envelopment analysis, DEA)方法論。
後續為增強DEA方法論區隔有效率DMU的能力，清楚地排列它們的優先順序，雖然已發展出凸性Andersen & Petersen (A&P)及Mehrabian, Alirezaee, Jahanshloo (MAJ)超效率模型，以及非凸性A&P FDH與MAJ FDH超效率模型，然而這些模型存在「求解不穩定」及「區隔能力不足」的兩大缺點，限縮DEA方法論的應用性。本論文分別以凸性MAJ模型與非凸性MAJ FDH效率區隔模型為基礎，發展了Bounded MAJ與Modified MAJ FDH兩個效率區隔模型，預期改善現有模型的問題。研究發現，第一：當被評估DMU數大於投入與產出項數和時，使用Bounded MAJ模型是可行的作法。第二、當面對部分投入0時，Modified MAJ FDH模型的求解穩定性較Cross Efficiency Measure (CEM)、A&P、MAJ及Bounded MAJ等模型為佳。第三、Bounded MAJ模型及Modified MAJ FDH模型已能改善A&P模型及MAJ模型的缺點，使DEA方法論的應用範圍更廣泛。

關鍵字

資料包絡分析 ； 自由配置階層 ； 效率 ； 區隔

並列摘要

Since the seminal paper of Farrel (1957), the measurement of productive efficiency focuses on relative distances between an observed input-output combination and the boundary of the prevailing production technology.Data Envelopment Analysis is introduced by Charnes, Cooper and Rhodes (1978) and Free Disposal Hull (FDH) is proposed by Deprins, Simar and Tulkens (1984). DEA and FDH may generate plural efficient DMUs, so that for these units no ranking can be derived. Previous research has done to discriminate between efficient DMUs in DEA and FDH.
Therefore, the purpose of this study to proposed Bounded MAJ and Modified MAJ FDH that can successfully remove the above mentioned difficulties arising from the previous super-efficiency models. Results of the study show: (i) as the number of DMUs is greater than the sum of the number of inputs and outputs, Bounded MAJ provides a full ranking of DMUs and seems quite apt; (ii) where some of input levels are equal to zero, Modified MAJ FDH provides more stability efficiency measure than Cross Efficiency Measure, A&P, MAJ and Bounded MAJ; and (iii) Bounded MAJ and Modified MAJ FDH provide more wider applications than A&P, MAJ, A&P FDHMAJ, and avoids the use of hypothetical reference technology or price as the base for measuring production efficiency that leads to the closest envelop to the data, and the radial efficiency score of any productive unit is necessarily always based on an (other) observed unit.

並列關鍵字

DEA ； FDH ； Efficiency ； Discriminating

參考文獻

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