資料包絡分析之折衷權重的探討

To Study the Common Compromise Weights of Data Envelopment Analysis

10.6626/MR.2012.11(2).04

薄喬萍(Chiao-Pin Bao)；蔡美英(Meei-Ing Tsai)；蔡明智(Ming-Chi Tsai)

資料包絡分析 ； 共同權重 ； 折衷權重 ； 判定係數 ； 適配性 ； Data Envelopment Analysis (DEA) ； Common Weight (CW) ； Common Coompromise Weight (CCW) ； Determinant Coefficient ； Goodness of Fitting

管理研究學報

11卷2期（2012 / 05 / 01）

89 - 110

繁體中文

為了提高效率評估之鑑別度，本研究提出一個眾人共同接受的“折衷權重”（Common Compromise Weights，CCW）效率評估方法，不但能提高績效評估時之鑑別度，而且計算出來的權重值和以CCR模式所求出者，對個別DMU最佳的權重値之間差異最小，因此較容易為全部DMU所共同接受。本研究以各權重函數之最小平方法，求得最適“折衷權重”，並以兩個定理佐證推論。文中，並以汪漢英等（2007）及Roll et al.（1991）論文之資料為範例，比較本研究之“折衷權重”法與既有三種評估方法之優劣。研究結果顯示，本研究所提之方法與另外兩種評估方法，其相關程度均達80%以上，而且本研究所提之“折衷權重”法，更具有顯著之鑑別度，再以迴歸分析方法，驗證四個評估模式的準確度，可看出有三個模式的效率值與投入變項皆為負相關，與產出變項皆為正相關，顯現投入越少、產出越多則效率越佳，三個評估模式的迴歸方程式均可合理的解釋評估結果。但本研究所提之“折衷權重法”，其判定係數R2為0.9721及0.9982，ANOVA檢定之P值為9*10^-6及1.4*10^-5，顯示有極佳的解釋力與線性適配性。

To increase the level of distinguish ability in efficiency evaluation, and this research proposes a Common Compromise Weights, CCW, method that is accepted easier by all the evaluated units. The proposed method not only increase the level of distinguish ability in efficiency evaluation, but also obtain a set of weights that have minimum difference with the set of weights obtained from the CCR model.By applying least square method to the function of weights, the common consensus weights are obtained. This research also provides evidence for the inference by two theorems. Moreover, data from Wang et al. (2007) and Roll et al. (1991) are used as examples to compare the virtues and defects of the proposed method with three existing evaluation methods.Results show that the correlation between the proposed method and two existing methods is greater than 80%. In addition, the proposed method provides better distinguish ability. Regression analysis is then used to verify the correctness of the evaluation models. And it appear that the regression equations of three models can interpret reasonably the evaluation results since the efficiencies of DMUs have negative correlation with their inputs and positive correlation with their outputs. However, the determinant coefficients, R^2, of the proposed method equal 0.9721 and 0.9982, respectively, and the P-value in ANOVA test of the proposed method is 9*10^-6 and 1.4*10^-5, respectively. These show that the proposed method provides excellent interpretation and goodness of fitting.

1. 王媛慧、李文福(2006)。我國大學院校技術效率之研究-資料包絡分析法的應用。輔仁管理評論，13(1)，163-186。
   連結：
2. 王斐青、洪維廷、尚瑞國(2005)。台灣地區國際觀光旅館產業生產力變動之研究。亞太經濟管理評論，9(1)，129-160。
   連結：
3. 李正文、陳翔修(2008)。台灣光電產業之經營效率分析―資料包絡分析法之應用。中原企管評論，6(1)，1-30。
   連結：
4. 汪漢英、黃文聰、黃開義、畢威寧(2007)。應用資料包絡分析法之大學學系績效評估實證研究。人文暨社會科學期刊，3(2)，55-66。
   連結：
5. 洪維河、江東亮、張睿詒(2005)。市場結構與組織特性對醫院營運效率之影響。管理學報，22(2)，191-203。
   連結：
6. Pareto, V. (1927). Manuel d'Economic Politique. (2nd ed.). Paris, Girard.
7. Charnes, A.,Cooper, W. W., Rhodes, E.(1981).Evaluating Program and Managerial Efficiency: an Application of Data Envelopment Analysis to Program Follow Through.Management Science,27(6),668-697.
8. Charnes, A.,Cooper, W. W.,Rhodes, E.(1978).Measuring the Efficiency of Decision Marking Units.European Journal of Operational Research,2(6),429-444.
9. Chen, Tien-Hui(2009).Performance measurement of an enterprise and business units with an application to a Taiwanese hotel chain.International Journal of Hospitality Management,28,415-422.
10. Doyle, J.,Green, R.(1994).Efficiency and cross-efficiency in DEA: derivations, meanings and uses.Journal of the Operational Research Society,45,567-578.
11. Farrell, M. J.(1957).The measurement of productive efficiency.Journal of the royal statistical society,120,253-290.
12. Hwang, S. N.,Chang, T. Y.(2003).Using data envelopment analysis to measure hotel managerial efficiency change in Taiwan.Tourism management,24,357-369.
13. Roll, Y.,Cook, W. D.,Golany, B.(1991).Controlling factor weights in data envelopment analysis.IIE Transactions,23,2-9.
14. Roll, Y.,Galony, B.(1993).Alternate methods of treating factor weights in DEA.Omega,21,99-109.
15. Thompson, R. G.,Singleton, F. D. Jr.,Smith, B. A.,Thrall, R. M.(1986).Comparative site evaluations for locating high energy lab in Texas.TIMS Interfaces,1380-1395.
16. 張銘哲(2009)。台中市，國立中興大學會計學研究所。
17. 陳美源(2009)。台中市，國立中興大學高階經理人碩士在職專班。
18. 陳家彬(2009)。台中市，國立中興大學企業管理學系研究所。
19. 詹達穎、林政賢(2004)。台灣半導體產業經營績效之研究―資料包絡分析法之應用。立德學報，2(1)，9-29。
20. 薄喬萍(2007)。績效評估之資料包絡分析法。台北:五南圖書。

1. 魏乃捷、薄喬萍、蔡美英、蔡明智(2016)。以二階段資料包絡分析衡量紡織產業之經營效率與市場能力。高雄應用科技大學人文與社會科學學刊，2(2)，33-48。