資料包絡分析之折衷權重的探討

To Study the Common Compromise Weights of Data Envelopment Analysis

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

《管理研究學報》 11卷2期 (2012/05) Pp. 89-110

https://doi.org/10.6626/MR.2012.11(2).04

摘要

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。

關鍵字

資料包絡分析 ； 共同權重 ； 折衷權重 ； 判定係數 ； 適配性

並列摘要

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.

並列關鍵字

Data Envelopment Analysis (DEA) ； Common Weight (CW) ； Common Coompromise Weight (CCW) ； Determinant Coefficient ； Goodness of Fitting

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