求解一組共同權重來衡量受評單位績效之二階段程序

Abstract

管理者利用多項指標進行績效評比時，權重的訂定通常為管理所面臨到的問題。資料包絡分析法(DEA)提供了一套方式來幫助管理者衡量決策單位(DMU)之績效表現，然而傳統DEA僅提供管理者分辨決策單位為高效或是非高效，在決策單位之績效衡量上面是一種相對績效的觀念，並沒辦法將決策單位之績效值進行排序，另外以傳統DEA為基礎下之交叉效率(cross efficiency)評估方法，應用在評估決策單位績效排序上面仍有其缺失，因此為了解決決策單位間績效值排序問題，本研究提出一二階段程序，第一階段利用決策單位之交叉效率值的平均當作組織所設定的參考水準。第二階段則是結合MCWA和距離函數之觀念，求出一組共同權重使所有受評單位距離參考水準的績效值差距總和最小。最後以台灣17個林區為例進行績效值之計算，並且比較其它學者所提出之距離函數方法之相同和相異處。

Managers usually assess the decision-making units (DMUs) under their governance with multiple input and output indices. However, making a decision to determine the weights attached to the indices across the units is a serious issue for managers. Data envelopment analysis (DEA) and cross efficiency support the alternative ways to measure the efficiency of the DMUs, while the conventional DEA only discriminates it into efficiency and non-efficiency and cross efficiency applied in the real world has its drawbacks. We could not rank DMUs directly as the measurement is a relative conception based on the structure of DEA; therefore, the methodologies propose a two-phase procedure to solve the problems before ranking those DMUs. Phase-one is to utilize the average scores of cross-efficiency to be organization’s target called reference level. Phase-two is to construct a general non-linear model to obtain a common set of weights and keep the total differences minimize between the efficiency of the assessment units and reference level through introducing the conception of MCWA and distance function. Finally, we illustrate the example by the data set of 17 forests in Taiwan to rank its efficiency and compare its similarity and difference to the methodologies.