多項績效指標之三階段評估程序

Abstract

在多指標的評量問題下，高階管理人常常面臨到要如何制定指標的權重，以客觀的方法將下屬單位(DMU, decision-making unit)排序。本篇文章提出一三階段的程序，第一階段先讓每個DMU輪流當主角，以資料包絡分析法(DEA)之CCR模式計算出其最高之績效值。第二階段以每個DMU在第一階段所求出之績效值當作基準，選擇一組指標的權重使得其他DMU與主角之績效值差距之總和為最小。不同於參考文獻中非線性規劃模型之計算，我們提出線性規劃模型，避免了一項關鍵常數ε值的設定所產生之不確定性。第三階段帶入交叉效率的技巧，利用第二階段所求出之各主角的權重去計算其他DMU的交叉績效值。每個DMU的總交叉績效值，作為排序依據。並以台灣17個林區進行評估為例導引計算之程序。

Managers usually employ multiple indices to assess decision-making units (DMU) under their governance. We developed a three-phase procedure to rank the DMUs. The typical data envelopment analysis (DEA) CCR model is implemented in Phase-one to compute each DMU’s most favorable efficiency score. In Phase-two, we constructed a general non-linear mathematical programming model to obtain a set of weights attach to the performance indices for each DMU so that the total differences between his most favorable efficiency score and the other DMUs’ cross-efficiency scores is minimized. Additionally, based upon the general non-linear model, we considered three criteria for the differences measurement: the rectilinear, Euclidian and mini-max distances. In the case of rectilinear distance measurement, the non-linear model is converted into a linear model, and furthermore the critical coefficient ε is eliminated so that the precise result is obtained. Phase-three is summarizing the relative efficiency scores obtained in Phase-two. The total and average cross-efficiency score for each DMU is computed. DMUs are ranked according to the total or average scores. We illustrate the procedure by the data set of 17 forests in Taiwan form the published paper by Kao and Yang (1992).