共同權重分析法應用於多個次級單位的最差績效評估

Abstract

以一高階管理者(central decision-maker , CDM)而言，他持續評量底下的次級作業單元(unit of assessment, UOA)，並適時將不合時宜的作業單元加以裁撤。本研究提供一完整考慮多投入與多產出的線性規劃模型，目的在於衡量高階管理者及其底下的次級作業單元的最差績效。藉由此模型，能幫助高階管理者決定出一組最保守的共同權重組合。根據此共同權重組合，高階管理者能得到自身的最差績效，藉此績效做為全體的績效底線。除此，此共同權重亦能得到次級作業單元的最差績效。此最差績效提供高階管理者裁撤的依據，亦警惕次級作業單元距離被裁撤的危險程度。當次級作業單元的最差績效等於一時，代表其虛擬投入等於虛擬產出，亦即虛擬差額等於零，已達危險邊界，將是首要被裁撤之次級作業單元。若次級作業單元的最差績效大於一，代表虛擬產出大於虛擬投入，亦即虛擬差額大於零，尚有空間減少虛擬產出貨增加虛擬投入，對於被裁撤尚有議價空間之次級作業單元。 本研究延伸Liu and Peng [7]提出之共同權重分析法(Common Weights Analysis, CWA)，建立一衡量最差績效之模型─Worst CWA。同時，為了避免某項指標過於顯著地凌駕其他指標，本研究亦將Worst CWA模型加入權重限制，提出一虛擬權重限制的模型─VWR-Worst-CWA。

In the presence of a set of inputs and outputs performance index, a central decision-maker (CDM) desires to assess a set of his subordinate units and shall be timely abolished. In the current paper, we introduced the linear programming models to measure the worst-practice efficiency score of the CDM and his subordinate units. The model would determine two sets of weights to attach to the indices. For each subordinate unit, the sums of weighted inputs and weighted outputs are its virtual input and virtual output, respectively. A subordinate unit the virtual gap is zero that its virtual input equals to virtual output. It is the one is cautioned they could be abolished. A unit has a virtual gap would have certain empty to increase its virtual input and to decrease its virtual output. According to the worst-practice efficiency score, the CDM is able to manage its subordinates and allocates its inputs and outputs. Each UOA concerns its worst performance degree for avoiding to be abolished. In addition, we considered several virtual weight restrictions (VWR-Worst-CWA) in order to avoid a particular index dominate the analysis results. It could help CDM to determine an objective common set of weight to assess each subordinate unit.