依據虛擬差額評量各受評者之績效

Abstract

本研究提出虛擬差額分析(virtual-gap measurement, GVM)模型以解決資料包絡分析(data envelopment analysis, DEA)問題。VGM計算出各產出與投入項之最優權重值，最小化主角DMU之虛擬差額即各投入項加權後的總和(虛擬投入)與各產出項加權後的總和(虛擬產出)之差。最大化主角DMU之績效值等於虛擬產出與虛擬投入比值。VGM之對偶模型提供各投入項與產出項之改善目標。本文將與輻射型模型和非輻射型模型如CCR, BCC, ADD, MIP, RAM和SBM做對比。根據虛擬投入與虛擬產出值，將所有DMU標記在平面圖上可以直觀看出其相對績效表現。在變動規模報酬條件下，規模報酬判斷值可能小於、等於、或者大於零來判斷DMU分別屬於遞增、固定、或者遞減規模報酬。本研究將規模報酬判斷值分別分給虛擬投入和虛擬產出兩項，並解析在規模報酬遞增(遞減)情形下，績效值隨著投入(產出)項改善而隨之遞增。

In the current paper we introduced virtual-gap measurement (VGM) model to solve data envelopment analysis (DEA) problems. VGM assigns an optimal set of weights of input and output measures to the decision-making unit (DMU) under evaluation so that its virtual-gap between its sum of weighted inputs (virtual-input) and the sum of the weighted outputs (virtual-output) is minimized. Its maximum efficiency score equals to the ratio of the virtual-output to virtual-input. The dual of VGM model provides the target of improvement ratio for each input and output measure. We compare VGM to the main radial and non-radial DEA models such as CCR, BCC, ADD, MIP, RAM and SBM. Plot all DMUs on a plane graph according to their virtual-input and virtual-output values would enable us to virtualize their relative efficiencies directly. With the condition of variable return-to-scale, the obtained scale adjustment value could be either less, equal or greater than zero that indicates the DMU under evaluation is increase, constant and decrease of return-to-scale, respectively. The scale adjustment value is partitioned into two parts to adjust virtual-input and virtual-output separately. For the case of increase (decrease) return-to scale, the efficiency score is monotone increasing as the improvement ratios on inputs (outputs).