以虛擬差額模型為基底:測量指標間影響力差異化之績效分析

Abstract

傳統的 DEA 認為各項投入指標對於各項產出指標之間的影響力不具差異化,然而 在實務上卻存在著各項投入的資源以不同比例分配給各產出項目的情形。(Cook & Imanirad, 2010)提出此論點,稱為指標間具有局部影響力(Partial-effect)。(Imanirad et al., 2013) ,(Imanirad et al., 2015)延續此論點並提出更新的方法。這些方法侷限於投入導向 之 DEA 模型,且影響力比例值為決策變數需提供其上、下限值,存在著理論與實務上 的缺陷。本研究利用「成對比較矩陣」的方法計算出投入指標與產出指標之間的局部影 響力之比例值,再以 VGM-DEA 模型為基底,量測在具有局部影響力條件下各決策單位 的績效值。本研究分為固定規模報酬與變動規模報酬兩種條件下進行分析,考慮三種情 形:投入指標有局部影響力、產出指標有局部影響力、以及投入與產出均有指標有局部 影響力。本研究發現指標間影響力差異化會使得低效點的改善幅度增加,並增加各決策 單位間績效值的差異化。

Traditional DEA models generally assumed that all outputs are impacted by all inputs. (Cook & Imanirad, 2010) proposed a DEA model to measure the technical efficiency in situations where only partial input-to-output impacts exist. (Imanirad et al., 2013) and (Imanirad et al., 2015) improved the method and model. Even though, there are still some defects in the theory and the reality. Including the method could be used only in input-oriented DEA model and the effect ratio between each pair of input and output is a decision variable with given upper and lower limits. This paper adopts the method of pairwise comparison matrix that frequently used in Analytical Hierarchy Process (AHP) to determine the partial effect between outputs respect to a specific input. We further consider the situation that a specific output has partial effected by the inputs. We adopt virtual-gap measurement (VGM) DEA model to measure efficient scores of DMU when the partial-effect exists. This paper analyze under two different conditions, constant return-to-scale (CRS) and variable return-to-scale (VRS). Consider the follow three situations, partial-effect on input indexes, partial-effect on output indexes and partial-effect on both input and output indexes. This research finds that the concept of partial-effect let the inefficient point have more room for improvement. This research also makes the differentiation of efficiency score between DMUs much obviously.