以虛擬差額方法評量超高效與超低效

Abstract

受評量的決策單位(decision-making unit, DMUk)以原始資料包絡分析法(Data Envelopment Analysis, DEA)量測其最佳綜合績效值時(best-practice, BP)，分別以產出導向或投入導向求得其最近的改善目標。若DMUk最佳綜合績效值為1時，可利用另行發展出的超高效計算模型(super-efficiency)，計算出DMUk綜合績效值超過1的最小值，分別以產出導向或投入導向求得其最近的惡化點，在該點其綜合績效值將等於1。DMUk以原始DEA量測其最差綜合績效值時(worst-practice, WP)，分別以產出導向或投入導向求得其最近的惡化點達到最低效外緣。若惡化程度量測模型(worst-practice)計算出 DMUk的的最差綜合績效值為1時，可利用另行發展出的超低效(hypo-efficiency)模型，計算出DMUk各投入與產出項改善後的目標值。該目標值若再以worst-practice模型計算出的最差綜合績效值為1。換言DMUk改善至目標點時，將脫離最差的DMU成員之一。文獻中可見到以輻射為基型(radial-based)的DEA模型如CCR-I, CCR-O, BCC-I, BCC-O。也可見到以差額為基型(slacks-based)的DEA模型如SBM, ADD, MIP等。本研究利用差額為基型(slacks-based)的VGM (virtual-gap-measurement) DEA模型建立了上述之 BPF, WPF, super-efficiency 和 hypo-efficiency四個議題的數學規劃模型。幾以一數據例子分別利用文獻以及本研究之模型加以分析，並比較其效能。

Original Data Envelopment Analysis (DEA) models measure the best aggregate efficiency score of the object decision-making unit under evaluation, DMUk. Either input-oriented or output-oriented model is used to obtain the improvement target (best-practice) of each input and output. If DMUk score equals 1, one may use the developed model to measure the minimum super-efficiency that is greater than 1. The deteriorate level of each input and output are identified. At the deteriorated level, DMUk still has efficiency score 1. Original Data Envelopment Analysis (DEA) models measure the worst aggregate efficiency score of DMUk. Either input-oriented or output-oriented model is used to obtain the deteriorated bound (worst-practice) of each input and output. For the case the worst-practice model measured the worst-efficiency score of DMUk equals 1, one could employ the hypo-efficiency model to identify the improvement target of inputs and outputs. At the target, its worst-efficiency score is no less than 1 that ensures DMUk is not one of the worst DMUs that were identified by worst-practice model. Radial-based DEA models such as CCR-I, CCR-O, BCC-I, and BCC-O and slacks-based DEA models such as SBM, ADD, and MIP could be employed to measure the four efficiency scores: best-practice, worst-practice, super-efficiency, and hypo-efficiency. The current research proposes to employ virtual-gap-measurement (VGM) DEA model to measure the four efficiency scores. A set of numerical example would be used to compute the four efficiency scores of the virtual and slacks based DEA models. Comparisons between the DEA models that are at different bases would made to see the strength of VGM model.