應用虛擬差額模型於多方向績效分析法

Abstract

資料包絡分析Data Envelopment Analysis (DEA)的起源模型分別以投入導向或是產出導向計算被評量的決策者(object decision-making unit, DMUk)的綜合績效，及其改善後各項投入與產出的值，使其綜合績效值改善成1。Bogetoft and Hougaard(1999)提出Multi-direction Efficiency Analysis (MEA)模型，求得DMUk各投入項及各產出項一共同的改善倍率，但是改善後的綜合績效值仍未達到1。Asmild and Pastor(2010)所提出兩階段的方法，試圖讓改善的綜合績效值達到1，但仍存在缺點。本研究延伸該方法，提出第三階段的Modified MEA模型，使得改善後的綜合績效值達到1。第三階段又分為以Slacks-Based-Measurement (SBM)與Virtual-Gap-Measurement (VGM)之兩種模型。每種模型又有三個變化型式，以不同的標竿量測綜合績效值。

Original Data Envelopment Analysis (DEA) models are either input-oriented or output-oriented to measure the object decision-making unit’s (DMUk) aggregate efficiency as well as the improvement target of its inputs and outputs levels so that the aggregate efficiency becomes 1. Multi-direction Efficiency Analysis (MEA) model computes the common ratio for all inputs and outputs for improvement. The improvement target still does not have full efficiency. Asmild and Pastor(2010) adds phase-2 model for improvement. The current research appends phase-3 to ensure the target has full efficiency. In Phase-3, we introduce two streams that are Slacks-Based-Measurement (SBM) and Virtual-Gap-Measurement (VGM) models. For each stream, we consider three variations on selecting the benchmarks. A numerical example is used to compare the characteristics of the referred models.