依據虛擬差額評量兩階段DEA分享投入及分攤產出

Abstract

本研究的運作系統包含兩個子系統，每個子系統分別擁有各自的投入指標，轉換為各自的產出指標。在兩個子系統之間有一組中間指標, 此兩個子系統分享一組額外的投入指標，並且分攤一組額外的產出指標，他們分享與分攤的比例介於上下限之間。一群決策單位(簡稱DMUs)在相同的系統下運作，收集了他們各指標的數據，本研究旨在發展一方法用以量測每個DMU相對於其他DMU的綜合績效值。此為DEA (Data Envelopment Analysis, 資料包絡分析)的延伸研究，我們提出兩步驟的方法。在第一步驟中，以一個混合二元整數規劃模型，將被量測的DMU(稱之為DMU-k)的中間指標區分為「視同投入」指標和「視同產出」指標。第二步驟以線性規劃模型計算各項指標的權重，以及各子系統分享與分攤的比例。各投入指標與「視同投入」指標改善的降低比率，各產出指標與「視同產出」指標改善的增加比率也同時求得。整體系統與各子系統的績效值也計算得知。

The aim of this research is to assess a group of Decision-Making Units (DMUs) under the operation systems that contain two internal subsystems. Each subsystem consumes respective inputs to convert to outputs. In addition, there is a set of intermediate measures between the two subsystem s. Moreover, the two subsystems may share an additional set of inputs and outputs with given the upper and lower bounds of the sharing proportions. We collect data of DMUs in same operation system. The current research comes from Data Envelopment Analysis (DEA). We develop a two-phase procedure to assess each DMU efficiency score. In Phase I, a mixed integer programming model is employed to partition the intermediate measures into ‘as-input’ and ‘as-output’ of each DMU-k. Phase II is a linear program to determine the weights of the inputs, outputs, as-inputs and as-outputs. The program also determines the best ratios with ‘as-input’ and ‘as-output’. The DMU under evaluation would have the highest aggregation efficiency score.