績效評量指標間交互影響效應之數學規劃分析模型

Abstract

本研究以多投入與多產出的數據進行評量多家有相似生產程序的生產公司的綜合績效。第一個步驟是應用AHP中「成對比較矩陣」的方法加入「群體決策」的概念找出投入與產出指標的交互影響效應的比例；第二步驟為每間公司會輪流當受評單位中的評量標竿，以極端差額模型評定出全部優質者(劉復華 & 吳明謙, 2017)，決定各投入與產出項的影子價格，並量測每間公司與標竿公司的虛擬差額，將最大差額最小化。傳統資料包絡分析法(Data Envelopment Analysis, DEA)僅能在效率前緣上找出一個參考對象，並以對偶模型之影子差額進行改善，與實務較不相符；而本研究能使被評量公司同時找到多個不論差額大小的參考對象，被評量公司可評量自己可改善程度，進行逐一改善，直至成為效率最好，較貼近實務。

In this paper we introduce a procedure to assess a set of similar production firms of an industry. We use the dataset of firms’ multiple inputs and outputs for assessment. In the first step of our procedure, we apply group decision-making method that is the pair-comparison method usually used in AHP, to determine the weights of partial effects between inputs set and outputs set. In the second step, each firm is evaluated to identify it benchmark firms. We employ the linear programming model, Extreme Gaps-based Measurement (EGM)(Liu & Wu, 2017), to establish a new min-max linear programming model to determine the shadow prices of the inputs and outputs bundle and to measure the virtual gaps of all outperformed firms, and the maximum gap is minimized. The shadow slacks of inputs and outputs are the decision variables of the dual form of the model. The advantage of our procedure is to allow the firm under evaluation has multiple targets to improve, from the nearest one to the furthest one. Unlike the legacy assessment models of Data Envelopment Analysis (DEA) that only find the single target on the frontier, which could be too far to reach in practical considerations.