以共同權重衡量指標重要性

Abstract

一類常見的績效評量的問題為多個作業單位將多項投入轉換成多項產出，本研究考慮管理者(簡稱為CDM, central decision-maker)欲以其次級單位(簡稱為UOA, unit of assessment) 在各指標的表現為依據，選擇一組合適的指標來做自我績效的評比。如何選擇一組合適的指標作為評量的基準，一直是一個很重要的問題。 本研究利用 Liu & Peng [10]所提出的共同權重分析法，並應用線性規劃中simplex method的概念提供一個指標重要性的排序方法。此外，本研究也將 Li & Liang [9]所提出的Shapley value的概念應用至共同權重分析法上來做指標重要性的排序。

Liu & Peng [10] considered a situation that a central decision-maker (CDM) assesses his/her subordinates with multiple inputs and outputs indices. The paper introduced a linear programming model to determine a set of common weights for the indices. This research is concerning one of the critical issues: what are the proper criteria to select the indices? We developed a procedure to rank the importance of the indices that is based on the characteristics of simplex method for linear programming models. We proof three theorems as the supporting. In addition, we also employed the method of Shapley value to rank the importance of indices.