績效評估對管理者而言，是一項很重要的議題，因爲它可以被用來當作效率改善的參考決策。在執行資料包絡分析(data envelopment analysis, DEA)模式時，會產生一組對偶變數(dual variable)。對偶變數之值可做爲調整投入產出變項之水準，以改進無效率決策單位之效率值。傳統的處理方式是，以一個對偶變數對應到原始模式中之正規方程式(normalizing equation)，此方式意味著每一個投入變項或產出變項均需調整相同的投入比例或產出比例，方能達到柏瑞圖之最佳效率值(Pareto efficiency)。本研究透過分解正規方程式的方法，修改傳統的資料包絡分析模式，期使每一個投入或產出變數能對應到不同的對偶變數，以提供決策單位另一個效率改善目標的選擇。本研究同時探討外生變數(exogenous variable)在非射線資料包絡分析模式之效率改善問題。

Data envelopment analysis (DEA) is a mathematical programming approach for measuring the relative efficiencies within a group of decision making units. An important outcome of such an analysis is a set of values for dual variables which indicate how the associated factors should be adjusted so that input wastages and/or output shortfalls can be eliminated. The traditional DEA model gives a dual variable to associate with the normalizing equation. This setting implies that the adjustment proportions of all input or output factors are the same for efficiency improvement. This study modifies the original DEA model by decomposing the normalizing equation in order to for it to be associated with different dual variables. As a consequence, to improve efficiency the adjustment proportion of each input or output factor can be different. In essence, the proposed approach can not only set targets of factors for inefficient decision making units to eliminate inefficiency, but can also deal with the exogenous variables in a DEA context.