用于广义 DEA 有效性的度量方法

摘要

在广义数据包络分析方法（data envelopment analysis，DEA）有效性度量方面还存在以下两个问题有待解决：第一，当广义 DEA 模型无可行解时，尽管被评价单元本身是有效的，但却无法用具体数值刻画其有效程度；第二，当单元为广义 DEA 有效时，某些单元的效率值存在被高估的情况。为解决这些问题，首先给出一个拓展的广义 DEA 模型。然后，给出了一种判定广义 DEA 模型存在无可行解情况的充要条件，以及单元效率被高估的判定条件。同时给出测定单元效率的3种方法，并讨论这些方法与原有测定方法的关系。最后，通过实际例子进行了对比研究。%There exist two problems that need to be solved on the efficient measure of generalized data eve-lopment analysis (DEA).Firstly,when the generalized DEA model is infeasible,the efficiency of the decision making unit cannot be expressed by detailed figures although it is efficient.Then,when decision making units are generalized DEA efficient,the efficiency of some decision making units may be over estimated.For these problems,first of all,a new generalized DEA model is given.Then,a necessary and sufficient condition for jud-ging the infeasibility of the generalized DEA model is given as well as the condition that the efficiency of decision making unit is overvalued.At the same time,three methods to measure the efficiency of decision making unit are provided,and the relationship between these methods and the original method is discussed.Finally,a com-parison study is done by an example.