基于C^2WY模型的广义数据包络分析方法

Generalized data envelopment analysis method based on C^2WY model

如果将评价的参照集分成"决策单元集"和"非决策单元集"两类,那么传统的DEA方法只能给出相对于决策单元集的信息,而无法依据任何非决策单元集进行评价,这使得DEA方法在众多评价问题中的应用受到限制.针对传统数据包络分析方法无法依据指定参考集提供评价信息的弱点,给出了综合的广义数据包络分析模型(Sam-C^2WY)和相应的Sam-DEA有效性概念.分析了Sam-C^2WY模型的性质以及它与传统DEA模型之间的关系,探讨了Sam-C^2WY模型刻画的Sam-DEA有效性与相应的多目标规划非支配解之间的关系.进而,分析了决策单元在样本可能集中的分布特征、投影性质等问题,Sam-C^2WY模型不仅具有传统C^2WY模型的全部性质,而且还能依据任意指定的参考单元集进行评价.

Suppose that the reference set of evaluation can be grouped into the decision-making unit set （DMU Set） and non-decision-making unit set （non-DMU Set）, then traditional DEA methods can only give the information which have relation to DMU Set but not any non-DMU Set. In order to make DEA method have the ability to provide information by using DMU Set and non-DMU Set, a generalized data envelopment analysis model （Sam-C2WY） and the corresponding conception of DEA efficiency（Sam-DEA） are given. Then the properties of （Sam-C2WY） model are discussed, and the relationships between （Sam-C2WY） model and the traditional DEA models are analyzed. In addition, this paper studies the relationship between Sam-DEA efficiency and the non-dominated solution of the relevant multiple objective programming. Finally, the properties on projection and distribution of decision making units are studied. Sam-C2WY model not only has all the properties of traditional C2WY model, but also can provide information by any frontier of reference set.