基于C^2W模型的广义数据包络分析方法研究

Generalized data envelope analysis method based on C^2W 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,给出了包含无穷多个样本单元的广义数据包络分析模型(Sam-C2W)和相应的Sam-DEA有效性概念。分析了(Sam-C2W)模型的性质以及它与传统DEA模型之间的关系,探讨了(Sam-C2W)模型刻画的Sam-DEA有效性与相应的多目标规划Pareto有效解之间的关系。进而,分析了决策单元在样本可能集中的分布特征、投影性质和模型含义等问题,(Sam-C2W)模型不仅具有传统C2W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 units set （non-DMU Set）, then traditional DEA methods can only give the information which have relation to DMU Set but any non-DMU Set. In order to make DEA method have the a- bility to provide information by using DMU Set and non-DMU Set, a generalized data envelope analysis model （Sam-C2W） and the corresponding conception of DEA efficiency（Sam-DEA） are given. Then the properties of （Sam-C2W） model are discussed, and the relationships between （Sam-CZW） model and the traditional DEA models are analyzed. In addition, this paper studies the relationship between Sam-DEA efficiency and the pareto effective solution of the relevant multiple objective programming. Finally, the properties on projection and dis- tribution of decision making units are studied. （Sam-C2W） model not only has all the properties of traditional C2W model, but also can provide information by any frontiers of reference set.