基于样本评价的广义数据包络分析方法  

Generalized Data Envelopment Analysis Method by Using Sample Units

作　　者：马占新[1,2] 马生昀[2,3] 

机构地区：[1]内蒙古大学经济管理学院,内蒙古呼和浩特010021 [2]内蒙古大学数学科学学院,内蒙古呼和浩特010021 [3]内蒙古农业大学理学院,内蒙古呼和浩特010018

出　　处：《数学的实践与认识》2011年第21期155-171,共17页Mathematics in Practice and Theory

基　　金：国家自然科学基金(70961005;70501012);内蒙古自治区自然科学基金重点项目(2010zd34)

摘　　要：传统DEA方法是一种依据自评体系评价的方法,而无法自主选择参照系.为了解决DEA方法可以同时依据自评体系和其它参照系进行评价问题,首先给出了广义DEA有效的概念.然后,给出了一类基于样本单元评价的广义数据包络分析模型,包括面向输入的广义DEA模型、面向输出的广义DEA模型以及加性广义DEA模型.最后,分析了上述这些模型与传统DEA模型之间的关系,探讨了广义DEA有效与相应多目标规划Pareto有效之间的关系,并给出了决策单元的投影性质以及决策单元的有效性排序方法.Traditional DEA method is evaluation method based on a self-assessment system, decision-makers can not choose a frame of reference freely. In order to solve the DEA method can also based on self-assessment system and other frame of reference for evaluation, the concept of the generalized DEA efficiency is presented at first. Then a class of generalized data envelopment analysis models based on the sample units are given, including generalized DEA model for input-oriented and output-oriented situation, and generalized additive DEA model. Finally, the relationship between these models and the traditional DEA models is analyzed, the relationship between the generalized DEA efficiency and corresponding Pareto efficiency of multi-objective programming is explored, and the property of projection and the method of ranking decision making units are given.

关 键 词：综合评价 多目标决策 数据包络分析 决策单元 样本单元 

分 类 号：N945.1[自然科学总论—系统科学] O242.1[理学—计算数学]