基于交叉效率和合作博弈的决策单元排序方法

Ranking Decision Making Units Based on Cross-efficiency and Cooperative Game

在数据包络分析中,大量的交叉效率模型已被提出。然而选择不同的目标模型将实现不一样的交叉效率评价。本文基于针对单个决策单元实施的对抗型和仁慈型两个交叉效率模型,用合作博弈方法来研究交叉效率模型的选取,并利用Shapley值对决策单元进行排序。最后通过实例分析显示该排序方法充分利用了最小交叉效率和最大交叉效率的信息完全排序了所有决策单元,具有一定的综合性和合理性。

In data envelopment analysis（DEA）,the cross-efficiency evaluation is an effective method for ranking decision making units（DMUs）,which is performed with peer-evaluation and self-evaluation.From different points of view,various secondary goals have been proposed such as the aggressive model and the benevolent model.Yet different secondary goal models lead to different cross-efficiency evaluation.In this paper,the cooperative game theory is used to choose the secondary goal model between the targeted aggressive model and the targeted benevolent model and then evaluate all DMUs.Specifically,it is assumed that a cooperative game is developed among all DMUs.Given a coalition of some DMUs,a DMU in this coalition will make the best appraisal of each DMU in the same coalition based on the targeted benevolent model,and choose the targeted aggressive model to evaluate the other DMUs which do not belong to the coalition.Further,each DMU is evaluated with its Shapley value in the cooperative game.Finally,an example is presented to show that the proposed method can make full use of the minimum crossefficiency and the maximum cross-efficiency and it is a comprehensive,fair and reasonable ranking method.