为解决交叉效率方法中存在的多解问题,进取型权重与仁慈型权重方法被提出,所有决策单元要么同时被视为盟友,要么同时被视为敌对方,这并不完全符合各决策单元的个人意愿.因此,提出一种竞合DEA交叉效率方法,将所有决策单元分为若干组,各个决策单元的偏好权重能最大化盟友的总效率而最小化敌对方的总效率.这种权重选择策略体现了不同决策单元的个人偏好,故可以更方便地应用于实践中.最后,通过一个算例演示了这一方法.

To eliminate the possible multiple solutions in the cross efficiency method, researchers proposed two approaches including the aggressive strategy and the benevolent strategy in which all of the other decision-making units are simultaneously treated as adversaries (allies) to the unit under evaluation. However, none of the strategy may accord completely with the individual preference of a specific DMU. Therefore this paper proposed a DEA cross-efficiency method considering both competition and cooperation among DMUs. All decision making units are divided into several groups. For a given DMU, its optimal preferential weights can maximize the aggregated efficiency of its allies and also minimize the aggregated efficiency of its adversaries. The proposed strategy allows for a specific DMU’s individual preference in differential treatment to other DMUs, which makes it more applicable. Finally a numerical example is provided to illustrate the proposed approach.