Global correlation coordination model for ranking decision-making units based on cross-efficiency game

Abstract

DEA cross-efficiency evaluation method can rank decision making units (DMUs) more reasonably than the classical DEA model, but the existing cross-efficiency evaluation methods still have many deficiencies. The most evident drawback is that the potential multiple solutions of the optimal weights lead to the non-uniqueness of the cross-efficiency value. Moreover, the traditional cross-efficiency ranking methods neglect the interaction between DMUs. It is a common scenario that the decision-making unit will incline to give high evaluation scores to those in same coalition, and relatively low evaluation scores to those with different coalitions on the contrary in the process of cross-efficiency evaluation. Aiming at solving the above problems, this study proposes a cross-efficiency game model considering correlation coordination degree among DMUs. The generalized Shapley value of cross-efficiency game is defined, and its desirable properties are proved in detail. Finally, a global correlation coordination (GCC) model is developed for ranking decision-making units comprehensively. The comparative example and practical application on R&D efficiency evaluation are provided to illustrate the rationality and feasibility of the GCC model.