Determination of the Weights of Ultimate Cross Efficiency based on the Solution of Nucleolus in Cooperative Game

This article firstly introduced the cross efficiency evaluation method, analyzed the flaws when the ultimate average cross efficiency were used to evaluate decision making units (DMUs), eliminated the assumption of average and combined the theory of cooperative games, the DMUs evaluated were considered as the players of the game, and we defined the coalitional game that included all DMUs and the characteristic function values of every coalition. On the basis of the analysis of solutions of the coalitional game, we chose the nucleolus to be final solution and the Genetic Algorithm (GA) was used to get the nucleolus, and the ultimate weight of each DMU was determined. In the end, an empirical example was illustrated to examine the validity of the proposed method.