The New Neutral Secondary Goal based on Ideal DMU Evaluation in Cross-Efficiency

Cross-efficiency is a famous ranking method for data envelopment analysis (DEA) that deletes unrealistic weights pattern with no need to a priori information related to weights restrictions. This method analyzes each decision making unit (DMU) taking into account the best weights resulted from assessing other DMUs. In cross-efficiency evaluation, secondary goals such as aggressiveness, benevolence and neutrality are used because there are alternative optimal solutions. The neutral secondary goal makes the decision maker have no problem in selecting the aggressive and benevolent secondary goals. In the article at hand, a new secondary purpose is introduced which selects the optimal weight among the multiple optimal weights based on the evaluation of ideal virtual DMUs corresponding to each DMU. Since this kind of weight selection does not lead to any increase or decrease in other DMUs' cross-efficiency, the new secondary goal is neutral. The advantage of this method over other methods is that the selected weights are the best possible weights, because it maximizes the ideal virtual DMUs' efficiciency score corresponding to each DMU. For this purpose, some examples are used to illustrate its difference with other methods.