A neutral DEA model for cross-efficiency evaluation

The Cross-efficiency method in data envelopment analysis (DEA) has widely been used as a suitable utility for ranking decision-making units (DMUs). In this paper, for overcoming the issue of the existence of multiple optimal solutions in cross-efficiency evaluation, we use the neutral strategy to design a new secondary goal. Unlike the aggressive and benevolent formulations in cross-efficiency evaluation, the neutral cross-efficiency evaluation methods have been developed in a way that is only concerned with their own interests and is indifferent to other DMUs. The proposed secondary goal introduces a new cross-efficiency score by maximizing the sum of the output weights. The first model is then extended to a cross-weight evaluation, which seeks a common set of weights for all the DMUs. Finally, we give two numerical examples to illustrate the effectiveness of the proposed neutral models and the potential applications in ranking DMUs by comparing their solutions with those of alternative approaches.