A cross-efficiency evaluation method based on evaluation criteria balanced on interval weights

Abstract

Cross-efficiency evaluation approaches and common set of weights (CSW) approaches have long been suggested as two of the more important and effective methods for the ranking of decision making units (DMUs) in data envelopment analysis (DEA). The former emphasizes the flexibility of evaluation and its weights are asymmetric, while the latter focuses on the standardization of evaluation and its weights are symmetrical. As a compromise between these two approaches, this paper proposes a cross-efficiency evaluation method that is based on two types of flexible evaluation criteria balanced on interval weights. The evaluation criteria can be regarded as macro policy-or means of regulation-according to the industry's current situation. Unlike current cross-efficiency evaluation methods, which tend to choose the set of weights for peer evaluation based on certain preferences, the cross-efficiency evaluation method based on evaluation criterion determines one set of input and output weights for each DMU. This is done by minimizing the difference between the weights of the DMU and the evaluation criteria, thus ensuring that the cross-evaluation of all DMUs for evaluating peers is as consistent as possible. This method also eliminates prejudice and arbitrariness from peer evaluations. As a result, the proposed cross-efficiency evaluation method not only looks for non-zero weights, but also ranks efficient DMUs completely. The proposed DEA model can be further extended to seek a common set of weights for all DMUs. Numerical examples are provided to illustrate the applications of the cross-efficiency evaluation method based on evaluation criterion in DEA ranking.