Determination of cross-efficiency under the principle of rank priority in cross-evaluation

As an extension to data envelopment analysis (DEA), cross-efficiency evaluation method not only provides a ranking among the decision making units (DMUs), but also eliminates unrealistic DEA weighting schemes without requiring a prior information on weight restrictions. A factor that possibly reduces the usefulness of the cross-efficiency evaluation method is that the cross-efficiency scores may not be unique due to the presence of alternate optima. As a result, it is recommended that secondary goals be introduced in cross-efficiency evaluation. In some cases, pursuing the best ranking is more important than maximizing the individual score. This paper seeks to propose a novel model for optimizing the ranking order for each DMU to determine the final cross-efficiency of all DMUs. Finally, preference voting application is presented to illustrate the differences between the proposed and existed models.