Using Directional Distance Functions to Determine Ranking Ranges in Cross-efficiency Evaluations

Having a ranking range for each unit allows for assessing the extent to which the choice of DEA weights may affect the ranking derived from the cross-efficiency evaluation and can deal with the most important difficulty of cross-efficiency evaluations (i.e., the possible existence of alternative optimal solutions for the DEA weights, which may lead to different cross-efficiency scores depending on the choice that is made). This may, furthermore, yields some useful information in the case of real life problems. This paper develops the ranking ranges by the use of directional distance functions in calculating cross-efficiency evaluations. In this case, by simultaneously accounting for the inefficiency in inputs and outputs, more comprehensive ranking ranges were achieved in crossefficiency evaluations. A numerical example is presented to show the validity of the proposed procedure by comparing the results with those of the previous approaches.