A note on "The cross-efficiency in the optimistic-pessimistic framework"

This note considers the model developed by Khodabakhshi and Aryavash (Oper Res Int J 17:619-632, 2017); in which the authors propose a new model for cross-efficiency in Data Envelopment Analysis. This procedure proposes the determination of the maximum and the minimum efficiency scores of each unit under the assumption that the sum of the efficiency values of all the units is equal to unity. A ranking of units is constructed on the basis of a score obtained as a combination of these maximum and minimum scores. In the present note, we show that the model developed in the aforementioned studied requires the inclusion of additional conditions in order to guarantee that the efficiency scores are properly computed, and the correct ranking is obtained.