Allocation of Weights Using Simultaneous Optimization of Inputs and Outputs Contribution in Cross-Efficiency Evaluation of DEA

Seyed Hadi Nasseri, Hamid Kiaei

Cross-efficiency evaluation, an extension of the data envelopment analysis (DEA), has found an appropriate function in ranking decision making units (DMU). However, DEA suffers from a potential flaw, that is, the existence of multiple optimal solutions. Different methods have been proposed to obtain a unique solution (based on a specific criterion). In this paper, we refer to Wang’s method for ranking DMUs but argue that his way of selecting the weights is not the appropriate one. Namely, in the cross-efficiency evaluation of DMUs, we always search for the weights which use minimum resources to increase the production. Therefore, we suggest that the selection of weights among the multiple weights should be determined by decreasing the contribution of inputs in the use of resources, and increasing the contribution of outputs in the production, which should overtly prevent the selection of zero solutions to the extent possible. To this end, some examples are given to illustrate differences and advantages of our method compared to those usually used.