Allocation of Weights Using Simultaneous Optimization of Inputs and Outputs' Contribution in Cross-efficiency Evaluation of DEA
cross-efficiency evaluation as 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). One of such methods in the allocation of weights for the ranking of the DMUs is Wang et al.’s method [Wang, Y. M., Chin, K. S., Jiang, P. (2011). Weight determination in the cross-efficiency evaluation. Computers $\&$ Industrial Engineering, 61, 497-502. ]. This method aims to choose a solution among the multiple solutions by increasing the contribution of inputs in their use of resources as well as by increasing the contribution of the outputs in production and to the extent possible to covertly prevent the selection of zero solutions in inputs and outputs. In the present article, we argue that such selection of weights is not appropriate because in the cross-efficiency evaluation of the DMUs, we always search for the weights that use the 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 yet it should overtly prevent the selection of zero solutions to the extent possible. To this end, some examples are illustrated which show how it differs with other methods.
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