Perturbation and uniqueness of optimal weights in cross efficiency evaluation: An application to Iranian Gas Companies

Data envelopment analysis(DEA) has been extended to cross-efficiency evaluation to better discrimination and ranking of decision making units(DMUs). Unfortunately, the optimal weights generated may not be unique which has reduced the usefulness of this powerful method. In addition, due to alternative optimal solutions, zero weights can be seen in cross-efficiency evaluation. To solve these problems, first the concept of perturbation and generation of unique solution is introduced. Then an alternative evaluation approach contains a perturbed model, is proposed based on the performance analysis without slacks. This modified model can generate unique and non-zero optimal weights, simulteneously. Furthermore, the structure of the model can ensure the dissimilarity of the generated optimal weights. All these factors make the cross-efficiency evaluation results more satisfied and acceptable by all the DMUs. Finally, the proposed approach is applied on a real case study of of Iranian Gas Company and the results show that in contrast to standard DEA model the propsed model can perform well.