A Cross-Efficiency Approach for Evaluating Decision Making Units in Presence of Undesirable Outputs

Data Envelopment Analysis (DEA) is a mathematical programming approach for measuring efficiency of Decision Making Units (DMUs). In traditional DEA, a ratio of weighted outputs to inputs is examined and, for each DMU, some optimal weights are obtained. The method of cross-efficiency is an extension to DEA by which a matrix of scores is computed. The elements of the matrix are computed by means of the weights obtained via usual models of DEA. The cross-efficiency may have some drawbacks, e.g., the cross-efficiency scores may be multiple due to the presence of several optima. To overcome this issue, secondary goals are used. However, this method has never been used for peer evaluation of DMUs with undesirable outputs. In this paper, our objective is to bridge this gap. For this end, we introduce a new secondary goal, test it on an empirical example with undesirable outputs, report the results, and finally, we give some concluding remarks.