Fernando Borrás (Departamento de Estadística, Matemáticas e Informática, Universidad Miguel Hernández), José Luis Ruiz and Inmaculada Sirvent (Operations Research Center, University Miguel Hernández of Elche)
Abstract: Cross-efficiency evaluates the performance of decision making units (DMUs) from the perspective of all of the others, through their individual Data Envelopment Analysis (DEA) weights. The main weakness with this methodology lies on the existence of alternate optima for the weights, which may lead to different results depending on the choice that is made. In fact, this issue is typically addressed by implementing an alternative secondary goal for the selection of weights among those optimal solutions. The present paper proposes a different approach, which puts the focus on reducing the sensitivity of the results to the choice of weights rather than on establishing a criterion to make such choice. Thus, we seek evaluations more robust against the specification of weights. It is an approach based on the structure of the DEA efficient frontier instead of on the solutions of a given DEA model. Specifically, the cross-efficiencies are defined as the classical efficiency ratios, but using weights associated with all of the maximal efficient faces (MEFs) that form the DEA strong efficient frontier of the production possibility set (PPS). This provides a peer evaluation of DMUs as well, but from the perspective of different reference sets, namely those consisting of the DMUs that span the corresponding MEFs. It is clearly a major change in the standard approach of the cross-efficiency, which selects weights by reference sets instead of by DMUs individually. As a consequence, the cross-efficiency evaluation based on reference sets has proven to be less sensitive to alternative optimal weights, because they have more support from the DMUs. In addition, it ensures non-zero weights in the calculation of cross-efficiencies, which means that no variable is ignored in the evaluations.