Weight profiles in cross-efficiency evaluation based on hypervolume maximization

In this paper, we propose and discuss a new model in order to obtain the weight profiles to be used in the calculation of cross-efficiency scores in Data Envelopment Analysis (DEA). In the standard DEA literature, total flexibility in the selection of weights has been strongly criticized due to the fact that some inputs and/or outputs may have no contribution (zero weights) to the efficiency scores. Although cross evaluation somewhat mitigates the effect of these unrealistic weighting schemes on the amalgamation of weights that standard DEA models produce, we propose a method that ensures strictly positive and balanced weights to be used in cross-efficiency evaluation. In particular, we propose an optimization model based on hypervolume maximization as a method for selecting a suitable weight profile for each evaluated unit to be used in cross-efficiency. The model is solved through Second-Order Cone Programming (SOCP). As a result, the solution obtained is unique and the Production Possibility Set (PPS) is not modified. Another advantage of the proposed method, among others, is that it does not need subjective expert opinions or full-dimension efficient facets of the polyhedral PPS, but if available, it can be easily incorporated into the model. The approach introduced is illustrated through a numerical example. We also present some theoretical results.