Ranking ranges in cross-efficiency evaluations: A metaheuristic approach

In the cross-efficiency evaluation, the existence of alternative optima for weights represents an inconvenience because the ranking obtained depends on the weights used. Alcaraz et al. (2013) design an algorithm that provides a range of positions for each unit, taking into account the entire spectrum of feasible weights that configure the optimal alternative solutions in DEA evaluation. This procedure involves nonlinear models that are solved using parametric mixed-integer non-linear programming problems that can become very complex and laborious and often makes it difficult to obtain the optimum. In this paper, ranking range is approached using metaheuristic techniques which, when well designed, are able to achieve good approximations and they are the preferred alternative when exact techniques require excessive computational effort or they are not able to provide an optimal solution. Some examples widely used in the context of cross-evaluation are used to verify the suitability of the proposed method.