Minimax and maximin formulations of cross-efficiency in DEA

In the conventional cross-efficiency formulation, the efficiency score of a DMU under evaluation is maximized as the primary goal while the average cross-efficiency of peer DMUs is minimized (or maximized) as the secondary goal. The proposed models replace the secondary goal with the minimization (or maximization) of the best (or worst) cross-efficiency of peer DMUs. We demonstrate the appropriateness of the proposed formulations of cross-efficiency for certain efficiency evaluation contexts, and show how they help enhance the usefulness of cross-efficiency evaluation in DEA using a randomly generated sample data set. For a solution method for the proposed models of cross-efficiency, we develop a bisection algorithm whose computational complexity is polynomial.