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.