A formulation of cross-efficiency in DEA and its applications

In the conventional cross-efficiency formulation, the efficiency score of a test DMU is maximized as the primary goal while an average of efficiency scores of peer DMUs is minimized (or maximized) as the secondary goal. The proposed model replaces the secondary goal with the minimization (or maximization) of the best (or worst) efficiency score of peer DMUs. We demonstrate the appropriateness of the proposed formulation of cross-efficiency for certain efficiency evaluation situations. As a potential use of the proposed model, we suggest its use in the context-dependent DEA.