DEA cross-efficiency evaluation based on Pareto improvement

Cross‐efficiency evaluation, as an extension tool of data envelopment analysis (DEA), has been widely applied in evaluating and ranking decision making units (DMUs). Unfortunately, the cross‐efficiency scores generated may not be Pareto optimal, which has reduced the effectiveness of this method. To solve this problem, we propose a cross‐efficiency evaluation approach based on Pareto improvement, which contains two models (Pareto optimality estimation model and cross‐efficiency Pareto improvement model) and an algorithm. The Pareto optimality estimation model is used to estimate whether the given set of cross‐efficiency scores are Pareto‐optimal solutions. If these cross‐efficiency scores are not Pareto optimal, the Pareto improvement model is then used to make cross‐efficiency Pareto improvement for all the DMUs. In contrast to other cross‐efficiency approaches, our approach always obtains a set of Pareto‐optimal cross efficiencies under the predetermined weight selection principles for these DMUs. In addition, if the proposed algorithm terminates at its step 3, the evaluation results generated by our approach unify self‐evaluation, peer‐evaluation, and common‐weight‐evaluation in DEA cross‐efficiency evaluation. Specifically, the self‐evaluated efficiency and the peer‐evaluated efficiency converge to the same common‐weight‐evaluated efficiency when the algorithm stops. This will make the evaluation results more likely to be accepted by all the DMUs.