WITHDRAWN: A multi objective model for Pareto optimality in data envelopment analysis cross efficiency evaluation

Abstract This manuscript proposes a new approach for addressing the non-Pareto optimality problem in data envelopment analysis (DEA) cross-efficiency evaluation. First, we propose a multi-objective model with a new non-self-denial weight-selection principle to obtain Pareto-optimal cross-efficiency scores. Second, the sum-weighted approach is adopted to solve the multi-objective model. Third, despite the nonlinearity and high complexity of the sum-weighted model, we find that a set of Pareto-optimal cross-efficiency scores can always be obtained by using a common-weight evaluation result, and a set of common weights can be obtained by a simple linear program. Further, we investigate a previous benchmark study and show that with a special assignment of the given cross-efficiency scores in their procedure, the benchmark approach can also obtain Pareto-optimal cross-efficiency scores as a common-weight evaluation result. Compared with the weight-selection principles provided in the previous benckmark study, our non-self-denial principle is more reasonable and more acceptable among the DMUs since it enforces no additional nonendogenous constraints when each DMU selects its optimal weights. Additionally, we have proved that a set of Pareto-optimal cross-efficiency scores always consociate the mechanisms of peer-evaluation, self-evaluation, and common-weight evaluation in DEA since it can always be calculated by using a set of common weights. More importantly, compared with the previous benckmark study, which must solve numerous linear programs for each DMU to obtain a set of Pareto-optimal cross-efficiency scores, our calculation process requires solving only one linear program. Finally, the proposed method is applied to perform green supplier selection.