On Pareto-optimality in the cross-efficiency evaluation

Uniqueness and Pareto-optimality of cross-efficiency scores are two main issues in the cross-efficiency evaluation. We address the Pareto-optimality issue in the cross-efficiency evaluation by presenting a natural notion of Pareto-optimality in the cross-efficiency evaluation which is based on a new self-prioritizing principle and aligned with the concept of dominance. This Pareto-optimality notion is devised using less stringent postulates, compared to those used to devise the existing Pareto-optimality notions in the current literature. We then propose a multi-objective model whose Pareto-optimal solutions generate all the Pareto-optimal cross-efficiency scores sets that fulfill the self-prioritizing principle. It is shown that there is a Pareto-optimal solution to the proposed multi-objective programming model which assigns a common set of weights to all decision making units. We then propose a linear model to obtain such an optimal solution using the weighted sum technique, thereby we can determine an optimal weights profile to generate a set of Pareto-optimal cross-efficiency scores by solving only one linear model. Having started with less stringent postulates, we have more flexibility in enhancing cross-efficiency scores of decision making units and can hence provide a non-dominated set of cross-efficiency scores as illustrated by a real data example. We also demonstrate the possibility of better, compared to other cross-efficiency evaluation methods, resource allocation using another real data example.