Performance measurement of decision-making units under uncertainty conditions: An approach based on double frontier analysis

Data envelopment analysis (DEA) is an approach to measure the relative efficiency of a set of decision-making units (DMUs) which uses multiple inputs to produce multiple outputs. In real world situations, due to uncertainty, DEA is sometimes faced with imprecise inputs and/or outputs. Therefore, performance measurement must often be performed under uncertainty conditions. Generally, the performance of DMUs can be evaluated from two perspectives—optimistic and pessimistic. As a result, two different evaluations are obtained for each DMU. In this article, we first obtain the efficiencies of the DMUs under evaluation from both optimistic and pessimistic views. The optimistic view evaluates each DMU with a set of the most desirable weights; the efficiencies measured by the optimistic approach are called optimistic efficiencies. The pessimistic view evaluates each DMU with a set of the most undesirable weights; the efficiencies measured by the pessimistic approach are called pessimistic efficiencies. Then it is shown that the outcomes of these two evaluations are conflicting with each other, being undoubtedly biased, unrealistic, and unconvincing. To overcome this problem, we propose a new measure of overall performance which is used for integrating the measures obtained from optimistic and pessimistic views and we will use it to identify the DMU with the best performance under uncertainty conditions. Also, we propose new fuzzy DEA models that evaluate a DMU from the pessimistic perspective in a fuzzy context. The proposed measure will be shown with two numerical examples, including the selection of a flexible manufacturing system.