Evaluating the performances of decision-making units based on the ‎optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a methodology for assessing the performances of a group ‎of decision making units (DMUs) that utilize multiple inputs to produce multiple outputs. It ‎measures the performances of the DMUs by maximizing the efficiency of every DMU, ‎respectively, subject to the constraints that none of the efficiencies of the DMUs can be less ‎than one. The efficiencies measured in this way are referred to as optimistic efficiencies or the ‎best relative efficiencies. The way to measure the optimistic efficiencies of the DMUs is ‎referred to as self-evaluation. If a DMU is self-evaluated to have an efficiency score of one, ‎then it is said to be DEA efficient; otherwise, the DMU is said to be non-DEA efficient. ‎There is a comparable approach which uses the concept of inefficiency frontier for ‎determining the worst relative efficiency score that can be assigned to each DMU. DMUs on ‎the inefficiency frontier are specified as DEA-inefficient, and those that do not lie on the ‎inefficient frontier, are declared to be DEA-non-inefficient. In this paper, we argue that both ‎relative efficiencies should be considered simultaneously, and any approach that considers ‎only one of them will be biased. For measuring the overall performance of the DMUs, we ‎propose to integrate both efficiencies in the form of an interval, and we call the proposed ‎DEA models for efficiency measurement the bounded DEA models. In this way, the ‎efficiency interval provides the decision maker with all the possible values of efficiency, ‎which reflect various perspectives.