Interval inefficiency assessment using data envelopment analysis

ABSTRACT:The performances of decision-making units (DMUs) can be evaluated from two different points of view—optimistic and pessimistic—and accordingly, two different efficiencies can be calculated for each DMU: the best relative efficiency and the worst relative efficiency. In the conventional methods of data envelopment analysis (DEA), only the best relative efficiency is evaluated. We argue that both efficiencies must be considered simultaneously, and any approach that considers only one of them will be biased. In this paper, we propose to integrate both efficiencies in the form of an interval that evaluates the overall performance of each DMU. To this end, we use a virtual DMU called the ideal DMU (IDMU). The new DEA models with upper and lower bounds on efficiency are called the bounded DEA models. We introduce and use the index for comparing and ranking the intervals. This will be illustrated using a numerical example.