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. It is
argued here that both efficiencies must be considered simultaneously, and any approach that considers
only one of them will be biased. In this paper, it is proposed that to integrate both efficiencies in the
form of an interval evaluates the overall performance of each DMU. To this end, a virtual DMU is
used called the ideal DMU. The new DEA models with upper and lower bounds on efficiency are
called the bounded DEA models. A numerical example is presented to illustrate the application of the
proposed DEA models.
