%0 Journal Article %A H. Azizi, %A R. Jahed, %T An Improvement for Efficiency Interval: Efficient and Inefficient Frontiers %J International Journal of Applied Operational Research %V 1 %N 1 %U http://ijorlu.liau.ac.ir/article-1-47-en.html %R %D 2011 %K %X 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. Keywords: Data Envelopment Analysis (DEA), Optimistic and Pessimistic Efficiencies, Bounded DEA Models, Efficiency Interval. %> http://ijorlu.liau.ac.ir/article-1-47-en.pdf %P 49-65 %& 49 %! %9 Research %L A-10-2-10 %+ Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran %G eng %@ 2251-6867 %[ 2011