A Note On Dual Models Of Interval DEA and Its Extension To Interval Data‎‎

Document Type: Research Paper

Authors

1 Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, ‎Iran.‎

2 Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

3 Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

Abstract

In this article, we investigate the measurement of performance in DMUs in which input and/or output values are given as imprecise data. By imprecise data, we mean that in some cases, we only know that the actual values are inside certain intervals, and in other cases, data are specified only as ordinal preference information. In this article, we present two distinct perspectives for determining the upper and lower bounds of the efficiency the DMU under evaluation can have with imprecise data: (1) The optimistic perspective, which uses DEA-efficient production frontier, and seeks the best score among various values of the efficiency score; the measured efficiency in this perspective is called the best relative efficiency or the optimistic efficiency. (2) The pessimistic perspective, which uses inefficiency frontier, also called input frontier, and seeks the lowest score among various values of the efficiency score; the measured efficiency in this perspective is called the worst relative efficiency or the pessimistic efficiency. For this reason and contrary to some DEA-related studies, we do not restrict our attention only to precise data. We will investigate a more general case of dealing with imprecise data, providing a method for obtaining the upper and lower bounds of efficiency. Two numerical examples will be presented to illustrate the application of the proposed DEA approach.‎‎

Keywords