Efficiency analysis with interval-scale data based on separating hyperplane of decision making units

Abstract

The traditional data envelopment analysis (DEA) model can evaluate the relative efficiencies of a set of decision making units (DMUs) with ratio scale inputs and outputs, but it cannot handle interval scale data. This study develop an approach to efficiency analysis to deal with both interval-scale data and ratio scale data. This approach introduces a measure of inefficiency and identifies efficient units as is done in DEA models with VRS technology. The basic idea in the approach is to obtain a separating hyperplane of DMUs so that the hyperplane can separate the maximum number of DMUs whose performances are not better than a DMU under evaluation, from the rest of the DMUs. Performance measure is defined as a ratio of not-better units to all units. Also, this paper presents a relationship between the performance measures with those in DEA models with VRS technology.