Efficiency Analysis Based on Separating Hyperplanes for Improving Discrimination among DMUs

Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs. The original DEA models use positive input and output variables that are measured on a ratio scale, but these models do not apply to the variables in which interval scale data can appear. However, with the widespread use of interval scale data, the emphasis has been directed towards the simultaneous consideration of the ratio and interval scale data in DEA models. This study, introduces a measure of inefficiency and identifies efficient units as is done in DEA models with VRS technology based on separating hyperplanes. 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.