Efficiency Analysis of DMUs Based Separation Hyperplanes in PPS with VRS Technology to Deal with Interval Scale Data

Abstract

In this paper, in order to evaluate the performance of a DMU in Production Possible Set (PPS) with Variable Return to Scale (VRS) technology, we provide models to obtain non negative weights for inputs for outputs and a nonnegative scalar corresponding to inputs and a nonnegative scalar corresponding to outputs which for the weights and scalars, the number of which DMUs for each one its virtual output plus the scalar corresponding to inputs does not exceed (is less than, if any) its virtual input plus the scalar corresponding to inputs be maximum, provided that for DMU under evaluation, the virtual output plus the scalar corresponding to inputs does not exceed (is less than, if any) the virtual input plus the scalar corresponding to inputs and the virtual input will be positive. We call these weights and scalars the relatively best weight in input-oriented (the relatively strongest weight in input-oriented, if any) for the DMU under evaluation, and if all the weights be positive we call them the best weight in input-oriented (the strongest weight in input-oriented, if any) for the DMU under evaluation. Also, we define input-oriented efficiency and input-oriented strictly efficiency (input-oriented strongly efficiency), respectively, as ratio the number of which DMUs for each one per the relatively best weight in input-oriented and the best weight in input-oriented (the relatively strongest weight in input-oriented), its virtual input plus the scalar related to inputs does not exceed (is less) its virtual input plus the scalar related to outputs, to the total DMUs. Similarly we define the relatively best weight in output-oriented (the relatively strongest weight in input-oriented, if any), the best weight in output-oriented (the strongest weight in output-oriented, if any), output-oriented efficiency and output-oriented strictly efficiency (output-oriented strongly efficiency). The relatively best weight in input-oriented (the relatively strongest weight in input-oriented) indicates normal vector of a superface in the PPS with VRS assumption that the DMU under evaluation is on the superface and the maximum number of which DMUs their performance are no worse than (is better than) the DMU under evaluation separate from the rest of DMUs, with the constraint that the virtual input be positive. Accordingly, we can interpret the rest of the definitions of non-negative weights for inputs and for outputs and nonnegative scalars related to inputs and outputs. In this paper, we present the relationship between these definitions of efficiency with efficiency in the DEA models with VRS assumption.