Efficiency Analysis of DMUs based on Separation Hyperplanes in PPS with CRS Technology to Deal with Interval Scale Data

Abstract

In this paper, in order to evaluate the performance of a Decision Making Unit (DMU) in a Production Possible Set (PPS) with Constant-to-Scale (CRS) technology, we provide models to obtain nonnegative weights for inputs and outputs which for the weights, the number of which DMUs for each one its virtual output does not exceed (is less than, if any) its virtual input be maximum, provided that for DMU under evaluation, the virtual output will be equal to the virtual input and the virtual input will be positive. We call these weights the relatively best weight (the relatively strongest weight, if any) for the DMU under evaluation, and if all the weights are positive, we call them the best weight (the strongest weight, if any) for the DMU under evaluation. Also, we define efficiency and strictly efficiency (strongly efficiency), respectively, as the ratio of the number of DMUs for each one for the relatively best weight and the best weight (the relatively strongest weight); its virtual input does not exceed (is less) its virtual input, to the total DMUs. The relatively best weight in input-oriented (the relatively strongest weight, if any) indicates the normal vector of a surface in the PPS with CRS assumption that the DMU under evaluation is on the surface and the maximum number of which DMUs their performance is 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, it can be interpreted the rest of the definitions of non-negative weights for inputs and outputs based on separation hyperplanes. Also, in this paper, we present the relationship between these definitions of efficiency with efficiency in the DEA models with constant returns to scale assumption.