Classifying dual role variables in DEA: The case of VRS

Abstract

Data envelopment analysis is a mathematical programming methodology commonly used to evaluate the relative efficiencies of each of a set of decision-making units in terms of a selected set of input and output variables. In many situations, however, it can happen that certain variables can play roles of either inputs or outputs. This dual-role or classification concept was examined in earlier research for settings where the production possibility set was defined in terms of a constant returns to scale (CRS) technology. The current article extends the classification models to those cases where a variable returns to scale (VRS) technology is present. We show that if one simply adds a free-in-sign variable to the CRS model, the resulting VRS model can be unbounded. To alleviate this circumstance, we develop an altered version of the conventional VRS model which is shown to be feasible and bounded. We provide numerical examples to demonstrate the applicability and strength of the proposed methodology.