Bridging the gap between the constant and variable returns-to-scale models: selective proportionality in data envelopment analysis

In data envelopment analysis (DEA), the use of constant returns-to-scale (CRS) models requires the assumption of full proportionality between all inputs and outputs. Often such proportionality cannot be assumed, although there may be a subset of outputs proportional to a subset of inputs. By using the variable returns-to-scale (VRS) model, this information is effectively ignored and the efficiency of units is overestimated. This paper develops a hybrid approach that combines the assumption of CRS with respect to the selected sets of inputs and outputs, while preserving the VRS assumption with respect to the remaining indicators. The resulting hybrid returns-to-scale models exhibit better discrimination than the VRS model. In certain cases, their discrimination surpasses that of the CRS model, an example of which is given.