Developing selective proportionality on the FDH models: new insight on the proportionality axiom

Abstract

In many cases of DEA–based efficiency measurement systems, only a set of outputs has to be assumed to be proportional to a set of inputs. The assumption of constant returns to scale (CRS) is required with respect to the selected sets of inputs and outputs, preserving the variable returns to scale (VRS) assumption for the remaining factors. In such situations, neither CRS nor VRS–based models can provide valid results. In contrast to that, the selective proportionality axiom allows applying any desired combination of CRS and VRS. This paper proposes free disposal hull (FDH) technologies which incorporate the selective proportionality axiom. The considered technologies do not restrict themselves to convex technologies and are built solely on minimal axioms of non–emptiness and free disposability. The resulting FDH models are formulated as linear programming problems which are not only simple to solve but also provide an intuitive interpretation corresponding to the results. An illustrative numerical example is presented to explain the properties and features of the suggested FDH models.