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

Authors: Mohsen Afsharian; Heinz Ahn; Mohammadreza Alirezaee

Addresses: Department of Business Sciences, Technische Universität Braunschweig, Fallersleber-Tor-Wall 23, 38100 Braunschweig, Germany ' Department of Business Sciences, Technische Universität Braunschweig, Fallersleber-Tor-Wall 23, 38100 Braunschweig, Germany ' School of Mathematics, Iran University of Science and Technology, Hengam St., Resalat, 16846 Tehran, Iran

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.

Keywords: data envelopment analysis; DEA; selective proportionality; free disposal hull; FDH models; proportionality axiom; decision analysis; modelling; efficiency measurement; linear programming.

DOI: 10.1504/IJIDS.2015.068754

International Journal of Information and Decision Sciences, 2015 Vol.7 No.2, pp.99 - 114

Available online: 09 Apr 2015 *

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