On the Calculation of Directional Scale Elasticity in Data Envelopment Analysis

Abstract

In recent years, the notion of scale elasticity—the relative changes of outputs with respect to relative changes of inputs—has received a lot of ink in the literature. However, all prior studies, except a few of them, assume that changes are equi-proportional. This simplifying assumption makes scale elasticity measure to preserve the throughput mix and implicitly ignores both input independencies and decision-maker preferences. This paper seeks to investigate two main objectives. It initially proposes the notion of directional scale elasticity to allow evaluation of elasticity in any direction which may naturally alter the mix. Subsequently, by providing a tangible geometric interpretation, it attempts to clarify the measure. Relevant computations are used to construct cross sections of frontier in a given direction by enlisting the advantages of parametric optimization algorithm.

Directional scale elasticity considering the management preference of decision-makers

“…The latter is to measure the numerical value of SE, as noted, which can be used to offer a stronger quantitative characterization of RTS than the qualitative approach. Relatively recently, most DEA research efforts in developing the quantitative approach include, e.g., Golany and Yu [15], Førsund and Hjalmarsson [11,12], Podinovski et al [19], Podinovski and Førsund [18], Atici and Podinovski [1], Zelenyuk [27], Mirjaberi and Matin [16], Podinovski et al [17,20,21]. Our development also mainly contributes to the quantitative approach as outline below.…”