Scale elasticity and returns to scale in the presence of alternative solutions

Abstract

Scale elasticity (SE) and returns to scale (RTS) are important topics in performance analysis, which help managers to make decisions about the expansion or contraction of the operation of decision making units under assessment. In this paper, some new results about these topics in the presence of alternative solutions, regarding the concept of multifunction, are provided. At first, some properties of some multifunctions (functions), defined with respect to the optimal solutions of DEA models, are established which help us in what follows. In turn, the relationships between the considered multifunctions and the concept of RTS and SE are studied. Finally an approach for the estimation of the RTS classification of units is obtained, which leads to an important corollary as an interesting result which introduces a connection between two concepts, RTS and SE. This is important from an applied point of view. Also, from a technical point of view, the proofs of theorems which give this corollary use a main lemma of convex analysis literature and give a constructive proof about RTS.