Setting scale efficient targets in DEA via returns to scale estimation method
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Viewpoint Setting scale ef®cient targets in DEA via returns to scale estimation method Introduction Appa and Yue1 proposed a method for setting scale ef®cient targets in data envelopment analysis (DEA). In the presence of possible multiple optimal solutions, their best returns to scale (RTS) model yields the same scale ef®cient targets under both input-oreinted and outputoriented DEA models. They indicate that their unique scale ef®cient targets correspond to the largest most productive scale size (MPSS). Based upon RTS estimation method, this paper develops an alternative approach for setting the scale ef®cient targets which can correspond to either the largest MPSS or the smallest MPSS. Data envelopment analysis (DEA) has been proved a useful tool for evaluating the relative ef®ciency of peer decision making units (DMUs) which produce multiple outputs by consuming multiple inputs. Although DEA is originally developed to measure the technical or mix (technical and scale) ef®ciency, it has been modi®ed to characterise returns to scale (RTS) classi®cation=scale ef®ciency.2 DEA determines a unique best-practice frontier. However, because of the possible multiple optimal solutions=orientation of the DEA models, scale ef®cient targets on the best-practice frontier for inef®cient DMUs may not be uniquely determined. Appa and Yue1 developed a DEA-based method for setting unique scale ef®cient targets in DEA. In the presence of possible multiple optimal solutions, their approach yields the same scale ef®cient target for DMU under both input-oriented and output-oriented DEA models. They show that their scale targets are related to the largest most productive scale size (MPSS).3 However, in order to identify targets corresponding to the smallest MPSS, an additional constraint is needed. This paper shows that in fact, these unique scale ef®cient targets can be obtained directly from MPSS concept even if multiple optimal solutions (or multiple MPSS) are present. It is shown that these scale ef®cient targets are obtained from linear programming problems for determining the RTS classi®cation. Since the scale ef®ciency is related to the RTS classi®cation, it is desirable that the targets are determined via RTS estimation method. *Correspondence: Dr J Zhu, Department of Management, Worcester Polytechnic Institute, Worcester, MA 01609, USA. E-mail: [email protected]
Setting scale ef®cient targets In this section, we show that unique scale ef®cient targets determined by Appa and Yue's approach1 can actually be obtained from RTS estimation method based upon MPSS concept. Let us ®rst review a RTS estimation method based upon an input-oriented CRS (constant RTS) model.4 Suppose we have n DMUs. DMUj 1; 2; . . . ; n produces s different outputs, yrj
r 1; 2; . . . ; s), using m different inputs, xij
i 1; 2; . . . ; m). Then the CRS model can be written as m s P ÿ P si s min y ÿ e r i1
subject to n P
r1
lj
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