bstractThe main objective of this paper is to analyze DMUs efficiency from the perspective of variable returns to scale. Thus, a case study is proposed, where the efficiencies of DMUs suffer variation according to the methods used in the analysis. The classic models of DEA, CCR and BCC, and a new model proposed by the authors, will have their results compared to classical foundations of the economy. The case study will examine the efficiency of administrative units selected of Undergraduate Higher Education.
Abstract. The main objective of this paper is to analyze DMUs efficiency from different perspectives of variable returns to scale. For that, the authors use results of CCR, BCC and a new model proposed. The new model presents just in-creasing returns to scale. Thus, the efficient frontier must have specifics characteristics that guarantees increasing additional output beyond additional inputs verified. This study is going to show that the classic model of DEA BCC proposes variable returns of scale, however cannot ensure that all the efficient DMUs with increasing returns to scale is identified. The authors propose a new model where the measurement of efficiency is made by increasing returns to scale frontier.
The format of the efficient frontier is an important measure of technical efficiency; additionally, it determines the type of return to scale verified by the model. The classical Data Envelopment Analysis (DEA) model, CCR (Charnes et al., 1978), assumes constant returns to scale; conversely, the BCC (Banker et al., 1984) model presents a concave downward efficient frontier that presumes variable returns to scale. This study examines how different returns to scale can be revealed in DEA, considering the possibility of the existence of a concave upward efficient frontier. This kind of frontier, not yet explored by the DEA literature, can also represent viable production, seeing that an increase of the inputs causes an increase of the outputs. Considering this, a concave upward efficient frontier presents a variable return to scale, but with different characteristics from those of the concave downward BCC efficient frontier. This proposal is important because it considers the possibility of an efficient frontier that represents different samples of decision-making units (DMUs). An upward curve would better represent DMUs of smaller production scales that have increased marginal productivity but cannot act as efficiently as larger scale units.
When analyzed from the perspective of one input and one output, the classic Data Envelopment Analysis (DEA) model (known as BCC after its developers Banker, Charnes, and Cooper) presents an efficient frontier with "downward" concavity (convex), therefore delivering variable returns to scale. However, these returns show a decrease in marginal productivity as the number of inputs increases, that is, the frontier presents decreasing global returns to scale. Both the convex frontier (DEA BCC) and the concave frontier ("upward" concavity) present average productivities that vary along the curve; thus, the local returns to scale are variable. It is claimed that the two formats are complementary, and therefore both should be verified in the literature. Thus, this article proposes an algorithm capable of modeling an efficient frontier, for one input or one output, with increasing global returns to scale, whereby an increase in input causes an increase in marginal productivity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.