Algorithm modeling for constructing a concave efficient frontier

Abstract

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.