Improvements to smooth data envelopment analysis

¹ Post Graduation in Production Engineering, Universidade Federal Fluminense, Rua Passo da Pátria 156, 24. 210-240 Niterói/RJ, Brazil ;
luanabrandao@id.uff.br
² Production Engineering Department, Universidade Federal Fluminense, Rua Passo da Pátria 156, 24. 210-240 Niterói/RJ, Brazil ;
jcsmello@pesquisador.cnpq.br

Received: 3 March 2015
Accepted: 1 February 2016

Abstract

Classic data envelopment analysis (DEA) models do not provide unique solutions for multipliers of extreme efficient units. To overcome this problem, previous works have proposed the smooth DEA technique. However, multidimensional models with variable returns to scale (BCC) present deficiencies, as they do not fully ensure the frontier’s convexity. Therefore, the main contribution of this paper is to correct smooth BCC models, with regard to such property. Moreover, we propose improvements to smooth DEA models, so that all projections for the evaluated units, and their efficiency values, are non-negative. Furthermore, based on the corrected and improved smooth model, we propose a solution to avoid a classic BCC distortion, which may be called efficiency by default. Finally, we evaluate the operational performance of Brazilian airlines in 2010, to show the applicability of our model and to illustrate the practical effect of our contributions.