Uniformização da fronteira eficiente em modelos de análise de envoltória de dados com ganhos de soma zero e retornos constantes de escala

Abstract

ResumoNos modelos DEA com Ganhos de Soma Zero (DEA-GSZ) a restrição dos modelos DEA clássicos de total liberdade de produção ou de uso dos recursos é substituída pela restrição de soma total constante de inputs ou outputs. Neste artigo são apresentados o modelo DEA-GSZ com retornos constantes de escala (DEA-GSZ CCR) e um estudo de caso sobre a realocação do número de aprovados em um concurso vestibular.Palavras-chave: DEA; ganhos de soma zero; retornos constantes de escala; realocação da produção. AbstractWhen using Zero Sum Gains DEA models (ZSG-DEA), classical DEA models restriction of total freedom of production or resources use is replaced by the constant sum of inputs or outputs restriction. In this paper we develop ZSG-DEA models with constant returns to scale (ZSG-DEA CCR) and employ it in the reallocation of the quantity of approved students in the "vestibular".

Uniformization of frontiers in non-radial ZSG-DEA models: an application to airport revenues

“…These represent a situation similar to that of a zero sum game, in which all that is gained by one player is lost by the other(s) (Gomes, 2003;Gomes et al, 2003Gomes et al, , 2004Gomes et al, , 2005Lins et al, 2003;Gomes & Lins, 2008). In other words, the net sum of gains must be zero.…”

“…In order to solve the mathematical problem of determining one equation for each facet of the frontier, they used the smoothed frontier developed by Soares de Mello et al (2002,2004) and Nacif et al (2009). Gomes et al (2005) extended the use of ZGS-DEA models to constant returns to scale (Charnes et al, 1978), still with the redistribution of inputs. Gomes & Lins (2008), apply the uniformization of frontier techniques in the ZGS-DEA model to the distribution of an undesirable output, modelled as an input, in a case of environmental interest.…”

Modelling undesirable outputs with zero sum gains data envelopment analysis models

“…The formulation (1) represents the ZSG-DEA CCR model, input-oriented, for the case that just one DMU searches for the efficient frontier and with one constant sum input (Gomes, 2003;Gomes et al, 2005). In this model, h Ro is the DMU o efficiency under the restriction that the input sum must be constant; x j and y j are the inputs and outputs original values, respectively; y o and x o are the outputs and inputs for the DMU o; j are DMU contributions to the efficient projection.…”

“…Moreover, Lins et al (2003) show that 'the target of the DMU under consideration in the ZSG-DEA model with proportional reduction strategy is equal to the target in the corresponding classical DEA model multiplied by a reduction coefficient' (named by Gomes (2003) as 'Target's Assessment Theorem') and that 'in a ZSG-DEA model in which a proportional reduction strategy has been adopted, the value of the DMUs j contribution j , j different from DMU under analysis, equals its value in the traditional DEA model' (named by Gomes (2003) as 'Benchmarks' Contribution Equality Theorem'). Using all these theorems jointly (Gomes 2003;Gomes et al, 2003Gomes et al, , 2005 results in Equation (2), where W is the cooperative DMUs set, q i j = h i / h j is the proportionality factor that comes from the proportional strategy and h i , h j are the classical DEA efficiencies.…”

“…In this paper, we propose a new approach to modelling undesirable outputs, based on the zero sum gains DEA models (ZSG-DEA). These models consider the production dependence among the DMUs (Gomes, 2003;Gomes et al, 2003Gomes et al, , 2005Lins et al, 2003), including, as an additional restriction, the zero sum game property, in which whatever lost (or gained) by one of the players must be gained (or lost) by the others, that is the net sum of gains must be zero.…”