Modelos DEA com variáveis limitadas ou soma constante

Abstract

ResumoNeste trabalho são propostos dois modelos tipo DEA (Data Envelopment Analysis) em que um novo input (ou um novo output) deve ser distribuído de maneira justa para todas as unidades (DMUsDecision Making Units) de uma corporação. Uma característica interessante dos modelos propostos é que a forma dessa distribuição é influenciada pelos valores dos inputs já empregados e dos outputs já gerados em cada DMU. Os modelos foram construídos de acordo com o perfil geométrico da fronteira CCR, podendo ter forma côncava ou convexa conforme a natureza da variável que se quer distribuir. Mostramos que, sob essa hipótese de um formato geométrico específico para a fronteira, torna-se simples a distribuição do novo input (ou output) entre as várias DMUs, pois cada uma delas receberá a fração do novo input (ou output) que a torne eficiente, forçando sua posição sobre a fronteira pré-determinada.Palavras-chave: análise envoltória de dados; soma constante de variáveis; fronteira eficiente. AbstractIn this work we present two DEA (Data Envelopment Analysis) models in which a new input (or output) is to be fairly assigned to all units (DMUs -Decision Making Units) of a corporation. An interesting characteristic of those proposed models is that the way this distribution is influenced by both inputs and outputs used in each DMU. The models were built in accordance with the geometric shape of CCR frontier and they can be convex or concave, depending on the nature of the variables we intend to share. We show that, under this assumption, it becomes relatively easy the distribution of a new input (or output) among several DMU's, considering that each DMU will receive the new input (or output) fraction in order to become efficient, forcing its position on the specific frontier.

Allocating Financial Resources for Competitive Projects Using a Zero Sum Gains Dea Model

“…We propose the use of mathematical programming and DEA in this endeavor. Similar approaches can be seen in Cooper et al (2000), Yan et al (2002), Beasley (2003), Gomes (2003), Lins et al (2003), Lozano and Villa (2004), Korhonen and Syrjänen (2004), Avellar et al (2005Avellar et al ( , 2007, Gomes et al (2005Gomes et al ( , 2007. In Soares of Mello et al (2006) there is a revision on the theme.…”

“…the mn × input matrix. Notice that the element 0 r y ≥ is the 1 s × output vector of unit r and 0 r x ≥ is the 1 m × vector of inputs used by unit r to produce et al (2003), Lozano and Villa (2004), Korhonen and Syrjänen (2004), Avellar et al (2005Avellar et al ( , 2007, Gomes et al (2005Gomes et al ( , 2007. In Soares of Mello et al (2006) there is a revision on the theme.…”

Large discreet resource allocation: a hybrid approach based on dea efficiency measurement

“…The works of Avellar et al (2007Avellar et al ( , 2005 and deserve particular mention. The former propose DEA CCR type models based on limited inputs/outputs in which the allocation of resources/production can be influenced either by the inputs or the outputs.…”

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

“…Avellar et al (2005Avellar et al ( , 2007 and Guedes et al (2009) arbitrated a spherical form for this frontier. The Spherical Frontier DEA Model, as it is called, deals with the distribution of both new and existing resources.…”