Aplicação do Método Multiple Data Envelopment Analysis para avaliação de eficiência de assentamentos da reforma agrária

Abstract

In a recent article, Leonardo Melgarejo, Joao Neiva de Figueiredo and Carlos Ernani Fries (2009) developed a study to measure the efficiency of 90 agricultural settlements in the state of Rio Grande do Sul, Brazil, using a nonparametric statistical method DEA (Data Envelopment Analysis). This method selected inputs and out-puts variables, and using linear programming suggesting values for the variables that maximize the efficiency of the DMU’s (Decision Making Units), name given by the method to the settlements. Eight inputs and four outputs variables were selected on a set of over more than 100. Values were determined for three types of efficiency, production, technology and management. From the results presented, 47% of the settlements showed an efficiency unit in all three considered and due to this, we see a low discriminatory power in DEA method. In this dissertation we recalculate the values of the article, and then apply the method MDEA (Multiple Data Envelopment Analysis) which consists in dividing the entire space of the variables in subspaces across all possible combinations of inputs and outputs and in each one of these combinations DEA is applied, generating a large number of efficiencies for each DMU. A average is calculated and we consider this number the better representation of the efficiency of a DMU because involves all contexts between the inputs and outputs. For some DMU’s projected values are suggested by MDEA method for its vari-ables. We calculate mean, median, and mode of the values. We make comparisons with the DEA method used in the article by Melgarejo et.al, some simulations are done and we reach very interesting conclusions.