Multi-objective model based on goal programming associated with the non-archimedean infinitesimal: a case study applied to the agricultural sector.
Data Envelopment Analysis; Multiple Criteria Data Envelopment Analysis; Goal Programming; Variable Return to Scale; São Francisco Valley.
In view of the growth of fruit production in the São Francisco Valley (Brazil), the evaluation of technical efficiency represents a potential for improving the allocation of productive resources. This work presents a multi-objective model (Improved Weighted Goal Programming model - Multiple Criteria Data Envelopment Analysis, IWGP - MCDEA), based on Goal Programming (GP) and associated with the infinitesimal non-Archimedean (NAI,ε) which aims to overcome the deficiencies of the classic Data Envelopment Analysis (DEA) (low level of discrimination between the DMUs and the distribution of unrealistic weights), being able to be applied in real situations such as in irrigated fruit growing (IWGP - MCDEA - variable return of BCC scale). The case study comprised an agricultural export company located in São Francisco Valley (Northeast region of Brazil). The performance of the proposed multiobjective model (Improved Weighted Goal Programming model - Multiple Criteria Data Envelopment Analysis, IWGP - MCDEA) was compared to the classic Data Envelopment Analysis (DEA) model based on the Variable Return to Scale (BCC) and the weighted sum goal programming (WGP - MCDEA) model. The analysis of the results involved the use of statistical metrics (p-value, Spearman’s Correlation Test and coefficient of variation) which showed the best performance in discrimination Decision Making Units (DMU’s) through the inclusion of NAI. The sensitivity analysis associated with the stability of the weights of each input/output was performed through the coefficient of variation. The proposed model is capable of overcoming the deficiencies associated with classical DEA and provides the possibility of improving the company's competitiveness by increasing productivity from the reduction of input costs. An additional step comprised the application of a classical technique of non-hierarchical clustering (Fuzzy C-Means, FCM) aiming at the recognition of clusters and patterns of DMUs from their respective inputs and outputs. The results obtained by this unsupervised learning technique demonstrated consistency in relation to the recognition/identification of efficient DMUs obtained by the proposed method (IWGP-MCDEA).