Otimização probabilística: aplicação do modelo de distribuição Poisson inflacionada de zero (ZIP) em modelos de localização com demandas probabilísticas

Abstract

This work addressed problems of location and allocation of call centers with probabilistic demands. It was proposed to use a probabilistic optimization model proposed by Beraldi, Bruni and Conforti (2004), in which randomness is identified in the demand process assuming that the variables involved had a Poisson distribution. In this work, we also admit probabilistic demands, but with the distribution of poisson inflated zeros (ZIP), with such distribution we obtain a new redistribution that favors sectors with greater demand. The localization and allocation model is an integer linear programming model, where the probabilistic part is replaced by its respective deterministic equivalents, which were obtained for both distributions. As an application of this methodology, we found the distribution of emergency and emergency services, where calls were collected in 2017 in the city of João Pessoa, from these data, were made adherence test through the comparison statistics of Cramér Von-Mises and Anderson Darling, the distances matrix was obtained through the Google maps Distance API and the implemented model was solved using CPLEX. As a result, there was a difference in the choice of some service centers, as well as in their quantity, reducing this difference with the gradual increase of the distances offered for each scenario.