Um Modelo Matemático para um Problema de Planejamento de Produção em Indústrias Alimentícias

Abstract

This dissertation addresses a production planning problem observed in some Brazilian food industries that process packaged meats. The objective is to propose mathematical and computational tools to support the decision-making process in the considered industrial context. The problem studied takes into account several production lines that share the same productive resources (workers, tools and machines), so that, due to the scarcity of these resources, only a subset of the lines can operate in each production period. Thus, it is necessary to decide which production lines should be used in each period, respecting the capacity limits of the necessary resources and also considering that the items produced are perishable and may remain stocked for a limited period of time. The problem studied also assumes the existence of a deterministic demand and the limitation of production capacity, as well as the following costs: delay in meeting demands, storage of produced items, setup and configuration time. In this work, a mixed integer optimization mathematical model is proposed to represent the problem addressed. Then, by means of a reformulation, it is done the mathematical proof that the problem belongs to the class of NP-hard problems, that is, it is not possible to obtain solutions in polynomial time. A computational study is presented in order to identify the efficiency of a high-performance solver for obtaining solutions (primal and dual) in acceptable computational time. A sensitivity analysis was performed to evaluate the behavior of the model with changes in storage costs and resource costs of production resources. It was found that the model was able to elaborate efficient production plans that provided partial absorption of the cost increase, providing benefits for industries of all sizes.