Mathematical Modelling and Solution Approaches for Production Planning in a Chemical Industry

Abstract

ABSTRACT. This paper addresses a lot sizing problem in a Brazilian chemical industry where a product can be produced by more than one process, which can use different parallel machines and may even consume a wide range of raw materials. Moreover, most of the products are liquids and the inventories must be kept in a restricted number of storage tanks with a limited capacity. Hence, these two issues are barely addressed in the literature on lot sizing. The classical multi-level capacitated lot sizing problem was extended to address them and a mixed integer programming (MIP) formulation was developed to determine how many batches should be produced and in which tank products should be stored to meet the demands and minimize production costs. The results of computational experiments show that the commercial solver found poor quality solutions or could not find feasible solutions within one hour. Thus, we applied relaxand-fix and fix-and-optimize MIP based heuristics and we observed that these heuristics were able to obtain feasible solutions for more instances in shorter computational times and find better solutions than those obtained by the commercial solver to solve the proposed model.

ZIP Code Versus Georeference

“…A mathematical optimization model involves the representation of a problem or situation through a set of mathematical relationships such as equations, inequalities, logical dependencies, and functions (e.g. [20,21,19]). There are several reasons for building optimization models, among which we can highlight: increase the degree of understanding of the situation studied; analyze the situation and propose solutions that are not apparent; test various scenarios that would not otherwise be possible, or recommended [9,8].…”