MILP formulation and hybrid evolutionary algorithms for the glass container industry problem with multiple furnaces

Abstract

The present paper approaches a production planning problem in the glass container industry (GCI) to redesign the production process. The redesign defines new furnaces and related molding machines, considering demand requirements or expansion plans for the industrial plant. First, we introduce a mixed-integer linear programming (MILP) model for such a problem. Next, we compare the results achieve by an exact method and two hybrid evolutionary algorithms when solving the problem. The exact method is the branch & cut (B&C) algorithm from the CPLEX solver that executes over the MILP model. The genetic algorithms are a standard genetic algorithm (GA) and a multi-population genetic algorithm (MPGA). Both methods evolve binary variables whose values allow solving the linear program (LP) model obtained from MILP. A greedy heuristic is also integrated to GA and MPGA to build an initial feasible solution for the LP model. A set of instances is generated with data provided by a GCI. The results indicate that B&C returns few optimal solutions for small-size problems, while GA and MPGA can solve large problems with relevant results in terms of solution quality and execution time.