This paper addresses the Glass Container Industry Problem regarding a New Furnace (GCIP–NF), in which a company must jointly determine the new furnace’s melting capacity and the set of forming machines to be installed. To represent this integrated design problem, we propose a mixed-integer linear programming (MILP) formulation that combines furnace-capacity decisions, machine-selection decisions, and production-planning constraints. Since the problem is computationally challenging, we investigate both exact and hybrid solution approaches. The methods considered include a Branch-and-Cut algorithm, simple and multi-population genetic algorithms with tree- and grid-based topologies. The evolutionary methods are compared against a Sparrow Search Algorithm (SSA) adapted to the problem’s discrete-continuous structure. A Greedy Filter (GF) heuristic is also incorporated to discard clearly infeasible configurations and accelerate the evaluation of candidate solutions. The methods were tested on 200 instances generated from industrial data and divided into small and large cases. For small instances, the exact method obtained the largest number of optimal solutions and the smallest optimality gaps, while the GF-enhanced metaheuristics produced near-optimal solutions with competitive running times. For large instances, the exact method frequently failed to find feasible solutions within the time limit, whereas the metaheuristic approaches consistently returned feasible solutions of good quality. The GF-enhanced multi-population variants achieved the strongest overall performance, while the SSA proved to be a competitive and robust alternative. A real industrial case study further showed that the exact method, MPGAt-GF, and SSA converged to the same optimal design, supporting integrated decisions on machine selection and furnace sizing.
Amorim et al. (Sat,) studied this question.