Lagrangian heuristics for the capacitated multi-plant lot sizing problem with multiple periods and items

• We propose Lagrangian heuristics that outperformed the state-of-the-art heuristic.
• Our heuristics were competitive with CPLEX for these small-sized instances.
• Concerning large-sized instances, the Lagrangian heuristics were remarkably better.

Production planning plays an important role in the industrial sector. The focus of this paper is on the lot sizing of those companies composed by multiple plants, each of them with a finite planning horizon divided into periods. All plants produce the same items and have their demands to be met without delay. For producing items, all plants have a single machine with setup times and costs and a limited capacity of production. Transfers of production lots among plants and storage of items are allowed. Even though there are some studies to tackle this problem, to find feasible solutions for the entire set of benchmark instances remains a challenge. This paper introduces novel Lagrangian heuristics that, besides heuristically solving all benchmark instances, significantly outperformed the best heuristic from the literature.