A kernel search to the multi-plant capacitated lot sizing problem with setup carry-over

Lot sizing is one of the most challenging problems in production planning. This paper focuses on the multi-plant capacitated lot sizing problem (MPCLSP) with setup carry-over (MPCLSP-SC). To the best of our knowledge, the MPCLSP-SC has been the subject of one single study, despite the fact that it can bring financial benefits, primarily by considering case studies under tight capacity. Moreover, in spite of the significant improvement in the performance of benchmark optimization solvers over the years, they are still very time and memory consuming for large MPCLSP instances. Therefore, heuristics stand out among the solution methods to tackle this type of problem. This paper introduces a novel matheuristic, a kernel search (KS) method, to solve the MPCLSP-SC. Through computational experiments, it was possible to show the outstanding performance of the proposed method for large instances with diverse characteristics. The experiments also demonstrate that the introduced KS outperformed state-of-the-art methods to solve the MPCLSP.