Scaling on parallel machines unrelated to resource constraints: Matheuristic and meta-heuristic approaches

This study addresses the unrelated parallel machine scheduling problem with resource constraints, an NP-hard problem with broad practical application across various industrial sectors. To solve this problem, we propose two methods structured in a two-stage architecture: a heuristic approach using the Iterated Local Search (ILS) metaheuristic hybridized with a greedy heuristic, and a matheuristic combining the ILS metaheuristic with a constraint programming model. We compare our results with those obtained by an exact model and a metaheuristic from the literature. Both approaches outperform the reference metaheuristic and compete effectively with the exact method in generating optimal solutions. Additionally, the heuristic method's low computational time highlights it as an efficient alternative for real-world scenarios with larger instances, enabling rapid decision-making and adjustments in production scheduling.