A resource-constrained optimization model for parallel machine scheduling with constraint programming

This study investigates an NP-hard parallel machine scheduling problem, a critical challenge in manufacturing, healthcare, and logistics industries where efficient resource allocation is essential. The issue involves scheduling operations where each task requires an additional resource, with multiple resource types available, each limited to a single copy. The objective is to minimize the makespan, which is defined as the total completion time of all tasks. A novel constraint programming model is designed to solve the problem to optimality. The proposed model is benchmarked against two existing linear mathematical formulations, achieving up to 95% faster computational times while solving instances with up to 20 machines, 40 resources, and 90 operations per resource—scenarios the linear models failed to handle within reasonable computational limits. Furthermore, the model exhibits excellent scalability, effectively solving more extensive and complex instances. These findings underscore the potential of constraint programming as a powerful tool for tackling complex scheduling problems in resource-constrained environments, with applications in industries where resource-sharing is critical.