MIP models and a matheuristic algorithm for an identical parallel machine scheduling problem under multiple copies of shared resources constraints

If parallel machines use shared resources during production, jobs on machines must wait until the required resources are available. If the shared resource is single, only one job can use it at a time, but if there are multiple copies of this resource, multiple jobs can be scheduled up to the number of copies at a time. For this reason, it is crucial to consider resource usage when scheduling this type of machine. In recent years, various studies have been carried out to address identical parallel machine scheduling problems. However, although shared resources in parallel machines are an important aspect of this problem, resources are rarely considered in these studies and, in fact, have not been studied for this particular aspect. In this study, an identical parallel machine scheduling problem with sequence-dependent setup times, machine eligibility restrictions and multiple copies of shared resources (IPMS-SMS) is considered. Mixed-integer programming (MIP) models and a model-based genetic algorithm (matheuristic) are proposed, and the objective function of the problem seeks to minimize the total weighted completion time. Randomly generated instances are solved using the proposed models and the matheuristic. Optimal schedules are obtained for almost all small problems using a mixed-integer programming model. However, better solutions are obtained for medium and large instances using the proposed matheuristic.