Scheduling jobs and maintenance activities on parallel machines

In this article, we deal with the problem of scheduling N production jobs on M parallel machines. Each machine should be maintained once during the planning horizon. We consider the case where the maintenance of the machines should start at time zero and the resources that ensure the maintenance are not sufficient. For such a reason, the maintenance tasks must be continuously run during the planning horizon. We aim to find a schedule composed of the production jobs and the maintenance tasks for which the total sum of the jobs’ weighted completion times and the preventive maintenance cost are minimized. We optimally solve the problem by an integer linear programming method. We also propose a heuristic method computed in two phases. Computational experiments are performed on randomly generated instances and the results show that the proposed methods produce satisfactory solutions for the problem.