Scheduling jobs and preventive maintenance activities on parallel machines

We propose in this study a hierarchical method for the problem of scheduling N jobs on M parallel machines where each machine should be maintained once during the planning horizon. The maintenance tasks should be continuously executed because the maintenance resources are not sufficient. Our objective is to find a schedule composed of the jobs and the maintenance tasks in which the total sum of the job's weighted completion times and the preventive maintenance cost are simultaneously minimized. The proposed hierarchical method is essentially based on a linear model and an Evolutionary algorithm. Computational experiments are performed on randomly generated instances. The results show that the proposed method is able to produce appropriate solutions for the problem.