Scheduling variable maintenances and jobs on unrelated parallel machines to minimize the total completion time

We investigate an unrelated parallel-machine scheduling problem in which each machine must perform a variable mandatory maintenance prior to a given deadline. A variable maintenance means that the duration of the maintenance depends on its starting time, i.e., the later the maintenance starts, the longer it takes to complete. The task is to schedule all the jobs and determine the starting times of each maintenance such that the total completion time is minimized. We show that the problem is strongly NP-hard. Furthermore, we provide a fast heuristic algorithm, followed by a numerical example. © 2016 Taylor & Francis Group, LLC.