Unrelated parallel-machine scheduling simultaneously with rate-modifying activities and earliness and tardiness penalties

In this paper, we consider a scheduling problem simultaneously with rate-modifying activities and earliness and tardiness penalties on an unrelated parallel-machine setting. We assume that each machine has at most one rate-modifying activity to improve its production efficiency during the scheduling horizon and all the jobs have a common due-date. The objective is to determine jointly the optimal positions of rate-modifying activities, the optimal common due-date of all jobs, and the optimal schedule to minimize the sum of earliness and tardiness costs. We show that the problem can be optimally solved in polynomial time.