Scheduling a maintenance activity and due-window assignment on a single machine

We study a single machine scheduling and due-window assignment problem. In addition to the traditional decisions regarding sequencing the jobs and scheduling the due-window, we allow an option for performing a maintenance activity. This activity requires a fixed time interval during which the machine is turned off and no production is performed. On the other hand, after the maintenance time, the machine becomes more efficient, as reflected in the new shortened job processing times. The objective is to schedule the jobs, the due-window and the maintenance activity, so as to minimize the total cost consisting of earliness, tardiness, and due-window starting time and size. We introduce an efficient (polynomial time) solution for this problem.