A multi-criteria scheduling with due-window assignment problem

We study a multi-criteria scheduling and due-window assignment problem, in which the cost components are: flow-time, earliness, tardiness and due-window cost. Jobs completed within the due-window are assumed to be on time, and no earliness ∖ tardiness cost is incurred. The due-window starting time is a given parameter, whereas the due-window completion time (i.e., the window size) is determined during sales negotiations with the customer, and is therefore a decision variable. The problem is shown to be solved (finding both the schedule and the due-window size) in polynomial time.