Single machine scheduling with common assignable due date/due window to minimize total weighted early and late work

Traditional scheduling models assume that due dates are predefined and the aim is to find a schedule that minimizes a given scheduling criterion with respect to the given set of due dates. A more recent trend consists of models that focus on coordinating two sets of decisions: due date assignment to customers and determining a job schedule. We follow this trend by analyzing a single machine scheduling problem, where the scheduler is tasked with assigning a common due date to all jobs in order to minimize an objective function that includes job-dependent penalties due to early and late work. We show that the problem is solvable in linear time if the common due date value is unbounded, and in O(nlogn) time if it is bounded from above. We then extend the analysis to the case where a common due window has to be assigned to all jobs. We show that when the location of the due window is unbounded, the problem is solvable in O(nlogn) time (and further in linear time if the length of the due window is unbounded as well). However, it becomes NP-hard when it is bounded. We complement our analysis by (i) providing a pseudo-polynomial time algorithm to solve this hard variant of the problem, and (ii) study two special cases of this hard variant that are solvable in polynomial time.