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(n log n ) 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(n log n ) time (and further in linear time if the length of the due window is unbounded as well). However, it becomes N P-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. (C) 2022 Elsevier B.V. All rights reserved.