Improved algorithms for single-machine common due window assignment and scheduling with batch deliveries

We consider a single-machine due window assignment and scheduling problem with batch deliveries, where all jobs have a common due window, and the start time and size of the due window are decision variables. Finished jobs are delivered in batches with unlimited batch capacity. The objective is to determine the due window, a job sequence, and the delivery times, so as to minimize the total cost which comprises earliness of delivery, job holding, start time of due window, size of due window, number of delivery batches, and tardiness penalty. We consider three different variants of the problem corresponding to different measurements of tardiness penalty. We present polynomial-time solution procedures for these variants with significantly lower computational complexities than those of known algorithms in the literature.