Scheduling Identical Parallel Machines with a Fixed Number of Delivery Dates

We consider the scheduling problem of a manufacturer that has to process a set of jobs on identical parallel machines where jobs can only be delivered at a given number of delivery dates and the total tardiness is to be minimized. In order to avoid tardiness, jobs have to be both, processed and delivered before or at their due dates. Such settings are frequently found in industry, for example when a manufacturer relies on a logistics provider that picks up completed jobs twice a day. The scheduling problem with fixed delivery dates where the delivery dates are considered as an exogenously given parameter for the manufacturer’ scheduling decisions can be solved by various optimal and heuristic solution procedures. Here, we consider a variant of this problem where only the number of deliveries is fixed and the delivery dates can be set arbitrarily. For example, a manufacturer may be entitled to assign the logistics provider two pick-up times per day and decide on the exact times of these pick-ups. Then, the machine schedule and the delivery dates can be determined simultaneously which may significantly improve adherence to due dates. Our findings can provide valuable input when it comes to evaluating and selecting distribution strategies that offer a different extent of flexibility regarding the delivery dates.