An approximation algorithm for a supply-chain scheduling problem with an assignable common due window and holding time

This paper studies single machine scheduling with batch deliveries, where a common due window for all jobs has to be determined, not given in advance. The objective is to minimize the overall cost for the process and delivery. Concretely, it includes the penalty of a job being early or tardy, the cost for holding and delivering a job, and the cost incurred by a late starting or a long duration of the common due window. Observing the NP-hardness, we provide an optimal algorithm of the problem and convert it to a fully polynomial time approximation scheme for a special case.