A scheduling problem on a single batching machine with batch deliveries

In this paper, we address a coordination problem of single batching machine scheduling and finished jobs delivery where the jobs are processed on a single batching machine and delivered by a transporter to the customer. The batching machine can handle several jobs simultaneously. The processing time of a batch is equal to the longest processing time among the jobs in a batch. For the objective to minimize the makespan, we present a polynomial-time algorithm based on optimal properties. For the objective to minimize the total weighted completion time, we prove that this problem is strongly NP-hard.