Production-transportation scheduling model on a single batching machine

In this paper, we study a scheduling model of production and transportation on a single batching machine. In this model, there are several vehicles with unit capacity that travel between the machine and a holding area. The batching machine can process several jobs as a batch in which the processing time of one batch is the largest processing time among all jobs in the batch. The batching machine needs a setup cost when it processes a new batch. The objective is to minimize the sum of the total completion time and total setup cost. We prove that the problem is strongly NP-hard. An integrated heuristic is developed for the general problem. We study the value of production-transportation integration by comparing our integrated approach with two sequential approaches where scheduling decisions for job production are made first, followed by job transportation decisions. Computational experiments show that a significant benefit can be achieved by integration in many cases.