Lot streaming multiple jobs in a flow shop

In this article we consider the advantages of applying lot streaming in a multiple job flow-shop context. The lot streaming process of splitting jobs into sublots to allow overlapping between successive operations has been shown to reduce makespan and thus increase customer satisfaction. Efficient algorithms are available in the literature for solving the problem for a single job. However, for multiple jobs, job sequencing, as well as lot sizing, is involved, and the problem is therefore NP-hard. We consider two special cases for which we provide polynomial time solutions. In one case, we eliminate diversity of the jobs, and hence the job sequencing decision, and in the other we restrict the number of machines. We show that for jobs with identical processing times and number of sublots, no advantage is obtained by allowing inconsistency in sublot sizing of consecutive jobs. For the two-machine case, we also explain why the sequencing and sublot size decision can be approached independently, and supply a polynomial time algorithm for minimising makespan, taking account of attached set-ups on the first machine and transportation times.