Lot streaming and scheduling multiple products in two-machine no-wait flowshops

We consider the problem of minimizing makespan in two-machine no-wait flowshops with multiple products requiring lot streaming. A ‘product’ (or lot) consists of many identical items. Lot streaming (lot sizing) is the process of creating sublots (or transfer batches) to move the completed portion of a production sublot to downstream machines so that operations can be overlapped. The number of sublots for each product is fixed. When the flowshop produces only a single product, we obtain optimal continuous-sized sublots. It is shown that these sublot sizes are also optimal for the problem of simultaneous lot streaming and scheduling of multiple products. The optimal scheduling of products can be accomplished by application of the algorithm due to Gilmore and Gomory. Then, we devise an efficient heuristic for the problem of simultaneous lot streaming (finding optimal integer-sized sublots) and scheduling of multiple products. Computational results indicate that this heuristic can consistently deliver close-to-optimal solutions for the problem. A comparison of this heuristic is also made with a heuristic that first divides items belonging to each product into nearly equal-sized sublots and then constructs a schedule for such sublots. Finally, we extend our solution procedures to a traditional and more general lot streaming model, where the number of sublots for each product is a decision variable.