On the equivalence of small batch assembly line balancing and lot streaming in a flow shop

In this article we compare two apparently dissimilar scheduling problems. The Small Batch Assembly Line Balancing problem is the process of dividing operations over multiple stations so as to produce a series of parts whose processing times are characterized by learning. The Lot Streaming in a Flow Shop problem is the process of splitting a given lot or job to allow overlap of successive operations in multi-stage production systems, thereby reducing the makespan of the corresponding schedule. We show that the two problems are formally equivalent. By exploring the mathematical equivalence of the two problems, a number of unexpected new results have been obtained.