A Study on Integration of Lot Sizing and Flow Shop Lot Streaming Problems

Lot streaming is a technique for splitting jobs, each consisting of identical items, into sublots to allow them to overlap on consecutive machines in multi-stage production systems. Through lot streaming, production can be accelerated and a significant decrease in makespan can be achieved. However, all lot streaming research assumes that the number of identical items of the product on each machine is given in advance. In other words, the lot sizing problem is not integrated into the lot streaming problem. Moreover, all lot streaming research assumes that machines are always available, in other words; no breakdowns or scheduled maintenance are allowed in which this is unrealistic. In addition, variable sublot-type seldom is considered in previous studies. In this paper, we develop mixed-integer linear mathematical models for the integration of lot sizing and lot streaming problems where machines are unavailable because they are undergoing preventive maintenance. All sublot types (equal, consistent, and variable) are considered in the proposed models. Proposed models are tested by numerical examples, and surprising results are presented.