Analysis of gap times in a two-stage stochastic flowshop with overlapping operations

The impact of transfer batching (also referred to as lot splitting) on the performance of flowshops has received widespread attention in the literature. Most papers have emphasized the usefulness of lot splitting in cutting down average flow times, as it enables the overlapping of operations at different stages of the flowshop. However, while most analytical papers have studied deterministic flowshops, an important downside of lot splitting has been overlooked; i.e., the occurrence of idle time between the processing of consecutive sublots belonging to the same process batch (referred to as gap times). Gap times add no value to the product; they merely increase the process batch makespan at the different stages. In deterministic systems, these gap times may be avoided by balancing the processing rates of the different machines in the shop; in stochastic settings, however, they may occur even when the system is perfectly balanced, due to the inherent variability in the setup and processing times. Studying a two-stage flowshop with a single product type, this paper provides insight into the behavior of the gap times, and develops an approximation for the process batch makespan at the second stage in terms of the system characteristics and the lot splitting policy.