The impact of lot splitting on lead times in a deterministic production line

It is generally known that the mechanism of overlapping operations allows to reduce the average job lead times in a production system. However, a machine may remain idle between two consecutive sublots belonging to the same job, due to a difference between its own setup and processing times and those of the preceding machine. These idle times are referred to as “gaps”. Until now, little formal results are available to calculate these “gaps” in terms of the system parameters and the transfer batch sizes used. In this paper, we derive expressions for these gaps and the transfer batch lead times in a single-product production line with deterministic arrivals, setup and processing times. We prove that in our setting, the average transfer batch lead time is minimized when the transfer batch size equals one product unit.