A queueing model for a two-stage stochastic manufacturing system with overlapping operations

This paper presents analytical expressions for estimating average process batch flow times through a stochastic manufacturing system with overlapping operations. It is shown that the traditional queueing methodology cannot be directly applied to this setting, as the use of the overlapping operations principle causes the arrival process of sublots at the second stage to be a non-renewal process. An embedded queueing model is then proposed, which provides a tool to estimate the flow time reductions caused by the use of overlapping operations. Moreover, we provide expressions to estimate the production disruptions occurring at the second stage. The results of our research confirm the general intuition that the overlapping operations principle leads to less congestion, and hence a smoother flow of work through the system. On the other hand however, lot splitting inevitably requires more material handling on the shop floor. The expressions provided in this paper allow the quantification of the trade-off between these two effects, e.g., by gauging them within the scope of a cost model.