Petri net modeling of ratio-driven flexible manufacturing systems and implications on the WIP for cyclic schedules

In this paper we present a systematic approach of modelling ratio-driven flexible manufacturing systems with Petri nets. We focus on the impact of universal or dedicated transport resources and the way the operation sequences are modeled as closed loops. For a particular problem setting, minimizing the necessary work in process (WIP) while saturating the critical machines, we show that the modeling approach based on timed event graphs, in the way it is commonly used, may induce unnecessary constraints on the WIP. In order to overcome this problem we propose a new technique for the modeling of production ratios and establish tight lower bounds for the WIP, giving thereby a measure for the performance increase obtained.