Safety analysis for a class of graph constrained scheduling problems

We consider a class of scheduling problems, common in manufacturing industries that consist of several interconnected subprocesses. We model the scheduling constraints of each subprocess and of the overall system using labeled directed graphs, forming the admissible set of schedules. Furthermore, we consider polytopic constraints on the state space. We approach the scheduling problem as a safety analysis problem utilizing reachability mappings, system and constraint structure. Consequently, we construct the safe schedules that guarantee constraint satisfaction at all times. The proposed framework is illustrated in a case study that concerns a simplified separation process.