Parsimonious deadlock-free Petri net models of flexible manufacturing systems

Petri net (PN) modeling of flexible manufacturing systems is generally performed through a sequential procedure that introduces additional constraint layers over an unconstrained PN modeling the production sequences. The constraints account for job limitations, resources usage, liveness, etc., and are typically all representable as generalized mutual exclusion constraints, that can be implemented as monitor places suitably connected to the PN's transitions. This sequential procedure typically yields a redundant model, that is not easily reduced a posteriori. An integrated modeling approach is here proposed to solve the redundancy problem by enforcing all the constraints in a single design step that optimizes the number of monitors. The monitor design task is reformulated as a classification problem, which is solved through an efficient branch & bound approach. Some examples emphasize the potential model size reductions that can be achieved.