Transformation of the cyclic scheduling problem of a large class of FMS into the search of an optimized initial marking of a linearizable weighted T-system

We show that Petri net is a pertinent model to compute analytically the cyclic scheduling of flexible manufacturing system (FMS) with shared non-preemptive resources and assembly or disassembly of multiple components. The proposed method is based on two techniques: 1) the linearization of Petri net conflicts on resources; and 2) the linearization of weighted T-system will give a deterministic marked graph if a specific condition of normalization of the transitions is satisfied. We show that it is possible to compute the best cyclic scheduling in p steps with respect to the cycle time by means of an optimal (min,+) set of linear equations. By using (max,+) algebra it is possible to discriminate among the candidate solutions, the solutions giving the minimum time cycle.