Petri nets for production management

We consider the case of cyclic and non-cyclic manufacturing systems (also called off-line and online manufacturing systems). The first approach concerns cyclic manufacturing systems which are modelled as event graphs. We show how to optimise these nets. The second approach proposed concerns non-cyclic manufacturing systems which can be modelled using decomposable nets, i.e. nets which can be expressed as the union of conflict-free subnets whose transitions correspond to the strictly positive components of a t-invariant. This first model concerns the planning activity. We show that the desirable qualitative properties are preserved if we restrict the set of planning decisions to the ones which consist in firing the transitions of a subnet according to the corresponding components of the related t-invariant. Knowing the short term planning, we propose two scheduling algorithms. One of them is based on the notion of critical path in the controllable net which is the model of the system from a scheduling point of view