Modelling integer linear programs with Petri nets

We show in this paper that timed Petri nets, with one resource shared by al l the transitions, are directly connected to the modelling of integer linea r programs (ILP). To an ILP can be automatically associated an equivalent P etri net. The optimal reachability delay is an optimal solution of the ILP. We show next that a net can model any ILP. I order to do this, we give a n ew sufficient reachability condition for the marking equation, which also h olds for general Petri nets without timed transitions.