In: Recherche Operationnelle, Vol. 34, No. 3, pages 283-303. 2000.
Abstract: The paper shows that timed Petri nets, with one resource shared by all the transitions, are directly connected to the modeling of integer linear programs (ILP). An optimal reachability delay is is an optimal solution of the ILP. The paper also shows that a net can model any ILP. In order to do this, a new sufficient reachability condition is given for the marking equation, which also holds for general petri nets without timed transitions.
Keywords: integer linear programs, reachability conditions, shared resources, timed Petri nets.