Very few Mathematical Tools are available to study the dynamics of discrete manufacturing systems. Petri Nets, and in particular a special type of Petri Nets called Timed Event Graphs, seem to be of special interest for studying discrete manufacturing systems. In this paper, we define Timed Event Graphs and emphasize the properties which are of interest for out purpose. Modeling job-shop systems as well as assembly systems using event graphs is then explained. The model obtained is a strongly connected event graph whose properties are presented in the first part of the paper. These properties are used to derive the properties of the manufacturing system. In particular, it can be shown that the productivity of the manufacturing system is defined by the cycle time of the critical circuit in its event graph model. Blocking conditions of the system are also studied.

Finally, we show how to use the previous results to maximize the productivity with a minimal in-process inventory when the sequences of product types are fixed at the entrance of each machine.