Firing Rate Optimization of Deterministic Timed Event Graphs by Server Performance Improvement

Timed event graphs are a subclass of Petri nets that are commonly applied for modeling and controlling manufacturing systems. In this paper, we investigate the problem of improving the performance of machines (servers) in timed event graphs in order to maximize the firing rate of a system. We show that the logic constraints on the cost of machines and the operation time of machines (firing delay of transitions) can be transformed into linear algebraic constraints. Furthermore, we formulate a mixed integer linear programming problem to maximize the firing rate of the net under a given budget for improving the performance of servers (decreasing the firing delay of transitions) that can provide an optimal solution. Finally, application to an assembly line is presented to show the effectiveness of the developed methodology.