Optimisation of invariant criteria for event graphs

The problem of obtaining a cycle time that is smaller than a given value in a strongly connected event graph, while minimizing an invariant linear criterion, is addressed. This linear criterion is based on a p-invariant of the strongly connected event graph under consideration. Some properties of the optimal solution are proved, and a heuristic algorithm and an exact algorithm which make it possible to reach a solution to the problem are given. Applications of the results to the evaluation of job shops and Kanban systems are proposed