Estimating machine startup timing with Petri nets

Machine startup timing is a crucial performance factor in large production facilities. Though Petri net is a well-proven methodology to solve problems in discrete event systems, Petri net is applied under the assumption that each operation starts when the preceding operations are completed; thus, the Petri net approach is assumed less effective and max-plus algebra (along with the dependency graph) is employed as the default tool for estimating startup timing. However, the max-plus algebra approach is iterative that takes O(n³) computations, where n is the number of machines. This paper proposes a procedure with which a dependency graph can be converted into a Petri net model and the startup timing can be estimated in linear O(n) computations.