Minimum Job Completion Time in Petri Nets

Petri Nets are well known as a tool to model discrete systems. Petri Nets possess arc weights that represent the number of tokens consumed by a transition from its input place (input arc weight) or deposited into its output place (output arc weight). The arc weights are fundamental during the simulation run (‘dynamic analysis’) of the Petri Net. Petri Net theory also offers static analyses (aka ‘structural analysis,’ or invariants), which are quicker and do not change with the dynamics (e.g., initial tokens or firing times of the transitions). This paper attempts to distribute ‘firing times’ as arc weights on Petri Nets so that more structural analyses can be performed - a so-called quasi-dynamic approach; for example, this quasi-dynamic analysis can find a faster route from a source to a destination (minimum job completion time). Otherwise, finding the minimum job completion time using simulations is slow and may not provide the correct answer. The approach presented in this paper for finding the minimum job completion time can be used in many branches of engineering, such as manufacturing.