A Petri Net based algorithm for minimizing total tardiness in flexible manufacturing systems

Petri Nets have been extensively used for modeling and simulating of the dynamics of flexible manufacturing systems. Petri Nets can capture features such as parallel machines, alternative routings, batch sizes, multiplicity of resources, to name but a few. However, Petri Nets have not been very popular for scheduling in manufacturing due to the Petri Net "state explosion" combined with the NP-hard nature of many of such problems. A promising approach for scheduling consists of generating only portions of the Petri Net state space with heuristic search methods. Thus far, most of this scheduling work with Petri Nets has been oriented to minimize makespan. The problem of minimizing total tardiness and other due date-related criteria has received little attention. In this paper, we extend the Beam A* Search algorithm presented in a previous work with capability to handle the total tardiness criterion. Computational tests were conducted on Petri Net models of both flexible job shop and flexible manufacturing systems. The results suggest that the Petri Net approach is also valid to minimize due date related criteria in flexible systems.