Supervisory control reconfiguration and optimization of resource allocation systems with a Petri net and mathematical programming approach

Presently, the number, types, and distribution of resources in a resource allocation system (RAS), may change frequently and dynamically due to fluctuant customer demands. Such changes in a resource allocation (RA) specification mean different production or service behaviors yielded by the providers. This new situation gives rise to a challenging problem, namely, how to switch smoothly the provider systems to support different production. This paper tries to address this problem from the viewpoint of discrete event system (DES) supervisory control. A Petri net (PN) controller of an RAS can be designed from a resource allocation specification using P-invariant. Once the RA specification is changed, the controller is updated following it. Moreover, if the changed specification is unreasonable, the whole control system, are reconfigured to reach a legal system state and a newly reasonable resource allocation solution is re-calculated. Specifically, the paper proposed a reconfiguration method of a PN control system that is transformed into PN reachability analysis problem using a mathematic programming approach. In our method, not only the transition firing costs but also the steps of concurrent firing are taken into account to achieve an optimal reconfiguration solution. Finally, an example is provided for illustrating the application of the mentioned methods.