A decomposition method for optimal firing sequence problems for first-order hybrid Petri nets

In this paper, we propose a general decomposition method for transition firing sequence problems for first order hybrid Petri nets. The optimal transition firing sequence problem for first-order hybrid Petri nets is formulated as a mixed integer programming problem. We propose a Lagrangian relaxation method for solving optimal transition firing sequence problems. The hybrid Petri net is decomposed into several subnets in which the optimal firing sequence for each subnet is easily solved. The optimality of solution can be evaluated by duality gap derived by Lagrangian relaxation method. The proposed method is applied to a small-scale example. Computational experiments demonstrate the validity of the proposed formulation.