In this paper, we propose a Petri Net decomposition approach for dynamic dispatching and routing for bi-directional AGV systems. For dynamic dispatching and routing, the static problem to determine an optimal firing sequence problem for Petri Net is solved repeatedly. A Petri Net decomposition approach is applied to solve the optimal firing sequence problem efficiently. In the decomposition algorithm, the entire Petri Net is decomposed into task subnets and AGV subnets. The penalty function algorithm is used to coordinate the solution of each subnet. A deadlock avoidance policy for bi-directional lane is used to ensure the generation of conflict-free routing. Computational results show the effectiveness of the proposed Petri Net decomposition approach with deadlock avoidance policy for dynamic situations.