We propose a simultaneous optimization method for task assignment and routing problems with multiple AGVs by the decomposition of Petri Nets. In the proposed method, Petri Net is decomposed into several subnets representing task subproblems and AGV subproblems. Each subproblem is solved by Dijkstra's algorithm. The subproblem on each subnet is repeatedly solved until a feasible solution for the original problem is derived. A solution method for subproblems with no final marking is newly developed. The effectiveness of the proposed method is demonstrated by comparing the performance with CPLEX as well as a nearest neighborhood heuristic method.