In this paper, we propose a decomposition and coordination method for routing problems for multiple automated guided vehicles (AGVs) using Petri Nets. An extended Petri Net model is created to represent concurrent motion of multiple AGVs. The routing problem to minimize total transportatin time is formulated by the proposed Petri Net. The optimization model for the Petri Net is decomposed into several subproblems which can be solved by Dijkstra's algorithm in polynomial order. The effectiveness of the proposed method is evaluated by several numerical examples.