Automated guided vehicles (AGV) systems are important for material handling in automated manufacturing systems (AMS). However, it is a great challenge to effectively manage them due to some of their features, e.g., the number of AGVs being fixed., prior unknown requests, and changing AGV initial positions. This paper aims to find the shortest time routing while both deadlock and blocking in them are avoided. We first find the shortest routing based on a layout of an AGV system, and then perform rerouting whenever necessary to avoid deadlock and blocking according to a deadlock avoidance policy previously developed by the authors. The algorithms are presented and illustrated through examples.