This paper discusses an on-line Tasks Assignment and Routing Problem (TARP) for Autonomous Transportation Systems (ATSs) in manufacturing systems. The TARP is a constrained version of the Pickup and Delivery Problem with Time Windows (PDPTW). In our former study, a cooperative algorithm, called the triple loop method, with autonomous distributed agents has been proposed. The Improving initial Task Assignment and Avoiding Deadlock method (ITAAD) is a faster algorithm than the triple loop method. In this paper, we propose a new vehicle routing method for the ITAAD. Results of computational experiments show effectiveness of the proposed routing method.