This paper discusses an on-line Tasks Assignment and Routing Problem(TARP) for Autonomous Transportation Systems(ATSs) in manufacturing systems. The TARP results in a constrained version of the Pickup and Delivery Problem with Time Windows(PDPTW). As an approach to this problem, a cooperative algorithm with autonomous distributed agents has been proposed. The algorithm is able to plan deadlock-free routes even though the buffer capacity is less, but includes reformability at the point that computation time of that case increases drastically. This paper proposes an initial task assignment method to reduce computation time on planning routes. Results of computational experiments show effectiveness of the proposed method.