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A graph-theoretic approach for determining an optimal task (or routing) assignment of p autonomous vehicles (AV's) among m workstations in a flexible manufacturing system which both minimizes the assignment completion time and balances the load among the AV's is presented. This task assignment problem is equivalent to an optimal routing assignmenl of destinating the m workstations to the p autonomous vehicles. A cost function is defined in terms of the job execution time and the traveling time performed by the AV's. Optimization of the objective function is based on the minimax of the job execution time and the minimization of max-min of the traveling time. This optimal task assignment problem is known to be NP-complete. Thus the problem is solved by a state-space search method-the A algorithm. The A algorithm is a classical minimum-cost graph search method. It is guaranteed to find an optimal solution if the evaluation function which utilizes the heuristic information about the problem for speeding up the search is properly defined. If potential collisions exist on the optimal routing assignment, then dynamic collision detection must be carried out during the state-space search to guarantee an optimal collision-free routing assignment. This collision avoidance can be taken care of by using an ordered collision matrix to adjust the arrival time of every AV arriving at the center of the "collision zone" if a potential collision is detected. Again, the A search strategy can be utilized to obtain an optimal collision-free routing assignment, and the optimal assignment obtained also achieves load balancing of the p AV's.