Task assignment and load balancing of autonomous vehicles in a flexible manufacturing system

This paper presents a graph-theoretic approach to determining an optimal task (or routing) assignment of p autonomous vehicles (AVs) among m workstations in a flexible manufacturing system (FMS) to minimize the assignment completion time, as well as to achieve load balancing among the AVs. The task assignment problem is equivalent to an optimal routing assignment of destinating the m workstations to the p autonomous vehicles. A cost function is defined in terms of job execution time and traveling time performed by the AVs. Optimization of the cost function is based on the minimax of the job execution time and the minimization of max-min of the traveling time. The optimal task assignment problem is solved by a state-space search method - the A* algorithm. 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 easily 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 with load balancing.