This paper considers new flowshop scheduling problems related to automated manufacturing systems in whichnjobs are processed on two machinesMaandMbin this order. The job transportation between two machines is done by a single automated guided vehicle (AGV), and is crucial because no machine has buffer storage for work-in-process (WIP) and hence a machine cannot release a finished job until the empty AGV becomes available at that machine, while the AGV cannot transfer an unfinished job to a machine until the machine is empty. O(n3) algorithms are given in this paper to find optimal sequences ofnjobs that minimize their maximum completion time (i.e., makespan). Some numerical results are also given to evaluate the effect of computing optimal sequences.