A method of controlling a transport vehicle for transporting exactly one sliver can (2) in a spinning mill between a filling station (3) for filling cans (2) with a sliver and can (2) working positions near workstations of spinning machines (4), which ensures that the spinning machines are supplied with full sliver cans (2), characterized in that a request to replace the can (2) at the respective workstation of the spinning machine (4) is made on the basis of information from the spinning machines (4) about the remaining amount of the sliver in the cans (2) near the individual workstations of the spinning machines (4), or on the basis of information about the removal of the can (2) by the operator during spinning, the information being passed to the control system (5) of the spinning mill, which on the basis of this request predicts the moment of the conveying of the can (2) by the transport vehicle (1) to the respective workstation, whereby the request is placed into a request queue which is optimized for the maximum utilization of the spinning machines (4 with respect to the amount of the sliver in the individual cans, the current position and utilization and the loading of the transport vehicles (1).