A gantry lift stacker comprising a straddle carrier having a spreader for containers and having a front first gantry frame part and a rear second gantry frame part which each have two vertical gantry supports extending with their respective longitudinal axis in parallel with the lifting and lowering direction, wherein the spreader is guided on the gantry supports of the gantry lift stacker during lifting and lowering and a lifting device for the spreader is attached to a gantry frame of the gantry lift stacker in a stationary manner, and having a locating system arranged on the gantry lift stacker, said locating system determining a position of the gantry lift stacker, wherein the locating system determines the position of the gantry lift stacker in relation to a point defined on a machine platform of the gantry lift stacker, wherein sensors are arranged on the gantry lift stacker, and wherein the sensors and the locating system are connected to a control unit, and wherein the control unit determines, from the position of the gantry lift stacker, using the signals from the sensors, a position of the spreader, of a container to be picked up or of a set-down location, and wherein the sensors arranged on the gantry lift stacker comprise at least one sensor for determining an inclination of the gantry lift stacker and at least one sensor for determining a relative position of the spreader on the gantry lift stacker, and wherein the relative position relates to the point defined on the machine platform for determining the position of the gantry lift stacker and includes a distance, measured in the lifting and lowering direction, of the spreader relative to the point defined on the machine platform for determining the position of the gantry lift stacker.