A transportation system for a building with multiple floors includes a shaft in the building, a traction sheave drive type elevator and a lift. The elevator vertically conveys persons using an elevator car that is movable in the shaft together with at least two counterweights, the elevator car and the counterweights moving in opposite directions. The elevator car and the counterweights are driven by drive engines with traction sheaves. The lift vertically conveys objects and is designed as a self-propelled lift. The lift has a lift platform designed as a vehicle for supplying goods, which vehicle can be brought in and out the shaft and which lies, when located in the shaft, within a vertical projection of the elevator car.