There is proposed a unit including a station for preparing orders, controlled by a control system. The station has a first circuit that includes a first outward conveyor, which receives containers for storing products, and an accumulator for accumulating a predetermined quantity of storage containers received on the first outward conveyor. The accumulator includes: at least one first shaft comprising superposed mobile positions that can each receive and downwardly move at least one storage container, the at least one first shaft vertically accumulating and sequentially dispensing storage containers previously placed in the positions; and at least one first elevator moving vertically along the at least one first chute up to each of the locations of the at least one first chute.