Assembly comprising a post picking governed by a government system, taking the place of preparation a first circuit comprising a first conveyor leg (31) which receives containers product storage, and first accumulation means a certain amount of storage containers received by the first conveyor leg comprising said first storage means at least one first chimney (35) comprising overlapping mobile sites that each can receive and downshifting at least one storage container, forming said at least one first chimney means vertical accumulation and distribution sequenced storage containers previously placed on the sites, wherein the first storage means comprise at least one first lift (34), adapted to move vertically along said at men I first chimney (35) to each of the locations of said at least one first chimney (35); that the preparation station comprises means for reading an identifier carried by a storage container as coming from the first conveyor back, and the steering system is adapted to: - select one of the locations of said at least a first chimney, according to the read identifier and a predetermined sequence defining the order in which the storage containers must leave said at least one first chimney; - govern the said at least one first elevator in order to enter the storage container as the selected location.
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