The sorting installation (1) of the invention includes sorting outlets (2) aligned along a sorting conveyor (3), each outlet being provided with a recess (4) for receiving a tray (5) in which sorted mailpieces (6) are stored. The installation also includes a tray conveyor (8) that extends in a certain conveying direction (F2) under the sorting outlets for the purpose of transporting trays filled with sorted mailpieces from the sorting outlets to a feed inlet (7) of the sorting conveyor. The installation further includes a shuttle robot (9) suitable for traveling on the floor (S1) in autonomous manner along the sorting outlets, the robot including handling means (12) suitable for extracting a tray from a recess of a sorting outlet and for placing it lengthwise on the tray conveyor.