A facility for scheduling the picking of a plurality of items specified for an item shipment is described. When a first-picked item of the plurality is picked, the facility selects a first period of time of a target length during which the first-picked item is expected to arrive at a sorting machine. For each of the items specified for the item shipment other than the first-picked item, the facility designates a picking period for the item that, when shifted forward in time by an amount of time the item will take to arrive at the sorting machine once picked, falls completely within the first period of time.