Scheduling shipments in closed-loop sortation conveyors

At the very core of most automated sorting systems— for example, at airports for baggage handling and in parcel distribution centers for sorting mail—we find closed-loop tilt tray sortation conveyors. In such a system, trays are loaded with cargo as they pass through loading stations, and are later tilted upon reaching the outbound container dedicated to a shipment’s destination. This paper addresses the question of whether the simple decision rules typically applied in the real world when deciding which parcel should be loaded onto what tray are, indeed, a good choice. We formulate a short-term deterministic scheduling problem where a finite set of shipments must be loaded onto trays such that the makespan is minimized. We consider different levels of flexibility in how to arrange shipments on the feeding conveyors, and distinguish between unidirectional and bidirectional systems. In a comprehensive computational study, we compare these sophisticated optimization procedures with widespread rules of thumb, and find that the latter perform surprisingly well. For almost all problem settings, some priority rule can be identified which leads to a low-single-digit optimality gap. In addition, we systematically evaluate the performance gains promised by different sorter layouts.