In-transit freight consolidation of indivisible shipments

This paper studies the multi-period freight consolidation problem for a third-party logistics (3PL) provider that transships multiple products from multiple suppliers to a single end customer. The shipments are first transported to select consolidation terminals where the 3PL provider aims to consolidate the inbound shipments so as to reduce costs. This imposes a complex decision problem to the 3PL provider since consolidation may require that the inbound shipments spend more time at the terminals, whereas all shipments have prespecified pickup dates and delivery deadlines. Moreover, the shipments picked up from the suppliers are indivisible, that is, a shipment cannot be split into multiple lots and assigned to separate routes. This paper presents a mixed-integer linear programming model and proposes a heuristic for solving the resulting problem. The proposed heuristic partitions the multi-period problem into multiple subproblems by splitting the planning horizon into smaller mutually exclusive units which makes the planning problem relatively insensitive to the length of the planning horizon and hence scalable. The effectiveness of the proposed heuristic is demonstrated via a real-life problem: a close-to-optimal solution for a 360-day planning problem that could not be solved using commercial solvers due to its size is obtained within two hours.