Airfreight Forwarding Under System-Wide and Double Discounts

Abstract

We consider the shipment consolidation and freight forwarding problem under two discount schemes: the system-wide and the double-discount. In the system-wide scheme, the cost associated with one flight does not only depend on the quantity of freight assigned to that flight, but also on the total freight assigned to other flights operated by the same carrier. In the double-discount scheme, there are cost savings based on the quantity shipped on a given flight on top of the system-wide discount. We propose models based on multi-commodity network flow formulations that take into account practical aspects such as cargo unsplitability, shipment volume and over-declaration. We propose solution methodologies based on Lagrangian relaxation and local branching. Numerical testing reveals the efficiency of the approaches presented and sheds light on some managerial implications. We find that freight forwarders do not only reduce costs from the system-wide and the double-discount schemes, but are also likely to engage with fewer airlines, thus reducing administrative fees.

Keywords: Transportation, System-wide discount, Double discount, Lagrangian relaxation, Column generation, Local branching, Network planning