Freight consolidation with divisible shipments, delivery time windows, and piecewise transportation costs

Abstract

This paper studies the freight consolidation problem for a third party logistics (3PL) provider that transships products from multiple suppliers to a single business customer over a contracted multi-period horizon. Under a two-echelon setting, shipments from geographically dispersed sources that are en route to the customer are first transported to intermediary facilities for possible consolidation into full-container loads. Each shipment has a preset pickup date at the source and a delivery time window at the destination. Further, each shipment can be partitioned into multiple shipments that can be routed to different intermediary facilities. Shipments reaching the intermediary facilities are consolidated and forwarded to the final destination in the second echelon. A mixed integer programming model is developed for this problem, which employs piecewise cost functions to capture the economies of scales that are common in transportation. To speed up obtaining solutions, an exact solution methodology is proposed. The proposed solution method lends itself to container load relaxation, temporal decomposition, and valid cut generation. The effectiveness of the proposed algorithm is demonstrated via a real-life problem faced by a large 3PL provider. A computation study is carried out to investigate the proposed method's sensitivity to key factors such as the demand structure, delivery time windows, number of gateways and the consolidation cost breakpoints.