Shippers' Collaboration in Dynamic Lot Sizing Problem with Shipment Consolidation

We consider a collaborative logistics problem where a group of shippers in a logistics network, each facing a time-varying deterministic demand, collaboratively make the production schedules together in order to reduce transportation cost by shipment consolidation; a common third-party logistics provider (3PL) is hired by them to carry the shipments, which offers incremental discounts to large-load shipments. First, we solve the centralized problem by studying the decomposed subproblems and characterize the optimal policy. Then, we show that the associated cooperative game has a nonempty core. Finally, we point out that the popular proportional rule allocation scheme is generally not in the core, except in some special cases.