Cost allocation in a full truckload shipment consolidation game

In this paper we used principles of cooperative game theory to analyse the cooperation (inventory pooling) between multiple retailers replenishing their inventory by full truckload shipments to satisfy a deterministic and constant rate demand of final customers while minimising the associated total transportation and inventory costs. For this model, we derive structural properties of the resulting cost function. We use these to prove not only that it is cost effective to consolidate the shipments between the retailers, but also that this shipment consolidation strategy can be supported by a stable cost allocation, i.e., the core of the associated cooperative game is non-empty. We further identify a stable cost allocation that is shown to give strong incentives for the retailers to cooperate. In the particular case of identical retailers, this allocation coincide with Shapley value and lies at the centre of gravity of the core. In the general case of non-identical retailers, Shapley value is not a core allocation and is compared to our allocation with regards of four criteria: stability, complexity, fairness and practical settings.