Shipment consolidation: Who pays for it and how much?

This paper examines the subject of cost allocation in a multiple product inventory system, allowing for consolidation of shipments. If we order multiple items using an economic order quantity policy, and consolidate shipments, part of the ordering cost is shared, and part is specific to each item; we want to find the consolidation choice with optimal total cost and divide the cost fairly among the individual items. Such a fair division is central to a costing system in which no group of items subsidizes the others; there are no free riders! We use a cooperative inventory game to determine when this can be done. This game is usually not concave, so we want to know what consolidation combinations determine when this cost can be fairly divided, using the core of the game. We prove that consolidation of all the items is cheaper exactly if there are fair cost allocations (core of the game is not empty), which happens when the portion of the ordering cost common to all items is not too small. We further show how sensitive the nonempty core result is to adjustments in the cost parameters and show how to determine a threshold value for the shared ordering cost, which assures the existence of a fair cost allocation.