Spare parts inventory pooling games

We study a situation where n independent companies separately stock spare parts of the same item for a technically advanced machine. They may reduce expected joint holding and downtime costs by pooling inventory. We analyze these situations by defining a cooperative cost game. We examine the conditions under which such a game has a nonempty core, i.e. a stable cost allocation exists. For situations allowing companies to have non-identical demand rates and base stock levels and for situations allowing companies to have non-identical downtime costs, we show that the core of the associated game is non-empty. However, when companies have non- identical downtime costs along with non-identical base stock levels or demand rates, the associated game may have an empty core.