Cooperation and game-theoretic cost allocation in stochastic inventory models with continuous review

We study cooperation strategies for companies that continuously review their inventories and face Poisson demand. Our main goal is to analyze stable cost allocations of the joint costs. These are such that any group of companies has lower costs than the individual companies. If such allocations exist they provide an incentive for the companies to cooperate. We consider two natural cooperation strategies: (i) the companies jointly place an order for replenishment if their joint inventory position reaches a certain reorder level, and (ii) the companies reorder as soon as one of them reaches its reorder level. Numerical experiments for two companies show that the second strategy has the lowest joint costs. Under this strategy, the game-theoretical Shapley value and the distribution rule—a cost allocation in which the companies share the procurement cost and each pays its own holding cost—are shown to be stable cost allocations. These results also hold for situations with three companies.