Cooperative Inventory Control ∗

A two-echelon one-warehouse multi-retailer inventory system is considered. Everyday, each retailer faces a stochastic demand and must choose whether to replenish or not from the warehouse. Decisions are made locally with the objective of minimizing individual ordering, storage/shortage and fixed transportation costs. The last are shared among all retailers who choose to replenish, thus motivating a certain coordination of replenishment strategies. Critical to coordination is communication. Hence, retailers are modeled as dynamic agents of a communication network. We show that each i retailer’s optimal strategy is to order only in conjunction with at least other li − 1 retailers, where the threshold li is computed locally by the i-agent. In particular, we propose i) a decentralized Neuro-Dynamic Programming algorithm for the search of the sub-optimal thresholds; ii) a distributed consensus protocol for minimal information interchange between retailers thus to guarantee the best coordination of orders. We point out some analogies with the iterated dominance method to find noncooperative equilibria in the class of externality games.