Optimization of a Periodic Review Joint Replenishment Policy for a Stochastic Inventory System

A stochastic inventory system with multiple products controlled by a periodic review joint replenishment policy P(s, S-i)is considered. This system places a joint replenishment order to bring the inventory position of each item i to its order-up-to level Si when the aggregate reorder point of all items drops below s at each review moment. By imposing service levels on the system, we propose an algorithm for optimizing the policy to minimize the total cost of the system. The performance of this algorithm is evaluated by numerical experiments on randomly generated instances.