Coordinating replenishments in a supply chain with quality control considerations

We study the impact of coordinated replenishment, a popular supply chain initiative, on a quality control system. We use the (Q; S) policy to manage a two-item inventory control system. If the items are jointly replenished, the number ordered for each item varies from lot to lot. As the number varies, the sampling plan will also be changed. Companies have to determine sampling plans to minimize quality cost when the order is mixed with several items and the number of each item varies from order to order. Management's primary concern is to determine the optimal sampling sizes and acceptance numbers for all items in an order.