You play a Retailer in the Beer Game. You receive orders directly from the Customer and place orders with the Wholesaler. When you place an order, it takes 2 weeks for the order to be received by the Wholesaler and 2 weeks for the shipment from the Wholesaler to arrive to your warehouse. One period is one week in the game. You are charged $0.5 for each unit of inventory per week, and $1.00 for each unit of backlog per week.

It has been estimated that the Customer weekly demand follows a normal distribution with a mean 50,000 cases and a standard deviation 10,000 cases. What should be the order-up-to level to minimize holding and backorder costs? What safety stock should you keep? Assume that the Wholesaler keeps enough inventory to cover your demand and delivers the beer after the lead time with no uncertainty.