ACold Inc.is a frozen food distributor with 10 warehouses across the country. Iven Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while still maintaining quick delivery to ACold’s customers. Since the warehouse carries hundreds of different products, Iven decided to study one. He picked Caruso’s Frozen Pizza (CFP). The demand for CFP averages 400 per day with standard deviation of 200. ACold orders daily and the replenishments arrive four days after the order. Further, it costs ACold $0.01 per day to keep one CFP in inventory while one unit of back order is estimated to cost ACold $0.45.

a. What base stock level should Iven choose for CFPs if his goal is to minimize holding and back order costs?

b. Suppose the base stock level 2800 is chosen. What fraction of customer demands is met immediately from stock?

c. Suppose the base stock level 2800 is chosen. What is the average amount of inventory on order?

d. Suppose the base stock level 2800 is chosen. What is the annual holding cost? (Assume 365 days per year).

e. What base stock level should Iven choose if he wants to maintain a 97% in-stock probability?