A Cold 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. Demand for CFPs averages 400 per day with a standard deviation of 200. Weekly demand (five days) averages 2,000 units with a standard deviation of 555. Since ACold orders at least one truck from General Foods each day (General Foods owns Caruso's Pizza), ACold can essentially order any quantity of CFP it wants each day. In fact, ACold's computer system is designed to implement a base stock policy for each product. Iven notes that any order for CFPs arrives four days after the order. Further, it costs ACold $0.01 per day to keep a CFP in inventory, while a 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 2,800 is chosen. What is the average amount of inventory on order?
c. Suppose the base stock level 2,800 is chosen. What is the annual holding cost? (Assume 260 days per year.)
d. What base stock level minimizes inventory while maintaining a 97 percent in-stock probability?