ACold Inc. is a frozen-food distributor with 10 warehouses across the country. Ivan 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. Because the warehouse carries hundreds of different products, Ivan decided to study one. He picked Caruso’s Frozen Pizza (CFP). Demand for CFPs averages 400 per day with a standard deviation of 152. Because ACold orders at least one truck from its supplier each day, ACold can essentially order any quantity of CFP it wants each day. In fact, ACold’s computer system is designed to implement an order-up-to policy for each product. Ivan notes that any order for CFPs arrives four days after the order.
a. Suppose it uses an order-up-to level of 2410. What is its expected on-hand inventory?
b. Suppose it uses an order-up-to level of 2500. What is its expected on-order inventory?
c. Suppose it uses an order-up-to level of 2000. What is its in-stock probability?
d. Suppose it wants a .90 in-stock probability. What should its order-up-to level be?