Daily demand for a certain product is normally distributed with a mean of 100 and a standard deviation of 50. The source of supply is reliable and maintains a constant lead time of 4 days. The cost of placing an order is $200, and the unit cost of the product is $40. The annual interest rate is 25% in this industry. Assume 360 days per year.

(a) Use the (Q, R) policy, and find the optimal order quantity and reorder point to satisfy a lead time service level of 90%. What is the average inventory level? What is the annual total inventory-related cost (annual inventory holding cost + annual fixed ordering cost)?

(b) Suppose the manager wants to make it simple and sets the safety stock level equal to the average demand during the lead time. What is the annual total inventory-related cost? What is the service level ? How many times of stock-outs do you expect per year (hint: the stock-out probability per order (1- ) multiply the number of orders per year)?