Consider an item whose inventory is controlled by a periodic review, base-stock policy. Suppose the review period is 1 week (7 days), the replenishment lead-time is 4 days, and the daily demand is normally distributed with mean 80 and standard deviation 40. The cost of placing the order is $200, and the unit cost of the product is $50. The annual interest rate is 20% in this industry.

1. What is the basestock level (order-up-to level) S to assure that the coverage probability (Type I service level) is 0.95? What is the average inventory level? What is the annual total inventory-related cost? How many stock-outs might you expect per year? (Assume 52 weeks per year).
2. Suppose the manager simply sets the safety stock level equal to one week of average demand. What is the service level? What is the average inventory level? What is the annual total inventory-related cost? How many stock-outs might you expect per year?
3. * Suppose all customers permit a grace period or service time of 2 days. That is, a customer demand on day t can be satisfied on day t + 2. How would you modify the base stock in light of this relaxation of service expectations? By how much does the average inventory change?
4. * Ignore the assumptions in (b) and (c). Recently, the retailer noticed the supplier became not so reliable. The lead time now is equally likely to be 3, 4, 5 days. Please find the base stock S to satisfy a service level of 95%. What is the average inventory level