Problem
FSU bookstore is selling a new souvenir. Weekly demand is normally distributed with mean 35 and a variance of 100. Stanford bookstore manufactures the new souvenir at a cost of $80 per item; the processing cost for each order is $300 and the lead time is 4 weeks. The annual inventory holding cost rate is 70%. Under the current inventory policy, Stanford bookstore purchases 120 carpets whenever the inventory falls below 150. Assume that there are 52 weeks this year.
1. What is the fill rate under the current inventory policy?
2. What order quantity and reorder point would minimize the total annual setup, holding and shortage costs subject to having a fill rate at least equal to 98%? What is the expected total of annual setup, annual holding and annual (imputed) shortage costs under the inventory policy?
3. Would the solution in part (2) change if Stanford bookstore has a minimum Type I service level constraint of 80%?