Weekly demand of books at Books-On-Line is independent and normally distributed with a mean of 50,000 and a standard deviation of 25,000. The yearly inventory holding cost is $2 per book per year. Books- On-Line replenishes inventory every 3 weeks and aims for a 97.7% cycle service level [F-1 (0.977,0,1) =2]. The replenishment lead time is 1 week. Books-On-Line’s warehouse is designed to carry 33 percent more than the replenishment order (Q) plus safety stock (ss), i.e, 1.33Q + ss. The fixed cost of a warehouse per year is $20,000 + x, where x is its capacity in books. The weekly operating cost of the warehouse is $0.01y, where y is the number of books shipped.
a. What is the average replenishment order quantity?
b. What is the safety stock level?
c. What is the yearly cost of the warehouse?
d. What is the yearly inventory holding cost?