Books-On-Line, an on-line bookseller, charges its customers a shipping fee of $4 for the first book and $1 for each additional book. The average customer order contains 4 books. Shipping cost incurred by Books-On-Line per customer order is $2. Weekly demand of books is independent and normally distributed with a mean of 50,000 and a standard deviation of 25,000. Each book costs on average $10 and is sold on average for $12. The yearly inventory holding cost incurred by Books-On-Line is $2 per book per year. BooksOn-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 Books-On-Line’s gross profit per year (only consider book cost, warehouse cost, inventory holding cost, and shipping cost), assuming there are 50 weeks in a year?