Books-On-Line, an online bookseller, charges its customers a shipping charge of $4 for the first book and $1 for each additional book. The average customer order contains four books. Books-On-Line currently has one warehouse in Seattle and ships all orders from there. For shipping purposes, Books-On-Line divides the United States into three zones - Western, Central, and Eastern. Shipping cost incurred by Books-On-Line per customer order (average four books) is $2 within the same zone, $3 between adjacent zones, and $4 between nonadjacent zones.
Weekly demand from each zone 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 the holding cost incurred by Books-On-Line is 25 percent. Books-On-Line replenishes inventory every week and aims for 99.7 percent CSL. Assume a replenishment lead time of one week.
A warehouse is designed to carry 50 percent more than the replenishment order plus safety stock. The fixed cost of a warehouse is $200,000 + x, where x is its capacity in books. The weekly operating cost of a warehouse is $.01y, where y is the number of books shipped. Books-On-Line is planning its network strategy. Which zones should have warehouses?