Books-On-Line, an online bookseller, charges its customers a shipping charge of $4 fro the first book and $1 for each additional book, the average customer order contains 4 books. Books-On-Line currently has one warehouse in Seattle and ships all orders from there. For shipping purposes, Books-On-Line divides the US into three zones - western, central and eastern. Shipping cost incurred by Books-On-line per customer order (average 4 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 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 a 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 +safety stock. The fixed cost of warehouse is $200,000 + x, where is x is its capacity in books. The weekly operating cost of a warehouse is $0.01 y, where y is the number of books shipped. Books-On-Line is planning its network strategy. Which zones should have warehouses? Detail all costs.

Add as many sheets as necessary for each alternative. And provide calculation detail.

					Western	Central	Eastern
Wkly Demand mean (per zone)					50000	50000	50000
Wkly Demand Std Dev (per zone)					25000	25000	25000
Average order size			4
Cost	per book		$10
Shipping Revenue	per order		$7
Order Cycle, T	weeks		1			Total Cost of this Solution:
Order Lead Time, L	weeks		1			$7,588,566
T+L	weeks		2

Annual Holding cost			25%
Desired CSL			99.7%
Warehouse fixed cost		$200000 + x (x = capacity in books)
x = capacity =		1.5*(replenishment order+ safety stock)
Weekly operating cost		.01y (y = number of books shipped)
Current State -One Warehouse (Western)
Wkly Demand			150,000
Wkly Std Dev			43,301
T+L Std Dev			61,237
Safety Stock z factor			3
Inventory	Safety Stock		168,267
	Cycle Inv		75,000
	In Transit Inv *		150,000
Average Inventory On Hand			393,267
Wkly Orders Processed			37,500
Warehouse Capacity			477,400

Annual Costs
Inv. Hold			$983,166
Whse Fixed			$677,400
Whse Opr			$78,000
Shipping			$5,850,000
TOTAL			$7,588,566
* This is likely an overestimate since the transportation time is not given. Part of lead time can be order processing time. This assumption does not affect the solution since the cost is not region-dependent.