Question

The Gap is trying to decide which products to carry at its 900 retail stores or at its central warehouse to only be sold online. Weekly demand for large Khaki pants at each store is normally distributed with a mean of 800 and a standard deviation of 100. Each pair of pants cost $30. Weekly demand for purple cashmere sweaters at each store is normally distributed with a mean of 50 and a standard deviation of 50. Each sweater costs $100. The Gap has a holding cost of 25%. The Gap uses continuous review policy and the supply lead time for both products is 4 weeks. The Gap also expects a 95% service level.

How much reduction in holding cost per unit sold can The Gap expect from moving each product from its stores to its central warehouse?

Which of the two products would you move from the stores to online?

Answer 1

Reorder point = demand during lead time + safety stock
Reorder point, R = d*L+z*?d*?L
	khaki pants	purple cashmeres
Inventory at retail stores option:
# retail stores	900	900
Weekly demand, d	800	50
std dev, ?d	100	50
unit cost, p	$                      30	$                          100
Holding cost, Cc (25%)	$                   7.50	$                      25.00
Lead time, L (weeks)	4	4
service level	95%	95%
z	1.64	1.64
safety stock	329	164
R	3529	364
total Safety stock at 900 stores	296074	148037
cost of holding inventory	$ 2,220,552.40	$        3,700,920.66
Inventory at Central Warehouse option:
demand variance at each store	40000	10000
total demand variance	36000000	9000000
Demand std dev, ?d	6000	3000
Safety stock	9869	4935
Inventory holding cost	$        74,018.41	$            123,364.02
Savings	$ 2,146,533.98	$        3,577,556.64
hence, the company should move both its products from the stores to online

formulae used;