Exercise 12-14: The Gap
Inputs Khaki Pants Cashmere Sweaters
Expected demand, D 800 50
Lead time, L 4 4
SD of demand per unit time, σD100 50
Target cycle service level, CSL 0.95 0.95
Costs per unit 30 100
Holding costs 0.25 0.25
Number of retail stores 900 900
Store Operations (Disaggregate)
Distribution of Demand during Lead Time per Store
Output
Safety Inventory per store = 329 164
Total Safety Inventory = 296,074 148,037
Total Value of Safety Inventory = 8,882,210$ 14,803,683$
Total Annual Safety Inventory Holding Cost = 2,220,552$ 3,700,921$
Holding Cost per Unit Sold = 3.08$ 82.24$
(as a percentage of product costs) 10.28% 82.24%
Online Channel (Aggregate)
Distribution of Demand during Lead Time at Central Warehouse
Mean demand during lead time 2,880,000 180,000
Total Value of Safety Inventory = 296,074$ 493,456$
Total Annual Safety Inventory Holding Cost = 74,018$ 123,364$
Holding Cost per Unit Sold = 0.10$ 2.74$
(as a percentage of product costs) 0.34% 2.74%
Online Channel vs. Store Operation
Difference in Total Value of Safety Inventory = (8,586,136)$ (14,310,227)$
Difference in Total Annual Safety Inventory Holding Cost =
(2,146,534)$ (3,577,557)$
Difference in Holding Cost per Unit Sold = (2.98)$ (79.50)$
The Gap has started selling through its online channel along with its retail stores. Management has to