The Gap is trying to decide which products to carry at its 900 retail stores or

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?

Explanation / Answer

Give service level for both products = 95 % (probability of 0.95)

Corresponding , Z value for probability = 0.95 will be = NORMSINV( 0.95) = 1.6448

Calculation for Pants :

Annual unit holding cost for pants = 25% of $30 = $7.5

Standard deviation of weekly demand at each store = 100

Standard deviation of demand during lead time of 4 weeks = 100 x Square root ( 4) = 100 x 2 = 200

When products of 900 stores are moved to central warehouse, standard deviation of demand during lead time at central warehouse

= Standard deviation of demand during lead time at each store x Square root ( number of stores )

= 200 x Square root ( 900)

= 200 x 30

= 6000

Safety stock at each retail store = Z value x Standard deviation of demand during lead time = 1.6448 x 200 = 328.96

Hence cumulative safety stock requirement at 900 stores = 900 x 328.96 = 296064

Safety stock requirement at central warehouse = Zvalue x Standard deviation of demand during lead time= 1.6448 x 6000 = 9868.8

Therefore, reduction in cumulative safety stock requirement = 296064 – 9868.8 = 286195.20

Hence, reduction in holding cost = reduction in safety stock x Annual unit holding cost = 286195.20 x 7.5 = $2146464

Annual demand of Khaki pant at each store = 800 / week x 52 weeks = 41600

Cumulative annual demand of Khaki pants at 900 stores = 41600 x 900 = 37440000

Hence reduction in holding cost per unit sold = $2146464/37440000 = $0.0573

REDUCTION IN HOLDING COST PER UNIT SOLD WHICH GAP CAN EXPECT = $0.0573

Calculation for Sweaters :

Annual unit holding cost for pants = 25% of $100 = $25

Standard deviation of weekly demand at each store = 50

Standard deviation of demand during lead time of 4 weeks = 50 x Square root ( 4) = 50 x 2 = 100

When products of 900 stores are moved to central warehouse, standard deviation of demand during lead time at central warehouse

= Standard deviation of demand during lead time at each store x Square root ( number of stores )

= 100 x Square root ( 900)

= 100 x 30

= 3000

Safety stock at each retail store = Z value x Standard deviation of demand during lead time = 1.6448 x 100 = 164.48

Hence cumulative safety stock requirement at 900 stores = 900 x 164.48 = 148032

Safety stock requirement at central warehouse = Zvalue x Standard deviation of demand during lead time= 1.6448 x 3000 = 4934.4

Therefore, reduction in cumulative safety stock requirement = 148032 – 4934.4 = 143097.6

Hence, reduction in holding cost = reduction in safety stock x Annual unit holding cost = 143097.6 x 25 = $3577440

Annual demand of Khaki pant at each store = 50 / week x 52 weeks = 2600

Cumulative annual demand of Khaki pants at 900 stores = 2600 x 900 = 2340000

Hence reduction in holding cost per unit sold = $3577440/2340000 = $1.528

REDUCTION IN HOLDING COST PER UNIT SOLD WHICH GAP CAN EXPECT = $1.528

Since reduction in Holding cost per unit by moving to central warehouse as well as reduction in cumulative holding cost is higher for Sweater, we must move SWEATERS to Central Warehouse

REDUCTION IN HOLDING COST PER UNIT SOLD WHICH GAP CAN EXPECT = $0.0573

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