Aggregation Safety Inventory Analysis

The Gap company has started selling through its online channel along with its retail stores. Management has to decide

which products to carry at the retail stores and which products to carry at a central warehouse to be sold only via the

online channel. Gap currently has $(900+$ Your course ID$)$ retail stores in the United States. Weekly demand for size large

khaki pants at each store is normally distributed, with a mean of $800$ and a standard deviation of $100.$ Each pair of

pants costs $$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.$ Gap has an annual holding cost of $25$ percent. Gap manages

all inventorries using a continuous review policy, and the supply lead time for both products is $4$ weeks. The targeted

CSL is $95\%.$ Assume demand across stores and from one week to the next to be independent.

How much reduction in holding cost per unit sold can Gap expect on moving each of the two products from the stores

to the online channle? Which of the two products should Gap carry at the stores, and which should it carry at the

central warehouse for the online channle? Why?

Standard deviation of demand during lead time ${}_L=\sqrt[\phantom{2}]{L}$

$z=$NORMSINV$(CSL)$

safety inventory $SS=z**{}_L$

Aggregated demand $D^C=kD,$

${}_D^C=\sqrt[\phantom{2}]{k{}_D^2}=\sqrt[\phantom{2}]{k}{}_D$

${}_L^C=\sqrt[\phantom{2}]{L}{}_D^C=\sqrt[\phantom{2}]{Lk}{}_D$

Aggregation safety inventory $SS=z**{}_L^C$

Safety invntory reduction $=$ All location total inventory $-$

Central location safety inventory

Total holding cost saving $=H^{**}$ safety inventory reduction

Holding cost saving per unit $=$ Total holding cost saving $/$

Annual demand DThe Gap company has started selling through its online channel along with its retail stores. Management has to decide which products to carry at the retail stores and which products to carry at a central warehouse to be sold only via the online channel. Gap currently has $(900+$Your course ID$)$ retail stores in the United States. Weekly demand for size large khaki pants at each store is normally distributed, with a mean of $800$ and a standard deviation of $100.$ Each pair of pants costs $$30.$ Weekly demand for purple cashmere sweaters at each store is normally distributed, with a mean of $50$ and a standard deviation of $50.$ Each sweater costs $$100.$ Gap has an annual holding cost of $25$ percent. Gap manages all inventorries using a continuous review policy, and the supply lead time for both products is $4$ weeks. The targeted CSL is $95\%.$ Assume demand across stores and from one week to the next to be independent.

How much reduction in holding cost per unit sold can Gap expect on moving each of the two products from the stores to the online channle? Which of the two products should Gap carry at the stores, and which should it carry at the central warehouse for the online channle? Why?