Weekly demand for size large khaki pants at each store is normally distributed with a mean of $1000$ and a standard deviation of $120.$ Each pair of pants costs $\backslash (\backslash$$ $30\backslash ).$

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 $\backslash (\backslash$$ $100\backslash ).$

The Gap has a holding rate of $25$ percent. The Gap manages all inventories using a continuous review policy, and the supply lead time for both products is four weeks. The targeted CSL is $95$ percent.

Which of the two products should the Gap carry at the stores, and which should it carry at the central warehouse for the online channel? $($Assume demand from one week to the next to be independent.$)$

The following table helps you analyze the two options

Retail Operations $($Disaggregate option$)$

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|\}$

$\backslash$hline & Khaki Pants & Cashmere Sweaters $\backslash \backslash$

$\backslash$hline Mean demand during lead time: & & $\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

Standard deviation of demand during lead $\backslash \backslash$

time:

$\backslash$end$\{$tabular$\}$ & & $\backslash \backslash$

$\backslash$hline Safety stock per store & & $\backslash \backslash$

$\backslash$hline Total safety stock: & & $\backslash \backslash$

$\backslash$hline Total value of safety stock: & & $\backslash \backslash$

$\backslash$hline Total annual safety sock holding cost: & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Online Operations $($Aggregate option$)$

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|\}$

$\backslash$hline & Khaki Pants & Cashmere Sweaters $\backslash \backslash$

$\backslash$hline Aggregate mean demand: & & $\backslash \backslash$

$\backslash$hline Aggregate standard deviation: & & $\backslash \backslash$

$\backslash$hline Aggregate demand during lead time: & & $\backslash \backslash$

$\backslash$hline Aggregate standard deviation during lead $\backslash \backslash$

time: & & $\backslash \backslash$

$\backslash$hline Total aggregate safety stock & & $\backslash \backslash$

$\backslash$hline Total value of safety stock: & & $\backslash \backslash$

$\backslash$hline Total annual safety sock holding cost: & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$