Question $7$

$3$ pts

Kate's Mini$-$Mart uses a periodic review, order$-$up$-$to inventory model to manage inventory. For one of their more popular products, Tofu Jerky, Kate $($the owner$)$ insists on maintaining a $80\%$ cycle service level. Kate buys Tofu Jerky for $$1\mathrm{.}00$ per pack and it sells for $$3\mathrm{.}50.$ It costs Kate $$0\mathrm{.}10$ per pack per week to hold inventory. The supplier has a $2$ week lead time $($with no randomness$).$ Average demand is expected to be $30$ per week. Standard deviation of forecast errors is expected to be $6.($Please use the Gamma distribution to model demand during the exposure period.$)$ Kate orders every week. Suppose a slick consultant convinces Kate that she should use a fill rate service level target rather than cycle service level to set inventory control parameters. Which statement best describes the change in inventory levels that would happen if Kate decides to stop using the $80\%$ CSL target and instead use a $98\%$ fill rate target.

Safety stock would increase and cycle stock would decrease

Only safety stock would increase

Safety stock would decrease and cycle stock would decrease

Only safety stock would decrease

None of the above