Daily demand is normally distributed with mean $22$ units per day and standard deviation $=6.$ Ordering cost is S $=$ $$21\mathrm{.}00$ per order, carrying cost is H $=$ $$2\mathrm{.}50$ per unit per year. The item is used $365$ days per year.$$ Inventory replenishment lead time $($from ordering to receipt of inventory$)$ is $4$ days.

Determine the appropriate $($Q$,$R$)$ ordering policy for this item.$($Find the value of Q$,$ and find the value of R$.)$ The order point should have a $99\%$ target service level.

Also compute:

Average inventory level $($cycle stock $+$ safety stock$)$

Average number of orders per year

Average number of stock$-$outs per year

Average time $($years$)$ between stock$-$outs.

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