From the order up to model, we know that Inventory level at the end of a period

equals to S minus demand over l $+1$ periods. Explanation via an example with S $=8,$ l $=$

$2,$ and $3$ units Inventory level at the start of period $1.$

Peiod$1$ Peiod$2$ Peiod$3$ Peiod$4$

Inventory Level at the start of the period $($after

receiving the incoming order$)3$

Demand

$3433$

Inventory Level at the end of the period$($after

supplying the demand$)$

Inventory Position $($before ordering$)$

Ordering

Inventory Position $($after ordering$)$

$8888$

$17.$ Suppose inventory is managed using the order$-$up$-$to model. Your inventory position

is $20$ and demand in the last period was $10.$ Your optimal order quantity is $10$ units.

Your target fill rate is