Periodic Review Inventory $3$ System Problems

Below are $10$ questions designed $to$ calculate the Order Quantity for a high$-$demand product managed

under a Periodic Review Inventory System. Each question provides demand data over $12$ weeks, a review

period, lead time, cycle service level $(with$ corresponding $Z-$value$),$ standard deviation $of$ weekly demand,

and current inventory position. The protection period $is$ the sum $of$ the review period and lead time.

Use the following formulas for calculations:

Average weekly demand: $=\frac{{\displaystyle \underset{i=1}{\overset{12}{}}}{D}_i}{12}$

Average daily demand: $d=\frac{}{7}$

Mean demand during protection period: ${}_{PP}=d$ Protection Period

Standard deviation during protection period: ${}_{PP}={}_{\text{w}\text{e}\text{e}\text{k}}\sqrt[\phantom{2}]{\frac{\text{P}\text{r}\text{o}\text{t}\text{e}\text{c}\text{t}\text{i}\text{o}\text{n}\text{P}\text{e}\text{r}\text{i}\text{o}\text{d}}{7}}$

Order$-Up-To$ Level: $T={}_{PP}+Z*{}_{PP}$

Order Quantity: $Q=T-$ Inventory Position

Provide only the final Order Quantity $(in$ units$)$ for each question. Question $1$

A warehouse uses a Periodic Review Inventory System with a review period $of14$ days and a lead time

$of7$ days. The cycle service level $is95\%(Z=1\mathrm{.}65).$ The inventory position $is500$ units. Weekly demand

over the last $12$ weeks $is$:

Standard deviation $of$ weekly demand $is25$ units. Calculate the Order Quantity.

Question $2$

A retail store reviews inventory every $12$ days with a lead time $of6$ days. The cycle service level $is99\%$

$(Z=2\mathrm{.}33).$ The inventory position $is400$ units. Weekly demand over the last $12$ weeks $is$:

Standard deviation $of$ weekly demand $is20$ units. Calculate the Order Quantity.

Question $3$

A distribution center uses a review period $of10$ days and a lead time $of5$ days. The cycle service level

$is97\%(Z=1\mathrm{.}88).$ The inventory position $is350$ units. Weekly demand over the last $12$ weeks $is$:

Standard deviation $of$ weekly demand $is30$ units. Calculate the Order Quantity. Question $4$

A store reviews inventory every $8$ days with a lead time $of4$ days. The cycle service level $is$

$1\mathrm{.}7598\%$

$(Z=2\mathrm{.}05).$ The inventory position $is600$ units. Weekly demand over the last $12$ weeks $is$:

Standard deviation $of$ weekly demand $is35$ units. Calculate the Order Quantity.

Question $6$

A retail chain reviews inventory every $9$ days with a lead time $of6$ days. The cycle service level $is94\%$

$(Z=1\mathrm{.}56).$ The inventory position $is450$ units. Weekly demand over the last $12$ weeks $is$:

Standard deviation $of$ weekly demand $is22$ units. Calculate the Order Quantity. Question $10$

A retail store reviews inventory every $14$ days with a lead time $of4$ days. The cycle service level $is96\mathrm{.}5\%$

$(Z=1\mathrm{.}81).$ The inventory position $is700$ units. Weekly demand over the last $12$ weeks $is$:

Standard deviation $of$ weekly demand $is40$ units. Calculate the Order Quantity. Question $7$

A distribution center uses a review period $of11$ days and a lead time $of5$ days. The cycle service level

$is99\mathrm{.}5\%(Z=2\mathrm{.}58).$ The inventory position $is300$ units. Weekly demand over the last $12$ weeks $is$:

Standard deviation $of$ weekly demand $is28$ units. Calculate the Order Quantity.

Question $8$

A store reviews $3$