Using a periodic review model, given an average daily demand of $3$ units, a standard deviation of daily demand of $2$ days, $8$ days between inventory reviews, $4$ days lead time, $49$ units of inventory on hand, and a $$z$-$value$$ of $1\mathrm{.}96,$ what is the vulnerable period?

Answer:Question $3$

$12$

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T is the time between order or the frequency with which orders are placed.

For example, if orders are placed every Sunday $($i$.$e$.,$ weekly$),$ then T$=7.$

L is the lead time which is the time that elapses between an order being placed and the shipment arriving.

For example, if the lead time is two days, then L$=2.$

The vulnerable period is T $+$ L$.$

For example, if T$=7$ and L$=2,$ then the vulnerable period is T$+$L$=9$

The correct answer is: $12$

Question $4$

Correct

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What is the average demand over the vulnerable period?

Answer:Question $4$

$27$

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The average demand over the vulnerable period $($T $+$ L$)$ can be calculated using the following formula

where is the average demand for a single period.

The correct answer is: $36$

Question $5$

Incorrect

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What is the standard deviation over the vulnerable period in days $($round answer to two decimal places$)?$

Answer:Question $5$

$9$

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The vulnerable period is T$+$L $($see previous question$)$

The formula for calculating the standard deviation over the vulnerable period is

When calculating the standard deviation over the vulnerable period, it is important to keep in mind that you can NOT add standard deviations, but you can add variances. So if the standard deviation of demand for a single time period is given, you need to square it $($i$.$e$.,$ multiple if be itself$)$ and use the above formula.

The correct answer is: $6\mathrm{.}93$

Question $6$

Tries remaining: $3$

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What is the order quantity $($round to closest integer$)?$

Answer:Question $6$