The following discussion expands upon the topics of reorder point and safety

$($buffer$)$ stock as presented in the text in Jacobs chapter $20.$

REORDER POINT:

On pages $572-83,$ the text refers to the fixed order quantity model.

$($This is also referred to as the reorder point $($ROP$)$ model or the continuous

review system. I will generally refer to reorder point or ROP.$)$ The primary

formula that we will be using $($page $581,20\mathrm{.}5)$ is:

R $$ dL $$ z$$ L

where R is the reorder point $($ROP$),$ dLis the average demand during lead time

$($from equation $20\mathrm{.}4,$ page $579),$ and z$\backslash$sigma L is the safety stock.

From equation $20\mathrm{.}4,$ average demand during lead time is R $=$ dL where d

is the average demand per some time period $($typically day, week, or month$),$

and is generally determined from the statistical forecast for the item; L is

the lead time expressed in the same units of time as the forecast. For

example, if a distributor's demand for cases of toothpaste is currently

forecast to be $150$ cases per month, and the mean lead$-$time from the

manufacturer is two weeks, then dL would be $150$ x $0\mathrm{.}5=75$ cases $($two weeks

being approximately equal to one$-$half of a month$).$

From the class discussion on exponential smoothing, you should remember

that a statistical forecast is a form of weighted moving average of past

demand. As a consequence, there is some degree of uncertainty regarding the

accuracy of the forecast number. There is$,$ therefore, a lingering question

in terms of how far we can safely base management decisions upon such a

number.

When utilizing a statistical forecast to direct our decisions regarding

when to order additional inventory, the concept of safety $($buffer$)$ stock

$($shown as $$SS$$ in equation $20\mathrm{.}9,$ page $582)$is employed to quantify the risk of

the forecast being inaccurate. To estimate the amount of safety stock, we

apply probability.

Because it costs money to hold safety stock, we must carefully weigh

the cost of carrying safety stock against the reduction in stock out risk

that it provides. Although progressively higher levels of safety stock will

yield progressively lower risks of stock out, it does so at a declining rate.

In other words, doubling the amount of safety stock will reduce the risk of

stock out by much less than half.

This concept also relates to the ICB $($Infor