When I decided to write this series of articles, I said: "Let me write two before I make the first available". I needed to protect myself from deadlines due to a variable work load and travelling away. This was a form of protection or safety stock.

Many companies do the same to protect their customers. They invest vast sums in safety stock of finished goods. I must admit that I do tend to get excited when talking to people on the subject of safety stock, as companies tend to waste that investment. Many companies have agreed on a policy of so many weeks cover, which may sound fine but it does in fact miss the basic point.

Let's ask ourselves: "What do we need safety stock for?".

If we have the situation where the overall forecast is good, which means that over a number of periods the total forecast quantity equals the actual demand, then all we have to worry about is the differences per individual period. This is referred to as demand variation. In other words, we have good periods when the demand exceeds the forecast and bad periods when the demand is less than the forecast, on average they cancel each other out. It is the good periods that give us a problem as we need more stock than was forecast. The question that arises is how much do we really need? This brings up the question of what level of service do we want to provide to our customers.

Are we prepared to have one stock out per month or only one stock out every two years? The answer will alter the amount of safety stock we need, therefore we need to be practical. The higher the service level required, the more safety stock we need for that item.

The third issue is, if demand exceeds the forecast, how long will it take to correct the situation. We have to allow for the replenishment lead time. The longer the replenishments lead time the longer it will take to fix if we run out of stock, therefore the more protection we need.

I must admit that for many years the safety stock principle was a total mystery to me so let's take a quick look at how to handle it from a practical point of view.

Variability of Demand

Although our forecast might be fairly good over a few periods, by individual period we will have peaks and troughs. We need to determine how high these peaks are and find a way of calculating how much safety stock we need to protect against them. One way is using the standard deviation. The statisticians tell us that this curve can be defined by two numbers. The average (mean), and the standard deviation which measures the spread or flatness of the curve. One standard deviation is denoted by the Greek symbol sigma.

If we now look at figure 1, the curve for normal distribution, we'll see that one standard deviation above the mean will cover 84% of demand. A second deviation will add a further 13,7% which means that 97,7% demands will be met. If you add a third deviation, you only improve by 2,2% which gives 99,9% of demands. From this you will gather that the first amount of safety stock is much more effective than the third.

A second and easier to use way of getting to grips with this problem is commonly known as the MAD formula which stands for the Mean Absolute Deviation. The MAD measure of variation is the sum of each period's difference, ignoring the sign, between the forecast and the actual demand divided by the number of periods. This is not that difficult to calculate from historical records. The statisticians have established the relationship between these two methods. The value of MAD x 1,25 is approximately equal to the standard deviation. We now have two ways of establishing the standard deviation. You may ask what good is that to us? We'll have a look in a moment.

Figure 1

 

There are various ways of measuring service level, but the most commonly accepted definition is the percentage of times a demand is satisfied when needed. A service level of 95% accepts the for every 100 demands for an item, 5 will not be satisfied. Statisticians have created a table which allows us to convert a service level into a number called the safety factor which you can then use in the safety stock calculation.

Replenishment Lead Time

If we can produce our finished product inside a week, it is not too difficult to get out of trouble if demand exceeds forecast, but if it takes us ten weeks to replenish our stock, then we need more safety stock. It is established that the relationship for safety stock needed to protect against lead time is the square root of that lead time. To ensure that the lead time unit and the forecast period units are the same, the formula shows the lead time divided by the forecast period.

Safety Stock Calculation

We have now looked at the three causes of stock outs so now let's look at the calculation we use taking these three factors into account.

The formula is SS = OR 

When = standard deviation

SF = safety factor

L = lead time

FP = forecast period

MAD = mean absolute deviation

Now let's work a little example. For product X the company decides on a 98% service level and this item has a MAD of 20 and a replenishment lead time of 4 weeks, the forecast being in week periods. What safety stock is required?

Using the table of safety factors for a service level of 98% the safety factor is 2,05.

Then SS = 

This calculation should be performed for each item we keep in our finished goods store. Notice we didn't use the actual demand or forecast in that calculation. Remember safety stock is provided to protect against the three causes of problems, variability of demand, service level and replenishment lead time, not the basic demand. This means that as the sales forecast fluctuates, safety stock remains static. This principle is important.

Although many companies keep so many week's stock, as you can see, this is not a very logical approach as it treats all items the same even though they have different characteristics. The result is you have more protection than you will ever need for some items and insufficient on others. Not the best investment to make. Statistical safety stock is the most effect way of protecting against uncertainty of demand.

Next month we will examine the problem of unreliability of supply.

June 1999