What error measure to use for setting safety stocks?

There has always been a lot of confusion about what error to use in calculating the safety stock measures for inventory management. Although the classic formula for safety stock setting says it is the average error over lead time, practitioners have interpreted this to mean various things. The more common and the most mistaken notion is to use the standard deviation of actual or historical demand pattern as the proxy for error in setting safety stock policies.

The safety stock formula is the product of three components – forecast error, lead time and the multiple for the required service level. Using the standard deviation is similar to saying that the supply chain does not believe in the accuracy of the demand plan. In other words, the finished goods planner is implicitly saying that the average demand over the last few weeks or months is a better predictor than the demand forecast that was sent to him by the demand planning team.

With all the investments that are made in the demand planning software, this is not an optimal outcome for any supply chain. Our belief is this is done in error failing to understand the implications of using the standard deviation over the forecast error.

In a recent question and answer session, many professionals advocated using the MAPE as the forecast error for calculating safety stocks. Although mathematically a little tricky, this is laudable since they are using one measure of forecast error to impact the safety stocks. With the popular adoption of MAPE as a classic measure of forecast performance, we can be rest assured that the safety stock strategy is synchronized with the demand planning performance. However, we can do better.

MAPE is a classic measure of forecast performance, particularly cross-sectional performance across a bunch of products say at the division level or the company level. This can be used to set safety stocks as well but the statistical properties are not so easily understood when one is using the absolute error.

The more appropriate measure is to use the root mean squared error for the SKU computed over either several weeks or several months depending on the forecasting unit. The RMSE weights the larger errors higher than others, so this gives you the cushion against an outage. Statistically speaking, the RMSE is just the standard error of the mean (forecast). Through the application of the Central Limit Theorem, we know that this is distribution-agnostic. This is allows us to simply assume normal distribution and use the standard normal tables for computations.

However supply chain classes and APICS courses very rarely mention the RMSE. Either people simply assume RMSE is the same as standard deviation or just simply do not understand it. RMSE becomes as simple as the standard deviation if your demand forecast is the same as a simple average. But this is a very bland assumption. As we stated above, many supply chain planners make this mistake in effect negating the value of a demand plan.

So here is the summary:

1. Correct measure is RMSE calculated as the square root of the average squared deviation between the Forecast and Actual.
2. The second best measure is MAPE since this also uses the forecast to calculate the forecast error.
3. The least desirable alternative is to use the Standard deviation, which totally ignores the forecast.

Here is a numerical example that illustrates the benefit of using a true demand forecast error compared to using the standard deviation.

In the above example, note that the demand forecast error is 13% as measured relative the average actual demand over the last five months. In any case, using the standard deviation would imply carrying unusually more safety stocks than necessary. You will be using 26 units as the error instead of the 10 units required by the true forecast error from using the RMSE calculation. If you use the MAPE, then you would use 9 units as the forecast error. Not bad, considering how close the MAPE and RMSE are.

So here is a final question for you: If you use the standard deviation in setting safety stock, you may actually end up being right under one scenario. What would that scenario be?