The Correct Safety Stock Level is not Simple. Part 3.

Perhaps you have come to this blog because you searched for “simple safety stock formula.” Or you’re just looking for a better, easier safety-stock tool. ”Simple” suggests that ease of use (usually in Excel) is more important than precision, so long as the result is close enough. Albert Einstein advised, “Make everything as simple as possible, but not simpler.” So can a safety-stock calculation be both simple and also close enough?

At what point is a safety-stock calculation simple enough, but not too simple? In two previous blogs, we acknowledged that most common safety stock calculations attempt to address these obvious factors:

• Target service level
• Lead time
• Demand variation
• Lead-time variation

In those blogs, we also discussed how the z factor may cause your safety-stock formula to drive excessive inventory levels. The z factor is simple, but it is not reliably close enough. Likewise, we discussed how safety-stock formulas ignore, or incorrectly address, replenishment interval. Again, a simple safety-stock formula is not close enough.

Now, we’ll consider how the normal-distribution calculations (involving mean and standard deviation) often used in simple safety-stock calculations may not be close enough.

Demand distributions are rarely normal. They are typically right-skewed. Additionally, many demand streams are intermittent, with a lot of zeroes in the demand distribution that increase the right-skewness. This does not keep you from determining a mean and a standard deviation using Excel AVERAGE and STDEV functions. However, it does mean that if you use a safety-stock formula that employs AVERAGE and STDEV, those two parameters do not represent what a right-skewed distribution really looks like.

But will the simple, Excel-friendly AVERAGE and STDEV get us close enough? NO.

The chart below shows a right-skewed demand distribution for a high-volume, non-intermittent item. Its AVERAGE = 100 and its (Excel) STDEV = 70.7. The solid black line is the actual distribution, and the dashed red line is the theoretical normal distribution with AVERAGE 100 and STDEV 70.7. Is this close enough?

Take a closer look at the right tail of the distribution, below. This tail contains the high-demand days that can cause stockouts. The normal distribution (dashed red line) shows virtually zero probability of demand being greater than about 380. But the solid black line shows actual demand activity greater than 380, and even beyond 600 per day. If this is a mission-critical item, then a normal-distribution-based simple safety stock formula may not be close enough.

Granted, Central Limit Theorem (CLT) may come into play – that is, a demand distribution during lead time may eventually behave normally, if the lead time is long enough. But is your lead time long enough to do this? And how would you know?

Can we adjust a simple safety-stock formula for non-normal, right-skewed distributions? Not while keeping it simple. And what right-skewed distribution should we use? Goodness of fit is not an Excel strength, and its right-skewed-distribution functions are limited. Can a simple safety-stock calculation assess whether CLT will allow us to use a normal-distribution-based analysis? Not a chance.

Are you looking for a correct way to set safety stock, so that you achieve your service-level targets without unnecessary inventory?

Nothing could be simpler than sending us your data, and we will send you your correct, comprehensive and optimal safety-stock levels. Contact us for more info on how simple we can help make it for you!