Why using Z-factors and service level percentages for stocks is total B***S*** (2024)

What prompted me to write this article are some thoughts that I had since long time (this sensation that something just doesn’t feel right), the advent of DDMRP with its (seemingly) over-simplistic way to size the red zone of the buffer (that’s the zone of the buffer which is there to absorb variability), several discussions I had with colleagues over the past years, and finally the reading of the Black Swan by Nassim Nicholas Taleb, which I strongly recommend to anyone who is in the business of making predictions (If you are a demand manager, that’s you).

It is common (best?) practice for professionals who manage inventories to use a formula to calculate the amount of safety stock necessary to provide a pre-determined “target” service level. This method calculate the standard deviation of demand and then extrapolate the amount of inventory necessary to cover the area under the bell curve that correspond to the desired service level using a so-called Z-factor.

For instance, I am selling a widget and I know that the demand is on average 100 units and that the standard deviation is 50 units.If I want to achieve a service level of 98% I just need to look-up what is the Z-factor corresponding to 98%, which is Z = 2.05. Therefore I need a safety stock equivalent to my average demand + 2.05 standard deviations, which is 100 + 2.05*50 = 202.5. Therefore, a safety stock of 203 units should guarantee a service level of 98%. There is a major problem with this and I will illustrate this problem through a simple example.

Imagine I tell you that my girlfriend is taller than 1.80 meter (5 foot 11 for the US reader). Now I ask you to guess with good confidence (at least 50%) how tall she actually is, within a range of 5 centimetres (2 inches).

The answer is quite intuitive and common sensical: If you answer between 1.80 and 1.85 meters (5 foot 11 and 6 foot 1) you would almost certainly be right. This is because the distribution of human size tends to fit a predictable gaussian distribution.

Let’s now go back to my widget with average demand is 100 units and a standard deviation of 50 units (per day). Imagine I tell you that the quantity of widgets ordered yesterday was more than 203 units. Can you estimate with good confidence how many widgets were ordered? Would it be reasonable to say “between 204 and 217 units and I am quite confident – at least 50% confident – of that”. It would be reasonable if my customers actually care about the order distribution. but they don’t. In fact, it is more likely that the total quantity was 300 or 400 units than anything between 204 and 217.

Order patterns do not follow normal distributions.According to the normal distribution above, the chances of selling 400 units or more (6 standard deviations) is one in a billion!

And yet it seems that almost all of us accept as best practice to size our safety stocks as if demand follows gaussian distributions and outliers don’t exist. The reality is that there is likely to be plenty of outliers that don’t fit the distribution - we just ignore this fact and continue as if the calculated safety stock actually correlates to a specific service level.

The difference between 204 and 217 units is the difference between 98% and 99% service level in the above example. So this leads us to believe that by increasing our safety stock from 204 units to 217 units we would capture half of the 2% of remaining demand in the tail of the distribution. This is obviously nonsense.

That’s why the approach used by DDMRP for sizing the red zone of the buffers, by being more rule-of-thumb is actually much more practical, less academic and makes a lot of more sense. Approximately right is way better than exactly wrong.

Let’s first clearly state that the Red Zone of a DDMRP buffer is NOT a safety stock. It is functionally different and its purpose is to absorb variability. The main difference is that MRP nets to zero even when there is a safety stock (it just sets the zero at a different level) thus enhancing the bullwhip effect, while DDMRP does not net to zero and thus allows the buffer to do its job: dampen variability and stop the bullwhip from propagating.

Another difference is that the safety zone of a DDMRP buffer is sized according to the expected variability of both demand and supply, whichever is predominant for any specific buffer.

DDMRP follows a very simple approach for sizing the red zone (safety zone):

• categorise your buffered products in high variable, mid variable and low variable.
• assign a factor (called variability factor) to each of those categories, according to what seems good common sense.
• track, monitor and analyse the buffers over time to provide a feedback loop and iteratively adjust the factors.
• assume that you will have outliers, but if you set-up the system correctly the Net Flow Equation will capture them: that’s what the “qualified future spikes” element of the equation is there for.
• If the visibility horizon for the qualified future spikes is shorter than the decoupled lead time (the time it takes to replenish the buffer) then you know there are risks, but you are not fooling yourself with the use of a meaningless service level percentage. You can still apply mitigating actions for those cases (e.g. increasing the red zone further, negotiating longer lead time with customer for big orders, etc.).

Merry Christmas ;-)