The formula
SS = Z × demand standard deviation × √lead time
What it means
Safety stock does not cover average demand: the reorder point covers that. It covers how far demand strays from its average while the order is in transit. So three things go in: how much demand varies, how many days the lead time lasts, and how much risk of running out you are willing to take, which is the Z factor. The square root of the lead time appears because the variability of several independent days grows with the square root of the number of days, not with the number.
How to work it out by hand
- Work out the standard deviation of your daily demand
- Pick a service level and look up its Z factor: 1.65 for 95 %
- Multiply the factor by the standard deviation
- Multiply by the square root of the lead time in days
What is worth knowing
Raising the service level from 95 to 99 per cent sounds small and costs forty per cent more buffer; going to 99.9 nearly doubles it against 95. That curve is what to look at before promising total availability, because the last percentage point is always the most expensive. This formula assumes the variability is in demand and not in the lead time; if the supplier also misses dates, you need the version that includes lead-time deviation.