Safety Stock (Statistical Buffer)

Safety stock is what you hold because demand during the lead time is a distribution, not a number. The statistical form is $\mathit{SS} = z\,\sigma_d\sqrt{L}$: the service level you want, times the day-to-day scatter in demand, times the square root of the lead time. At 95% service ($z = 1.65$), a scatter of 20 units a day and a nine-day lead time, that is $1.65 \ imes 20 \ imes 3 = 99$ units.

The square root is the part nobody expects and the part that matters most. Variability accumulates as the square root of time, not linearly, so quadrupling the lead time only doubles the buffer. Run that backwards and it becomes the strongest argument in lean purchasing: halving a lead time cuts the required buffer by about 29%, and a supplier who ships in four days instead of sixteen lets you hold half the stock at the same service level. That is worth paying for, and it almost never shows up in a price comparison.

The other lesson is in the $z$. Going from 95% to 99% service moves $z$ from 1.65 to 2.33, so the buffer rises 41% to remove four percentage points of stockout risk. Going to 99.9% moves it to 3.09. The cost of near-perfect availability is brutally non-linear, and deciding to be "always in stock" is a decision to double the warehouse. Use the daily standard deviation, not the monthly one, or the units will not match the lead time.