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Safety stock against demand uncertainty is the service factor multiplied by the daily demand standard deviation and the square root of lead time. The square root matters: doubling lead time increases the required safety stock by only about 41%, not 100%.
Safety stock
SS = z x sigma_daily x sqrt(Lead time in days)
Reorder point
ROP = Average daily demand x Lead time + Safety stock
1.28 for 90%, 1.65 for 95%, 2.05 for 98% and 2.33 for 99% cycle service level.
Because daily demand deviations are independent, so variances add over the lead time and the standard deviation grows with the square root of the days.