Calculate optimal safety stock levels based on demand variability, lead time variability, and desired service level.
Safety stock is the extra inventory held above expected demand during lead time, and its job is absorbing variability, not covering average demand. This calculator takes average demand, demand variability, supplier lead time variability, and a target service level, then returns the buffer size in your units plus the reorder point it implies. What surprises most users is that a 95% service level does not mean 5% of annual sales are lost. It means a 95% chance of surviving each replenishment cycle without a stockout - a different, stricter promise, and the number the tool produces reflects that.
A concrete input and expected output from the current implementation.
Input
Average demand: 100 units/day. Demand standard deviation: 20 units/day. Lead time: 5 days. Lead time standard deviation: 2 days. Service level: 95%.
Expected output
Safety stock: 337 units. Reorder point: 837 units (500 units of expected demand during lead time, plus the 337-unit buffer).
With a 95% service level, the z-score is 1.645. Safety stock = 1.645 * sqrt(20^2 * 5 + 100^2 * 2^2) = 1.645 * sqrt(42,000) = 337.1 units, rounded to 337. The reorder point adds average demand during lead time (100 * 5 = 500), giving 837 units.
With both variabilities supplied, the standard formula is SS = Z * sqrt(sd^2 * L + d^2 * sL^2): sd is the standard deviation of per-period demand, L the average lead time in the same periods, sL the lead time standard deviation. The first term inside the root captures demand variability alone; the second adds the effect of lead time variability. When lead time is fixed, the second term drops out and the formula becomes Z * sd * sqrt(L).
The service level is the probability of completing one replenishment cycle without a stockout, and the calculator converts it into a z-score from the standard normal distribution: 90% gives 1.28, 95% gives 1.65, 99% gives 2.33. The buffer scales linearly with the z-score, so moving from 95% to 99% service raises the required safety stock by about 41% (2.33 / 1.65) even when demand and lead time are unchanged.
To the reorder point. The order quantity decides how much you buy each time and therefore how often you order; the reorder point - expected demand during lead time plus safety stock - decides when you place that order. Adding the buffer to the order quantity changes cycle frequency, not stockout protection.
The calculator gives the quantity; the choice is a cost decision it cannot make. Going from 95% to 99% service raises the buffer roughly 41% at unchanged variability, so weigh the carrying cost of those extra units against the profit lost in one stockout, multiplied by how often stockouts occur. High-margin or cheap-to-hold items usually justify 99%; bulky, low-margin items often do not.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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