Glossary/Safety stock
What is safety stock?
Safety stock is the inventory held above expected demand to absorb variability while a replenishment order is in transit. It exists because both demand and lead time are uncertain: if either could be known exactly, a seller would order to arrive precisely as the last unit sold. Its size is set by how variable those two quantities are and by the service level chosen — the probability of not stocking out during a replenishment cycle — and the right service level is an economic decision, driven by the contribution lost when demand is missed against the cost of holding stock that does not move.
01/Formula
Formula
Safety stock = z × √( LT × σ²demand + demand² × σ²LT ) z = service-level factor (90% → 1.28, 95% → 1.65, 99% → 2.33) LT = average lead time σ = standard deviation of daily demand / of lead time Economic service level = Cu / (Cu + Co) Cu = contribution lost per unit short, Co = cost of holding one unsold unit
Example
Daily demand averages 20 units with a standard deviation of 7. Lead time averages 14 days with a standard deviation of 3. At a 95% service level (z = 1.65): √(14 × 49 + 400 × 9) = √(686 + 3,600) = 65.5 Safety stock = 1.65 × 65.5 ≈ 108 units Note that lead-time variance contributes 3,600 of the 4,286 — five times more than demand variance. Stabilising the supplier beats forecasting better.
02/In detail
How do you choose the service level?
Economically, not by convention. The critical ratio sets it: divide the contribution lost per unit of unmet demand by that same figure plus the cost of holding a unit that ends up unsold. A high-contribution, non-perishable product with stable demand deserves a service level in the high nineties, because missing a sale is expensive and holding stock is not. A thin-margin seasonal item deserves far less, because unsold units at the end of the season are written down and the contribution forgone on a missed sale was small anyway. Applying one target — 95% is the usual default — across a whole catalogue overstocks the thin products and understocks the fat ones simultaneously.
Why does lead-time variance dominate?
Look at the two terms inside the square root. Demand variance is multiplied by the lead time; lead-time variance is multiplied by the square of demand. For any product selling more than a handful of units per day, the second term grows much faster, which means an unreliable supplier drives the buffer more than unpredictable customers do. The practical consequence is counter-intuitive and worth acting on: for most marketplace sellers, getting a supplier to deliver in a consistent fourteen days releases more working capital than any improvement in demand forecasting, and it is usually the cheaper project.
Why is weeks-of-cover not a substitute?
Because it ignores variability entirely. Two SKUs both selling 20 units a day, one steady and one swinging between 5 and 60, need very different buffers, and a three-weeks-of-cover rule gives them the same one — over-stocking the steady product and stocking out on the volatile one. Weeks of cover is a useful reporting summary and a poor planning rule. It also breaks down exactly when it matters most, during campaign periods, because the trailing average it is computed from does not know about the demand spike that is coming.
03/Why it matters
The trap, in one paragraph.
Safety stock is where the stockout-versus-overstock trade-off is actually made, and most shops make it implicitly through a habit rather than explicitly through a number. The cost of getting it wrong shows up in two places that are never compared to each other: lost contribution and wasted ad spend on one side, and dead capital and end-of-season write-downs on the other. Setting it deliberately is what lets a shop hold less inventory overall and stock out less often.
Common mistake
Setting safety stock as a percentage of average demand. The buffer should scale with the standard deviation of demand and lead time, not with their level. A high-volume, perfectly predictable SKU needs almost no buffer; a low-volume, erratic one may need weeks of it. A percentage rule gets both backwards.
04/In DataGlass
How Safety stock is used in DataGlass.
DataGlass forecasts demand per SKU with an explicit uncertainty band rather than a point estimate, so the safety stock it proposes reflects how predictable that product actually is. Service levels are derived from the SKU’s own contribution and holding cost rather than from a catalogue-wide default, and known campaign windows are included in the demand the buffer has to cover.
05/Sources
- [1] Safety stock
The standard safety-stock formulation combining demand and lead-time variability with a service-level factor.
- [2] Newsvendor model
The critical-ratio result that sets the economically optimal service level from understock and overstock costs.
Keep reading