Safety stock formulas
Safety stock (SS) is the buffer for when usage jumps or a delivery runs late during replenishment. There are three common ways to size it, and the calculator does all three:
Demand varies only: SS = Z × σd × √L
Demand and lead time vary: SS = Z × √(L × σd² + d̄² × σL²)
Max minus average: SS = (max usage × max lead time) − (d̄ × L)
The reorder point works the same with any of them:
Reorder point = d̄ × L + SS
| Term | Meaning |
|---|---|
| d̄ | average daily demand |
| σd | standard deviation of daily demand: how far a day usually strays from the average |
| L | average lead time in days: from order to material ready to use |
| σL | standard deviation of the lead time, in days |
| Z | service level factor: 90% → 1.28; 95% → 1.645; 97.5% → 1.96; 99% → 2.33 |
If you do not know the standard deviation, paste your usage history (daily or weekly) and the calculator works out the average, the deviation and the maximum. Weekly history is turned into daily figures by dividing the average by the working days per week and the deviation by the square root of that number.
Worked example
The values already in the calculator are for a purchased part:
- Average usage: 120 units a day, standard deviation 25 units
- Average lead time: 9 days, standard deviation 2 days
- Service level: 95%, so Z = 1.645
- Order quantity: 1,800 units
With the first method, demand variability only:
- Deviation over the lead time = 25 × √9 = 25 × 3 = 75 units
- Safety stock = 1.645 × 75 = 123.4, rounded up: 124 units, about 1 day of usage
- Expected usage during the lead time = 120 × 9 = 1,080 units
- Reorder point = 1,080 + 123.4 = 1,204 units
- Average inventory = 123.4 + 1,800 ÷ 2 = 1,024 units
With the same inputs, the other two methods give:
- Demand and lead time varying: √(9 × 25² + 120² × 2²) = √63,225 = 251.4. SS = 1.645 × 251.4 = 414 units, reorder point 1,494. Two days of delivery variability weigh far more than the swings in usage.
- Max minus average, with max usage of 170 a day and a longest lead time of 12 days: 170 × 12 − 120 × 9 = 2,040 − 1,080 = 960 units. More than double the statistical answer, because it assumes the worst usage day and the slowest delivery always coincide.
Service level and fill rate
They are two different ways to measure “not running out”:
- Cycle service level is the chance of no stockout during one replenishment. At 95%, out of 100 orders, 95 arrive before stock hits zero. This is what sets Z.
- Fill rate is the share of units demanded that came straight off the shelf. When a stockout happens it is usually small and brief, so fill rate sits well above the service level. In the example, with orders of 1,800 units, the calculator estimates a fill rate of 99.91%.
That is why larger orders raise the fill rate with the same safety stock: fewer replenishments a year means fewer chances to run out.
How to read the result
- High safety stock points at a cause to fix: a supplier that runs late (σL) or usage that swings (σd). Cutting variability cuts stock without hurting service.
- The reorder point is the trigger to buy. Safety stock is only its bottom layer, the part that should be left when the delivery arrives.
- Average inventory is what sits on the shelf on average: safety stock plus half an order. To choose the order size, use the EOQ calculator.
- On the line, a card-driven pull loop is sized differently: see the kanban calculator. And by Little’s law, every unit sitting in stock turns into flow time.
Common mistakes
- Mixing time units. Daily usage with a lead time in weeks, or a weekly deviation in the daily formula. Everything must use the same period.
- Adding up standard deviations. The spread over 9 days is not 9 × σd, it is √9 × σd. Adding deviations badly overstates the stock.
- Calendar days for lead time, working days for usage. If usage is per working day, count the lead time in working days too.
- Calculating once and never again. Usage and delivery times change. Recalculate from recent history at least every quarter.
- One service level for every item. Separate the critical parts that stop the line from the cheap ones that are easy to replace.
Sources
- Silver, Edward A.; Pyke, David F.; Thomas, Douglas J. Inventory and Production Management in Supply Chains. 4th ed. CRC Press, 2017 (successor to Silver, Pyke and Peterson, 1998).
- Chopra, Sunil; Meindl, Peter. Supply Chain Management: Strategy, Planning, and Operation. Pearson. Chapter on safety inventory.