Safety Stock Formula and Reorder Point: A Worked Example

Safety stock is inventory held above expected demand to cover uncertainty during replenishment. The reorder point is the inventory position that triggers an order: expected demand during lead time plus safety stock. One answers how much protection to keep; the other tells you when to replenish.

Safety stock versus reorder point

Compare the reorder point with inventory position, not only what is on the shelf. For a basic continuous-review policy, inventory position is usable on-hand stock plus open replenishment orders minus backorders. Keep allocations and reservations consistent with your system’s definition so you do not subtract the same demand twice.

The order quantity is a separate decision. Use economic order quantity for how much to buy under its cost and demand assumptions.

The safety stock formula for fixed lead time

When daily demand is independent, lead time is fixed, and demand over lead time is reasonably approximated by a normal distribution:

safety stock = z * daily demand standard deviation * sqrt(lead time in days)
reorder point = average daily demand * lead time in days + safety stock

The standard deviation measures variation in daily unit demand, not a percentage or the average sales value. Use demand and lead time on the same time basis. With weekly demand, use lead time in weeks and the standard deviation of weekly demand.

The factor z represents the chosen cycle service level: the modelled probability of completing a replenishment cycle without a stockout. It is not the share of all units supplied immediately, and it is not a percentage of profit. See service level versus fill rate for that distinction.

These are rounded one-sided factors from the NIST standard normal distribution table. They are not the two-sided confidence-interval factors used for estimating a mean.

Worked example: one spare-parts SKU

Assume a fictional shop sells an average of 40 filter kits a day. Daily demand has a standard deviation of 10 kits. Replenishment takes a fixed nine days, and the planner chooses a 95% cycle service target.

expected lead-time demand = 40 * 9 = 360 kits
lead-time demand standard deviation = 10 * sqrt(9) = 30 kits
safety stock = 1.645 * 30 = 49.35 kits
rounded safety stock = 50 kits
reorder point = 360 + 50 = 410 kits

Suppose the shop has 300 usable kits on hand, 150 already on order and 20 on backorder. Its inventory position is 430, so it has not crossed the 410-kit reorder point. With no open order, that same shelf quantity would give an inventory position of 280 and trigger replenishment. Check confirmed arrival dates as well: an overdue order cannot cover demand before it arrives.

Keeping the same assumptions, the 90% target gives 38.46 kits of safety stock, rounded up to 39. The 99% target gives 69.78, rounded up to 70. A higher target costs more stock; it does not remove every source of shortage.

A fixed-days buffer when data is limited

A planner can start with an explicit number of extra coverage days:

safety stock = average daily demand * chosen buffer days

At 40 kits a day, two buffer days mean 80 kits. With the same nine-day lead time, the reorder point becomes 440 kits. This is a transparent planning rule, but it does not establish a particular service level. Record why two days were chosen, then compare the rule with actual shortages and excess stock as more history becomes available.

What changes when supplier lead time varies?

The fixed-lead-time example does not price uncertainty in arrival dates. Where daily demand is independent across days and independent of lead time, an approximate variance calculation is:

lead-time demand variance = average lead time * daily demand variance
                          + average daily demand squared * lead-time variance
safety stock = z * sqrt(lead-time demand variance)

Using the same fictional demand but a lead-time standard deviation of two days gives a variance of 9 * 100 + 1600 * 4 = 7300. Its square root is about 85.44 kits, so the 95% buffer is about 140.55, rounded up to 141. The reorder point becomes 501 kits. This example shows why ignoring delivery variation can materially understate the buffer.

If high demand and late supply arrive together, that independence assumption fails. Measure demand over actual replenishment intervals or simulate the policy instead of adding a factor to the simple formula. MIT’s inventory lecture explains the role of variability over total lead time.

When the standard formula needs a different model

Intermittent demand, promotions, seasonal changes and correlated supply delays need more than an average and a normal z factor. Sales history also understates demand when stockouts prevented customers from buying. Distinguish missing demand from a genuine zero before calculating variability.

Our statistical audit of safety-stock models covers non-normal demand. When combining warehouses, the square-root law of inventory pooling adds another assumption: how closely demand at the locations moves together.

For a periodic-review policy, the exposure includes the review interval as well as replenishment lead time. Do not reuse this continuous-review reorder point unchanged for a weekly ordering calendar. Check supplier calendars, minimum order quantities, pack sizes and shelf life before accepting the resulting policy.

Put the calculation into a repeatable stock review

Keep the demand period, usable stock definition, lead-time sample, service target and rounding rule beside each SKU’s calculation. Revisit the policy when the supplier, sales pattern or review frequency changes. Compare actual replenishment-cycle stockouts with the target rather than assuming the formula achieved it.

For help separating demand, supplier and stock-record problems across a catalogue, use InventoryPath’s inventory advisory service.