# Safety stock

Inventory protection against uncertainty: service definitions, protection periods, a bounded normal-demand example and replenishment-policy limits.

Reviewed: 2026-11-02

Tags: production, planning, inventory, safety-stock

The example assumes independent daily demand averaging **40 units** with **6-unit** standard deviation, fixed **9-working-day** lead time and a normal approximation at **95% cycle service** (**z = 1.645**). Continuous review gives **29.61 units** of buffer and a **389.61** reorder point, rounded upward to **390**. Reviewing every **7 working days** extends protection to **16 days** and gives **39.48 units** of buffer and a **679.48** order-up-to benchmark, rounded to **680 units**. The review order depends on inventory position.

NC State describes balancing shortage exposure against the carrying cost of inventory beyond expected demand. [NC State Supply Chain Resource Cooperative, January 28, 2011](https://scm.ncsu.edu/scm-articles/article/safety-stock-analysis-inventory-management-models-a-tutorial)

State the item, location, eligible stock, review policy and service objective.

## Specify what service means

Two common service measures answer different questions:

| Measure | Question |
| --- | --- |
| Cycle service level | What fraction of replenishment cycles experience no stockout? |
| Unit fill rate | What fraction of demanded units is supplied from the defined stock without shortage? |

Peter L. King's APICS article distinguishes stockout frequency from stockout volume. A cycle-based target therefore cannot be reported automatically as a unit fill-rate target. The required buffer depends on the selected measure and model. [King, “Crack the Code,” APICS magazine, July/August 2011, pp. 33–36](https://web.mit.edu/2.810/www/files/readings/King_SafetyStock.pdf)

Document any delivery-time allowance and whether unmet demand is backordered, lost, substituted or expedited. An inventory service metric also differs from an entire customer's order arriving complete and on time; several items and later production steps can affect that outcome.

## Define the protection period and policy

Under continuous review, a reorder-point policy responds when its defined inventory position reaches a threshold. In a simple model, the reorder point is expected demand during replenishment plus safety stock. A periodic-review order-up-to policy must also protect demand until the next review opportunity. MIT's inventory notes distinguish continuous and periodic review and use lead time plus review period for the latter. [MIT CTL, SC1x Key Concepts, v6.2 Fall 2016, inventory-policy sections](https://studio.edx.org/asset-v1%3AMITx%2BCTL.SC3x%2B2T2016%2Btype%40asset%2Bblock%40SC1x_KeyConcepts_v6.pdf)

Measure replenishment until usable material is available at the location being protected. Include the applicable ordering, production, inspection, transportation and receiving delay. Identify working-day conventions and closure periods. A quoted supplier runtime alone may not describe this full interval.

MIT's inventory-policy notation uses on-hand plus on-order minus backorders; its earlier EOQ notation also subtracts committed orders. State the convention being used rather than assuming all displayed inventory-position fields match. Resolve reservation treatment without subtracting the same commitment twice, and check quarantine and overdue receipts separately. [MIT CTL, inventory-position notation, printed pp. 44 and 55](https://studio.edx.org/asset-v1%3AMITx%2BCTL.SC3x%2B2T2016%2Btype%40asset%2Bblock%40SC1x_KeyConcepts_v6.pdf)

## A bounded normal-demand calculation

For normally distributed demand over a known protection period, a cycle-service calculation uses:

`safety stock = z × standard deviation of demand over the protection period`

Here z is the selected standard-normal quantile. If daily demand is independent with a constant daily variance and lead time is a fixed L days, its lead-time standard deviation is `daily standard deviation × sqrt(L)`. King's article explains matching the variability's time basis to the full protection period. These assumptions must be established rather than inferred from having an average and a standard deviation. [King, demand variability and time-basis conversion](https://web.mit.edu/2.810/www/files/readings/King_SafetyStock.pdf)

For independent daily demand and fixed lead time, standard deviation scales with the square root of the number of days. Recalculate the demand distribution when correlation, changing variance or uncertain lead time invalidates that rule.

## Original example: continuous versus periodic review

Assume an invented item with independent daily demands of mean **40 units** and standard deviation **6 units**, fixed lead time **9 working days**, and a normally distributed protection-period demand approximation. The model has no minimum order, capacity, shelf-life or timing-undershoot constraints. Select **95% cycle service**, using the approximate quantile **z = 1.645**.

| Continuous-review quantity | Calculation | Result |
| --- | --- | --- |
| Mean lead-time demand | 40 × 9 | 360 units |
| Lead-time standard deviation | 6 × sqrt(9) | 18 units |
| Safety-stock benchmark | 1.645 × 18 | 29.61 units |
| Reorder-point benchmark | 360 + 29.61 | 389.61 units |

With an explicitly assumed upward whole-unit rounding rule, a **390-unit reorder point** corresponds to **30 units above expected lead-time demand**. This is a threshold on the model's inventory position, not an instruction to buy 390 units or to hold exactly 30 physical units at every moment. Replenishment quantity is a separate policy decision.

Now change only the policy to review every **7 working days**. The protection period becomes **7 + 9 = 16 days**. Mean protection-period demand is **640 units**, its standard deviation is **24 units**, and the same quantile gives **39.48 units** of safety stock. The continuous order-up-to benchmark is therefore **679.48**, rounded upward to **680 units** under the same assumed rule.

In this periodic policy, the quantity proposed at a review depends on the gap between the order-up-to level and the relevant inventory position. The 680-unit level is not a fixed order quantity. These calculations illustrate the selected models; rounding and approximation mean they are not proof of a precisely achieved 95% operating result. They establish no fill-rate value or company service target.

## Check whether the distribution fits the problem

The University of Texas inventory-model documentation treats lead-time demand as a distribution and offers distinct normal, discrete and Poisson options. The normal model is one choice, not a universal description of spare parts or intermittent orders. [University of Texas, Stochastic Inventory Models](https://utw11041.utweb.utexas.edu/ORMM/omie/computation/unit/invent_add/stochastic.html)

Retain the data window, demand definition and treatment of stockout-censored sales, promotions, seasonality and exceptional events. Recorded sales during a shortage may understate requested demand. When expected demand varies over time, separate the forecast from the uncertainty around it rather than treating a predictable seasonal peak as random noise.

For intermittent, skewed or highly dependent demand, assess an appropriate distribution, empirical protection-period demand or simulation. Keep assumptions about lead-time dependence, receipt quantities and recovery actions explicit. Backtest the full policy with actual replenishment timing; a fitted variance alone does not demonstrate service.

## Operate the buffer and improve the inputs

Track usable stock, open replenishments, shortages, expedites and service using consistent boundaries. Identify whether a miss resulted from demand uncertainty, a late receipt, inaccurate records, rejected material or insufficient production capacity. Increasing a buffer does not correct a persistent deficit in average supply.

Review the target and inputs after demand, supplier performance, inspection time or replenishment frequency changes. Compare service and inventory together, and keep business approval of a service/cost tradeoff separate from calculation of its consequences. A useful handoff records item/location, policy, period, mean/variance basis, service definition, model, rounding, resulting threshold and review owner.

## Source versions

Reviewed **2026-11-02**. NC State dates its tutorial **January 28, 2011**; King's authored article is from **APICS magazine, July/August 2011**; MIT's notes carry **v6.2 Fall 2016**. No separately verified issue date was established for the Texas web documentation. Historical teaching sources explain the stated models; they do not establish present company policy. The numerical example and operating recommendations are original, bounded guidance.

## Related reference

[Production planning guides](index.md)