ITLS6002 Chap.2 Safety Stock and Periodic Review
Safety Stock and Periodic Review
Safety stock converts uncertainty and a service objective into a protection quantity. The calculation depends on what varies, how the lead-time demand distribution is represented, and whether the system is reviewed continuously or periodically. A continuous-review policy protects the lead-time exposure, whereas a periodic-review order-up-to policy protects the review interval plus lead time.
This chapter distinguishes cycle-service probability from fill rate, shows how independent variances combine, and emphasises that a z-value is not a service policy by itself. A defensible recommendation identifies the exposure period, units and operational assumptions before applying a formula.
Independent period demands allow standard deviation to scale with the square root of exposure time, but correlated or seasonal demand needs a better variance estimate. The periodic order quantity is the gap between the order-up-to target and the inventory position observed at review, not the target itself.
When demand and lead time are both uncertain, their contributions belong in the compound variance rather than being added as raw standard deviations. Service gains also have carrying-cost consequences, so the final comparison should report both protection and cost.
What this chapter covers
- 01
Demand uncertainty and lead-time exposure
- 02
Cycle service level and z-values
- 03
Continuous-review safety stock
- 04
Periodic-review protection intervals
- 05
Order-up-to levels
- 06
Service-cost trade-offs
Worked example · free
Comparing continuous and periodic review protection
- 2For continuous review, lead-time deviation is 24 x sqrt(2) = 33.94 units and safety stock is 1.645 x 33.94 = 55.83 units.
- 2The continuous-review reorder point is 120 x 2 + 55.83 = 295.83 units.
- 2For periodic review, the protection interval is 3 + 2 = 5 weeks and its deviation is 24 x sqrt(5) = 53.67 units.
- 2The order-up-to level is 120 x 5 + 1.645 x 53.67 = 688.28 units.
Key terms
- Safety Stock
- Inventory held above expected exposure demand to protect against uncertainty.
- Cycle Service Level
- The probability that a replenishment cycle finishes without a stockout.
- Protection Interval
- The total period of uncertainty that an inventory policy must cover.
- Order-Up-To Level
- The target inventory position after a periodic-review replenishment decision.
Safety Stock and Periodic Review FAQ
Why does periodic review usually require more protection than continuous review?
A periodic system may wait until the next review before responding, so it must cover both the review interval and the replenishment lead time. A continuous system can trigger as soon as the inventory position crosses its threshold.
Can fill rate and cycle service level use the same z-value directly?
No. Cycle service level is a no-stockout probability, while fill rate measures the fraction of demand supplied immediately. A fill-rate target generally requires an expected-shortage calculation rather than a direct normal quantile lookup.
When may standard deviations be combined with a square root of time?
That rule assumes independent, identically distributed period demands. If demand is autocorrelated, seasonal or measured in inconsistent time units, estimate exposure variance from an appropriate model instead of automatically scaling one-period deviation.
What quantity is ordered in a periodic-review system?
At each review, order the difference between the order-up-to target and the current inventory position, subject to rounding or capacity. The target covers expected demand and uncertainty across the review-plus-lead-time protection interval; it is not automatically the order quantity.
How should uncertain lead time enter a safety-stock calculation?
Use the compound demand-during-lead-time variance supplied by the course method, with demand and lead time expressed on compatible time bases. Do not add their standard deviations directly. Explain which source of uncertainty dominates the resulting protection stock.
Why should a service recommendation include carrying cost?
A higher service target raises the normal deviate and therefore safety stock. Multiplying the incremental stock by annual holding cost makes the trade-off visible. The recommendation should compare the service improvement with this cost rather than treating more protection as free.
Exam move
Underline the review policy and uncertainty source before doing arithmetic. Draw a timeline containing review interval, lead time and protection interval, then write the mean and deviation for that exposure. Label whether the requested service metric is cycle service or fill rate. Finish by interpreting the extra inventory as a service choice and by testing whether the assumed independent demand pattern is plausible.
Practise the same item under continuous and periodic review so the different protection windows become automatic. Recompute a case after changing only the review interval, then explain why both expected demand and variability move. Keep a compact audit order: units, exposure, mean, compound deviation, z-value, safety stock, trigger or target, and annual cost.
Where fill rate is requested, write the expected-shortage step explicitly rather than borrowing a cycle-service percentile. Close with the policy action a planner would take at the next observation.
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