Start with something familiar
A bus rider leaves early because travel time varies. The extra minutes are a buffer, but a buffer based on a quiet Sunday may fail on a weekday. The rider must match the data to the trip and decide how often being late is tolerable. Inventory buffers have the same discipline. They protect against a specified source of variation over a specified period, and their size depends on what service goal the planner is actually trying to meet.
Words to know: Safety stock, Cycle service level, Lead time.
Name the random quantity
Suppose Northstar’s daily demand has mean twenty bottles and standard deviation four, with independent days and a stable distribution. Lead time is exactly three days. Lead-time mean demand is sixty. Variances add across independent days, so lead-time variance is three times sixteen, or forty-eight bottles squared. Its standard deviation is the square root of forty-eight, about 6.93 bottles.
Standard deviation is not demand itself, and it does not add linearly under independence. Use a time unit consistently. A daily standard deviation cannot be combined directly with a lead time measured as three weeks. If demand follows a predictable weekday pattern, model the expected pattern first and examine remaining error; otherwise the buffer may compensate for a forecasting problem.
Translate a service choice
For a normal approximation and a 95 percent cycle-service target, use the supplied factor 1.645. Safety stock is 1.645 times 6.928, or 11.40 bottles; round upward to twelve whole bottles. The reorder point is sixty plus twelve, or seventy-two. Rounding creates a slightly different implied probability, so report the target and rounded policy separately.
This calculation assumes stable independent daily variation, fixed lead time, and a reasonable normal approximation for lead-time demand. It is not suitable without thought for sparse demand, large bursts, correlated days, or variable supply delays. Expected service is a model output; actual service still needs measurement. A normal quantile does not guarantee that every cycle will succeed.
Check sensitivity before adopting
If daily standard deviation doubles to eight, the buffer before rounding doubles to 22.79, rounded to twenty-three. If fixed lead time grows from three to twelve days, its square root doubles and the buffer also becomes twenty-three. These are different operational causes with a similar calculation, and they may call for very different improvement actions.
Keep policy choice separate from estimation uncertainty. A manager may choose a higher service target, while a planner may discover the variance estimate is unreliable. Record both. The lab asks you to test multiple items and horizons so you can see how units, rounding, and exposure interact rather than learning a formula as an unexplained button.
- Define units and event
- Reconcile eligible inputs
- Apply the stated rule
- Check feasibility
- Explain the decision
Northstar worked decision
All quantities and costs below are fictional and self-contained. Apply the stated timing and unit conventions.
| Input | Value |
|---|---|
| Mean bottles/day | 20 |
| Daily SD bottles | 4 |
| Fixed lead days | 3 |
| Normal factor | 1.645 |
- 1. Lead-time mean = 20 × 3 = 60.
- 2. Lead-time SD = 4 × sqrt(3) = 6.928.
- 3. Buffer = ceil(1.645 × 6.928) = 12; reorder point = 72.
Base buffer 12 and reorder point 72.
Assumptions
- Use only the quantities and timing stated; no hidden receipts, losses, or substitutions.
- Fractional mathematical results are rounded only where whole-unit or pack rules are explicitly stated.
Where this can fail: This is a transparent teaching model. Confirm calendars, data definitions, and operating constraints before using an analogous policy in practice.
Build, test and explain a plan
Build a policy table for Northstar Blue (mean twenty/day, SD four), Green (mean twelve/day, SD three), and Silver (mean eight/day, SD two). All daily errors are independent, lead time three days, and factor 1.645. Calculate fixed lead times one through twelve days for each item and ceil each buffer separately. The eight-hour allocation is a self-paced estimate, not experimentally validated; it includes model building, scenario testing, a memo, and teach-back.
Use paper or a spreadsheet. The estimates below include the study and worked example already on this page.
| Estimated hours | Activity |
|---|---|
| 0.5 | Study the reading and make a one-page definition sheet. Mark every unit, date convention, and inclusion rule. Explain the difference between the policy input and the outcome being measured. |
| 0.5 | Recalculate the worked example independently, without copying the displayed result. Show intermediate arithmetic and reconcile the answer to the physical story. Note one assumption that could change the decision. |
| 3 | Build a reusable multi-period spreadsheet from the supplied lab data. Build a policy table for Northstar Blue (mean twenty/day, SD four), Green (mean twelve/day, SD three), and Silver (mean eight/day, SD two). All daily errors are independent, lead time three days, and factor 1.645. Calculate fixed lead times one through twelve days for each item and ceil each buffer separately. Keep inputs separate from formulas, add a clear output table, and include a check column that flags any quantity or timing inconsistency. Walk through the first and last rows manually. |
| 2 | Create separate named scenario tabs. Recalculate all rows for factor 2.326, then double each SD under the original factor. Plot buffers against lead time and annotate why a curved relation appears. Preserve the baseline and record both changed inputs and changed outputs. Explain any outcome that stays the same, since a binding constraint or a measurement rule can make an intervention ineffective. |
| 1 | Write a 400-word decision memo naming your recommended action, evidence, assumptions, responsible role, and next check. Compare at least two alternatives using your table. State one limitation that could reverse the recommendation and what additional evidence would resolve it. |
| 1 | Teach the result aloud in five minutes using an original diagram. Then review every formula, answer the module questions relevant to this lesson, and write a short correction log. Use the remaining time to reproduce the key calculation from a blank sheet. |
Your deliverables
- An auditable multi-period workbook with baseline and named stress cases.
- A decision memo with numerical evidence and explicit limitations.
- An original explanatory diagram and a correction log.
Check your practice work
- Base buffer 12 and reorder point 72.
- With SD eight, buffer 23 and reorder point 83.
- With lead twelve, buffer 23 and reorder point 263.
- At three-day lead and factor 1.645, Green buffer is 9 and reorder point 45; Silver buffer 6 and reorder point 30.
- At three-day lead and factor 2.326, Blue buffer 17, Green 13, Silver 9; corresponding reorder points 77,49,33.
Keep these three ideas
- Compute a fixed-lead-time normal safety-stock approximation and expose its assumptions.
- Keep the unit, timing, and denominator visible.
- Treat model outputs as conditional on their stated assumptions.
Common mistakes
- Changing an input definition without changing all affected formulas.
- Presenting an expected or proposed quantity as confirmed usable supply.
Optional video study
Compute a fixed-lead-time normal safety-stock approximation and expose its assumptions.
- Name the random quantity
- Translate a service choice
- Check sensitivity before adopting
First half: foundation and first worked check.
Open the module media & quizPut this idea to use
Carry your assumptions into a practical tool, then compare your result with a short guide.
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