Safety Stock Review

The textbook formula assumes roughly normal demand. Real portfolios contain SKUs where that assumption fails badly - the skill's job is to compute the number AND say where it can be trusted.

Required data

Per-SKU demand history (sku, period, qty, 12+ periods), lead time (with variability if available), and the service target. Clarify early which service the target means: cycle service (probability of no stockout per cycle) or fill rate (share of units served) - contracts usually mean fill rate, formulas usually compute cycle service.

Workflow

1. Classify first. Compute CV and zero-period share per SKU. For CV >= 1.0 or intermittent demand, state up front that the normal-formula result will be optimistic.
2. Compute the formula result: SS = z * sigma_d * sqrt(LT), ROP = mu_d * LT + SS (demand-period units consistent with LT). If lead time varies, use the extended form with the sigma_LT term - ignoring lead-time variance is the most common silent understatement.
3. Stress-test empirically. Set stock at mu + SS and replay the actual history: report both achieved cycle service (share of periods fully covered) and achieved fill rate (units served / units demanded). Zero-demand periods pass cycle service for free - fill rate is the honest one on intermittent items.
4. Show the cost of nines. SS at 90/95/98/99% targets for the SKUs in question - service targets are pricing decisions, and the curve makes that visible.
5. Recommend per class, not globally: formula fine for X-class; formula + empirical check for Y; for Z-class recommend empirical/quantile-based sizing or a policy change (MTO, lead-time reduction) instead of a bigger z.
6. Validate. Reconcile the stress-test denominator (total units demanded) against the raw data sum before presenting.

Pitfalls to check explicitly

• Cycle service quoted where the contract says fill rate - a penalty clause waiting to be found.
• Normal formula on lumpy demand understates risk precisely on the items that hurt most.
• sigma computed over a period mixing trend or seasonality inflates SS everywhere; deseasonalize or use forecast-error sigma when a forecast exists.
• One global service target across the whole portfolio - targets should follow item criticality and margin.

Output format

1. Per-SKU (or per-class) table: mu, sigma, CV, class, SS, ROP, achieved cycle service, achieved fill rate
2. Trust statement per class ("formula reliable here / optimistic here, use X instead")
3. Cost-of-nines table for the discussed target range
4. Assumption footnote: service definition, lead-time treatment, sigma source

Worked stress test with charts: https://github.com/gulmezeren2-byte/abc-xyz-inventory

---

Source: industrial-engineering-ai-skills by Eren Gulmez (MIT). The full method pack - entry skill, role agents, data-hygiene rules and artifact templates - lives there.