Try

SS = z × √( P·σd² + d̄²·σL² ) — King (APICS, 2011)

If you forecast, use the RMSE of forecast error instead of raw demand σ.

0 = continuous review. Otherwise, how often you check and reorder.

Optional: fill rate & naive baseline

Enables the fill-rate estimate (share of demand served from stock).

Both maxima enable the max-min heuristic row — for comparison only.

Safety stock
Reorder point
Safety factor zσ of protection

Where your risk lives (share of variance)

Demand variability Lead-time variability
Safety stock vs service level — each extra “nine” costs more

Formula comparison

ApproachWhen it appliesSafety stock
Max-min heuristicNaive baseline — no service-level control, outlier-sensitive
Demand variability onlyLead time reliable (σL ≈ 0)
Lead-time variability onlyDemand steady (σd ≈ 0)
Linear sumDemand and lead time move together (conservative bound)

Assumptions: per-period demand i.i.d. and ~normal; lead time ~normal and independent of demand; demand and lead time in the same time units. Formulas targetcycle service level (frequency of stockout cycles), not fill rate. Sources: King,APICS Magazine 2011; Silver & Peterson 1985 via Chopra, Reinhardt & Dada,Decision Sciences 2004.

Decision-support model — not a substitute for validated engineering analysis of your specific operation.