Which formula gives safety stock as SS = Z * σ_DLT, where Z is the service factor and σ_DLT is the standard deviation of demand during lead time?

• A. Z + σ_DLT
• B. Z * σ_DLT
• C. σ_DLT / Z
• D. Z * Demand During Lead Time

Answer: (B)

Safety stock is the extra buffer you keep to guard against uncertainty in demand during lead time. When lead-time demand is treated as a random variable with standard deviation σ_DLT, choosing a service level corresponds to a Z-score that tells you how many standard deviations you want to cover. Multiplying that Z by the standard deviation gives the exact quantity of units needed as the buffer: SS = Z * σ_DLT. This makes the stock scale with how variable demand is and with how much protection you want against stockouts. If you added or divided by the standard deviation, or multiplied by the mean lead-time demand, you wouldn’t be correctly tying the buffer to variability and service level. For example, with σ_DLT = 5 units and a 95% service level (Z ≈ 1.65), SS ≈ 8.25 units.