What is safety stock?

Safety stock is the stock you keep on top of the demand you expect during the lead time, so that a busier than usual period or a late delivery does not leave you empty before the next order arrives. It is set for a target: most often a cycle service level, the share of order cycles that end without running out.

safety stock = z × σ, with σ = √(L × σ_d² + d² × σ_L²)

σ is the spread (standard deviation) of demand over the lead time. L is the lead time in days, d and σ_d the average and spread of daily demand, σ_L the spread of the lead time. z comes from the normal distribution: 1.645 for a 95% cycle service level, 2.326 for 99%. Then the reorder point is the demand during the lead time plus the safety stock.

Example (in the tool). 1,000 units a month with a spread of 250, a lead time of 21 days give or take 5 (one standard deviation). Per day that is 32.9 units with a spread of 45.3. The demand part of σ is √21 × 45.3 = 208, the lead-time part 32.9 × 5 = 164, together σ = 265. At 95%: 1.645 × 265 = 436 units. With a supplier who always delivers in exactly 21 days it would be 342: the ± 5 days cost 94 units.

What it assumes. Demand over the lead time roughly follows a normal curve, which fits steady, fairly high-volume items. For slow movers and items that sell only now and then the formula is not reliable. A 95% cycle service level is also not “95% of demand served”: that is the fill rate, a different and usually higher number for the same stock: Safety stock: 95% of what?

Sources

• Chopra, S., Reinhardt, G., & Dada, M. (2004). The effect of lead time uncertainty on safety stocks. Decision Sciences, 35(1), 1–24.
• Caplice, C. (2006). ESD.260 Logistics Systems, Lecture 11: Inventory Management, Probabilistic Demand. MIT OpenCourseWare.
• Axsäter, S. (2013). When is it feasible to model low discrete demand by a normal distribution? OR Spectrum, 35, 153–162.