OpenSpecEngineering

Finds the safety stock and the reorder point for a stocked item whose demand and supplier lead time both vary. When the stock on hand plus on order falls to the reorder point, a new order goes out. The safety stock is the part of that point held against a busy lead time or a late delivery. Planners and buyers use it to set the minimum level in a continuous-review (s, Q) system [1], [3].

The equations

σ_DLT = √(L·σ_d² + d²·σ_L²)

SS = z·σ_DLT    ROP = d·L + SS

d is the average daily demand and σ_d its standard deviation. L is the average lead time in days and σ_L its standard deviation. σ_DLT is the standard deviation of the demand during the lead time, which combines both sources of variation, assuming they are independent [1], [2]. z is the standard normal value for the cycle service level, the chance that a cycle ends without a stockout: 1.645 for 95 %, 2.326 for 99 %. SS is the safety stock and ROP the reorder point. d·L is the stock expected to be used while an order is on its way.

Limits and common mistakes

• The cycle service level counts cycles without a stockout. It is not the fill rate, the share of demand served from stock, which is usually much higher for the same safety stock [2].
• Use daily figures throughout. If demand is recorded weekly, divide the weekly standard deviation by √5 or √7 (the working days in the week), not by 5 or 7.
• The formula assumes demand during the lead time is roughly normal. For slow movers that sell a few units a month, a Poisson model gives better results.
• Lead-time variation is often the larger term. Enter 0 for σ_L only when deliveries really arrive on time.
• Safety stock rises steeply near 100 %. Going from 95 % to 99 % adds about 40 % more safety stock.

Worked example

A distribution center ships an average of 120 filter cartridges a day, with a standard deviation of 30. The supplier quotes 8 days, but deliveries vary with a standard deviation of 2 days. The target is a 97.5 % cycle service level.

1. Enter Average Demand Rate (d, units per day) 120 and Average Lead Time (L, days) 8.
2. Enter Std Dev of Daily Demand (σ_d) 30 and Std Dev of Lead Time (σL, days; 0 if fixed) 2.
3. Enter Cycle Service Level (%) 97.5.
4. Press Solve. The Solution shows: Safety factor z: 1.95996
   Lead-time demand (d·L): 960 units
   Std dev of lead-time demand σ_DLT: 254.558 units
   Safety stock: 498.925 units
   Reorder point: 1,458.93 units

Check: √(8 × 30² + 120² × 2²) = √(7,200 + 57,600) = 254.6. The lead-time term is eight times the demand term. 1.96 × 254.6 = 499, so the buyer reorders at about 1,460 cartridges, with 500 of them as safety stock.