Fill Rate Calculator: Unit, Line and Order Fill Rate, Stockouts and Safety Stock

How it works

Unit fill rate = units shipped ÷ units ordered · line (order) fill rate = complete lines (orders) ÷ all lines (orders) · order fill expected from line fill ≈ line fill^(lines per order) · z = safety stock ÷ σ_LT · expected shortage per cycle ESC = σ_LT × L(z), L(z) = φ(z) − z × (1 − Φ(z)) · fill rate = 1 − ESC ÷ Q · safety stock for a target fill rate: solve L(z) = (1 − target) × Q ÷ σ_LT

Fill rate measures service the way customers feel it: the share of demand shipped from stock, complete and on time. It can be counted by unit (or case), by order line or by whole order, and the three usually fall in that order because a single short line spoils an otherwise perfect order. If short lines were spread at random, the share of complete orders would be the line fill rate raised to the number of lines per order; comparing that with your real order fill shows whether shortages are concentrated or spread out. The model links fill rate to inventory policy. Safety stock divided by the standard deviation of demand over the lead time gives z. The standard normal loss function L(z) gives the expected units short per replenishment cycle (σ × L(z)), and dividing by the order quantity Q gives the expected fill rate. Run backwards, the same equation gives the safety stock needed for a target fill rate. Because a large order quantity means fewer exposures to stockout, fill rate is normally far above the cycle service level (the chance of no stockout in a cycle) for the same z. The model assumes normal lead-time demand, a reorder-point policy with continuous review and that shortages are backordered. Late supplier deliveries, forecast bias and inventory record errors lower the real fill rate, so compare the model with your measured unit fill.

Worked example

11,400 of 12,000 units shipped is a unit fill rate of 95.0% (600 units short); 790 of 850 lines is 92.9% and 255 of 300 orders is 85.0%. With 2.83 lines per order, random short lines would give 0.9294^2.83 = 81.3% order fill, so shortages are concentrated. With 360 units of safety stock against σ = 220 units, z = 1.636 and L(z) = 0.0213, so the expected shortage is 220 × 0.0213 = 4.7 units per 2,000-unit cycle: a modelled fill rate of 99.77% and a 94.9% cycle service level. For a 98% fill rate, L(z) = 0.02 × 2,000 ÷ 220 = 0.1818, z = 0.553, so about 122 units of safety stock would be enough.

Sources: Chopra & Meindl, Supply Chain Management, ch. 12 slides: ESC and fill rate examples (fr = 0.9975; ss = 67 for 97.5%) · DCL Logistics: fill rate definitions, formulas and benchmarks · Logiwa: fill rate calculator (line fill example 475 of 500 = 95%)

Frequently asked questions