What is fill rate in inventory?

In inventory, the fill rate is the share of demand shipped from stock on hand, without waiting for a backorder or a new delivery: 980 of 1,000 units ordered by customers shipped from the shelf is a 98% fill rate. It counts units. The cycle service level counts order cycles: the share of replenishment cycles that end without running out at all, however small the shortage.

The two give different numbers for the same stock. A cycle that runs short by a few units counts as a full failure in the cycle service level but costs only those few units in the fill rate. In the Safety stock example (1,000 units a month, orders of 1,008), the 436 units of safety stock that cover 95% of cycles fill 99.5% of demand. A 98% fill rate needs only 277 units, which covers 85.2% of cycles.

The fill rate depends on the order size; the cycle service level does not. Larger orders mean fewer cycles, so fewer chances to run short for each unit sold. With small orders it can turn round: at 100 units an order, the same 95% buffer fills only 94.5% of demand.

Formula (the standard approximation, continuous review): fill rate = 1 − σ × G(k) ÷ Q, where σ is the spread of demand over the lead time, k the safety stock divided by σ, G the normal loss function and Q the order size. The comparison in full, with what to set: Safety stock: 95% of what?

Sources

• Caplice, C. (2006). ESD.260 Logistics Systems, Lectures 11 and 12: item fill rate, P2 = 1 − σ·G(k)/Q. MIT OpenCourseWare.
• Silver, E. A., Pyke, D. F., & Thomas, D. J. (2017). Inventory and Production Management in Supply Chains (4th ed.). CRC Press.