Service levels: CSL vs fill rate

“We run at 95% service” sounds precise, but it can mean two very different things.

• Cycle service level (CSL) is the chance of getting through a replenishment cycle without running out. It counts events: a cycle either had a stockout or it didn’t.
• Fill rate is the share of demand served straight from stock. It counts units.

Here is why the gap matters. The café uses 1,200 kg of beans a year and orders 77.5 kg at a time, so it goes through about 15 replenishment cycles a year. Say it runs out in 2 of those 15 cycles, and each time it is short by about 3 kg before the delivery lands. Its cycle service level is about 87%, because 13 of 15 cycles had no stockout. But it missed only 6 kg out of 1,200 kg of demand, so its fill rate is about 99.5%.

So the same buffer can be described as “87%” or “99.5%” depending on the definition. The standard safety-stock formula (the one with $z$) targets cycle service level, while customers feel the fill rate. Large orders and small shortfalls push fill rate well above CSL.

Two more details matter in practice. When you run out, do customers wait (a backorder) or walk away (a lost sale)? And are you measuring units, order lines or whole orders? Many companies report OTIF (on time, in full), which is stricter still because an order counts only if every line arrives complete and on time.

Cycle service level comes straight from z

If demand over the lead time is roughly normal with standard deviation $\sigma_L$, a reorder point with safety stock $SS = z\,\sigma_L$ gives:

where $\Phi$ is the standard normal distribution. That is all the z-table does: $z = 1.645$ gives 95% and $z = 2.33$ gives 99%.

Fill rate needs the size of the shortfalls

Fill rate depends on how much you are short when you run out, not just whether you run out. The expected shortage per cycle is:

$G(z)$ is the standard normal loss function, and $\varphi$ is the normal density. Each cycle brings one order of $Q$ units, so with backorders:

Order size matters: the same shortfall is a smaller share of a large order.

Same café, very different numbers. A target written as “95%” means nothing until you know which measure it is.

From a target to a buffer

1. Agree which measure the business cares about. Customers feel fill rate; planning systems often set cycle service.
2. For a cycle service target, read $z$ from the normal table.
3. For a fill-rate target, compute $G(z) = (1 - \text{target}) \times Q / \sigma_L$ and solve for $z$ with a loss-function table or a spreadsheet.
4. Set $SS = z\,\sigma_L$, then check the result against what actually happened in past cycles.

Backorders or lost sales?

The fill-rate formula assumes customers wait for the next delivery (backorders). In retail, a customer facing an empty shelf usually buys something else or leaves, so the sale is lost. Lost sales change the maths slightly, because stock never goes negative, and change the economics a lot: a backorder costs some goodwill and expediting, while a lost sale costs the whole margin and sometimes the customer.

Units, lines, orders and OTIF

The same warehouse can report several “service levels”:

Order-level measures are much stricter. If each line is filled 98% of the time, independently, an order with 10 lines is complete only $0.98^{10} \approx 82\%$ of the time. Large retailers score suppliers on OTIF and often charge penalties for misses, so a supplier proud of 98% line fill can still fail its customer’s scorecard.

Setting the target from costs

Targets are often set by habit: 95% for everything. A cost-based target is better. If each unit short costs $p$ (lost margin, expediting, goodwill) and holding costs $H$ per unit per year, the best cycle service level in a (Q, R) system is approximately:

For the café, with a shortage cost of ₹600 a kg: $1 - (200 \times 77.5)/(600 \times 1200) \approx 97.8\%$. A costlier shortage pushes the target up; a cheaper shortage or a larger order pushes it down. Even when shortage costs are fuzzy, the formula makes the trade-off explicit instead of habitual.

Averages hide failures

A 98% average fill rate across 10,000 items can include a top customer’s key item failing every week. Report service by segment and by customer, and look at the spread, not just the average. Also watch for censored demand: when customers stop ordering items that are often out of stock, or sales staff don’t enter orders they know can’t be filled, the measured service looks better than the real one.