408. Cycle Service Level

408.1. Cycle Service Level (Type I, $𝛼$)

The probability of no stockout during a replenishment cycle. Counts events: did this cycle have any unmet demand, yes or no?

408.1.1. Definition

A cycle runs from one order arrival to the next. Stockout = any moment in the cycle where on-hand inventory hits zero with demand still present.

For a (Q, r) policy:

• Order placed when inventory position drops to $𝑟$.
• Order arrives $𝐿$ time later. During those $𝐿$ time units, lead-time demand ${𝐷}_{𝐿}$ consumes inventory.
• No stockout in this cycle iff ${𝐷}_{𝐿}\le 𝑟$.

So:

408.1.2. Setting $𝑟$ for target CSL

If ${𝐷}_{𝐿}\sim \mathrm{𝒩︀}\left({𝜇}_{𝐿},{𝜎}_{𝐿}^2\right)$:

Solve for $𝑟$:

The familiar “$𝜇+𝑧𝜎$” form.

408.1.3. What CSL does not count

CSL counts cycles, not units. A cycle with one unit short and a cycle with 1000 units short both count as one stockout. So a 95% CSL means 5% of cycles experience a stockout, but says nothing about how severe those stockouts are.

In practice this matters: a 95% CSL might correspond to 99% fill rate (most stockouts are tiny) or 80% fill rate (the stockouts are catastrophic) depending on the demand-distribution shape.

408.1.4. When CSL is the right metric

Use CSL when:

• The occurrence of any stockout is what matters (regulatory thresholds, contract penalties tied to “stockout incidents”, reputational concerns).
• Demand is fairly smooth — the gap between CSL and fill rate is small.
• You want a simple, interpretable number for executive reporting.

Don’t use CSL when stockout severity matters more than frequency — use fill rate instead.

408.1.5. Common $𝑧$ values