Ready Rate

410. Ready Rate

410.1. Ready Rate (Time-based service level)

The probability that on-hand inventory is positive at any random moment in time. Counts time, not cycles or units.

Ready rate = 𝛾 = 𝑃 (on-hand > 0)

410.1.1. How it differs from CSL and fill rate

Metric	Counts	What it means	Sample question
CSL ( $𝛼$ )	Cycles	P(no stockout in this cycle)	“What fraction of cycles have a stockout?”
Fill rate ( $𝛽$ )	Units	E[demand met] / E[demand]	“What fraction of unit demand is met?”
Ready rate ( $𝛾$ )	Time	P(stock > 0 at time $𝑡$ )	“What fraction of time are we in stock?”

All three are “service level” but answer different questions.

410.1.2. Ready rate = fraction of time with positive stock

In steady state, the inventory level over a (Q, r) cycle alternates:

Positive on-hand during most of the cycle.
Zero on-hand during any stockout window (the gap from when stock hits zero to when the order arrives).

If $𝑇$ is the average cycle length and $𝑊$ is the expected stockout duration per cycle:

𝛾 = \frac{𝑇 - 𝑊}{𝑇} = 1 - \frac{𝑊}{𝑇}

For (Q, r) with $𝑇 = \frac{𝑄}{𝑑}$ :

𝛾 \approx 1 - \frac{𝜎_{𝐿} \frac{𝐿 (𝑧)}{𝑑}}{\frac{𝑄}{𝑑}} = 1 - 𝜎_{𝐿} \frac{𝐿 (𝑧)}{𝑄}

The same expression as fill rate! Under continuous-demand assumptions, ready rate and fill rate coincide. They diverge only when stockout duration and shortage size aren’t proportional (e.g., very lumpy demand patterns).

410.1.3. When ready rate is the right metric

Use ready rate when:

Server availability: a service desk that can take orders only when stock is on hand. “Are we ready to serve?”
Compliance: regulations require a minimum % of time in stock (some pharmacies, parts depots).
Multi-product systems: aggregate ready rate = average of individual ready rates, easier to manage.

Don’t use ready rate when shortages have widely varying severity — use fill rate to capture how much demand was unmet rather than just whether you were stocked out at the moment.

410.1.4. Approximate equivalence to fill rate

Under standard assumptions (continuous time, smooth demand, no lumpy bursts):

𝛾 \approx 𝛽 \approx 1 - 𝜎_{𝐿} \frac{𝐿 (𝑧)}{𝑄}

In practice, choose whichever is more interpretable for your stakeholders:

Customer-facing metrics → fill rate (units of unmet demand)
Operations / compliance → ready rate (time in stock)
Executive reporting → CSL (binary cycle outcome, simpler)

Example

Given (same (Q, r) policy as CSL/fill rate examples):

$𝑄 = 775$ , $𝜇_{𝐿} = 462$ , $𝜎_{𝐿} = 18.7$ , $𝑑 = 33$ /day
Reorder point set for CSL = 95%: $𝑟 = 493$ , $𝑧 = 1.65$ .

Step 1 — expected stockout duration per cycle

Stockout occurs only if $𝐷_{𝐿} > 𝑟$ . Expected shortage in units:

𝐸 [shortage] = 𝜎_{𝐿} 𝐿 (𝑧) = 18.7 \cdot 0.0207 \approx 0.39 units

Convert to time: shortage $\approx 0.39$ units, daily demand 33, so:

𝑊 = \frac{𝐸 [shortage]}{𝑑} \approx \frac{0.39}{33} \approx 0.012 days \approx 17 minutes

Step 2 — ready rate

𝛾 = 1 - \frac{𝑊}{𝑇} = 1 - \frac{0.012}{\frac{775}{33}} \approx 1 - 0.0005 \approx 99.95 %

Step 3 — compare metrics

At the same reorder point $𝑟 = 493$ :

CSL: 95% (5% of cycles have a stockout)
Fill rate: 99.95% (0.05% of unit demand unmet)
Ready rate: 99.95% (in stock 99.95% of the time)

Fill rate ≈ ready rate (both unit/time-weighted). CSL is the strict outlier — it’s an event count, blind to severity.

Two stakeholder views:

CFO: “We hit a 5% stockout-cycle rate at this safety stock level — is that too lenient?”
Operations: “We’re shipping 99.95% of orders; nobody complains.” — fill rate / ready rate.

Both views are correct; just different denominators.