Cycle Stock

411. Cycle Stock

The portion of inventory that exists because we order in batches instead of unit-by-unit. Pure consequence of fixed ordering costs and the EOQ trade-off.

Cycle stock (average) = \frac{𝑄}{2}

411.0.1. Where it comes from

Order $𝑄$ units. Drain at rate $𝑑$ until empty. Order again. Repeat.

Inventory profile is a sawtooth: peaks at $𝑄$ just after each order, drops linearly to 0, jumps back to $𝑄$ . Average over the cycle: $𝑄 / 2$ .

If we ordered each unit immediately as needed, cycle stock would be 0 — but ordering has a fixed setup cost $𝑆$ , so we batch.

411.0.2. Why $𝑄 / 2$ ?

Linear drainage from $𝑄$ to $0$ over time $𝑄 / 𝑑$ . The time-average is the area under the triangle divided by the cycle length:

Average inventory = (\frac{1}{2}) 𝑄 \cdot \frac{\frac{𝑄}{𝑑}}{\frac{𝑄}{𝑑}} = \frac{𝑄}{2}

Always exactly half the order quantity for deterministic demand. For stochastic demand, the expected on-hand mid-cycle is approximately $𝑄 / 2$ plus the safety stock buffer.

411.0.3. Cost of cycle stock

Annual holding cost from cycle stock alone:

{HC}_{cycle} = ℎ \cdot \frac{𝑄}{2}

This is the standard EOQ holding-cost term. The basic-EOQ optimum balances this against ordering cost $𝑆 𝐷 / 𝑄$ → gives $𝑄^{*} = \sqrt{2 𝑆 𝐷 / ℎ}$ .

411.0.4. Reduce cycle stock by shrinking $𝑄$

Two ways to reduce cycle stock:

Shrink $𝑄$ directly — accept more frequent orders, more setup cost.
Reduce setup cost $𝑆$ — then EOQ shrinks naturally (lean / SMED — single-minute exchange of die — work targets exactly this).

Lean inventory practice = drive $𝑆$ toward zero so $𝑄$ can shrink, ideally toward 1 unit (just-in-time ordering).

411.0.5. How it composes with other stock types

Cycle stock is just one of five inventory components in a typical operation:

Component	Magnitude	Reason
Cycle stock	$𝑄 / 2$	Batched ordering
Safety stock	$𝑧 𝜎_{𝐿}$	Demand uncertainty
Pipeline stock	$𝑑 𝐿$	In-transit during lead time
Anticipation stock	planned	Forecasted demand spikes
Decoupling stock	planned	Buffer between production stages

Total average inventory = sum of all components.

Example

Given (the same shared params as EOQ / policies):

Annual demand: $𝐷 = 12000$ , daily $𝑑 = 33$
Order cost: $𝑆$ = $50, holding $ℎ$ = $2/unit/yr
Order quantity: $𝑄^{EOQ} = 775$

Step 1 — average cycle stock

Cycle stock = \frac{𝑄}{2} = \frac{775}{2} \approx 388 units

Step 2 — annual holding cost from cycle stock

{HC}_{cycle} = ℎ \cdot \frac{𝑄}{2} = 2 \cdot 388 \approx

$775 / year

This equals the annual ordering cost $𝑆 \frac{𝐷}{𝑄} = 50 \cdot \frac{12000}{775} \approx$ $775 — a property of basic EOQ (the two costs balance at the optimum).

Step 3 — reduce cycle stock

If we halve setup cost ( $𝑆$ → $25 via process improvement), new EOQ:

𝑄^{*} = \sqrt{2 \cdot 12000 \cdot \frac{25}{2}} \approx 548 units

Cycle stock drops to $548 / 2 = 274$ — a 30% reduction. Total holding cost falls to $ℎ \cdot 274 =$ $548/yr.

Halving setup → 30% smaller cycle stock. (Square-root law: cycle stock scales with $\sqrt{𝑆}$ .)

Step 4 — driving toward JIT

In the limit $𝑆 \to 0$ : $𝑄^{*} \to 1$ , cycle stock $\to 0.5$ unit, you order one (or near-one) unit at a time. This is the JIT / lean ideal.

Real lean operations don’t achieve $𝑆 = 0$ but get close enough that cycle stock becomes a small fraction of total inventory — most of the remaining inventory is safety stock and pipeline stock.