Lead-time Pooling

435. Lead-time Pooling

Reducing safety stock by shortening or stabilizing lead times, not by aggregating demand. Substitutes responsiveness for inventory — a different lever than location pooling.

435.1. The lever

Safety stock scales with lead-time demand standard deviation:

SS = 𝑧 \sqrt{𝐿 𝜎_{𝐷}^{2} + 𝜇_{𝐷}^{2} 𝜎_{𝐿}^{2}}

where $𝐿$ is mean lead time and $𝜎_{𝐿}$ is lead-time variability. If you cut $𝐿$ or $𝜎_{𝐿}$ , safety stock falls.

435.2. Two distinct mechanisms

1. Shorter lead time: $𝐿$ falls, lead-time demand variability falls as $\sqrt{𝐿}$ . Safety stock for demand-side variability scales as $𝑧 𝜎_{𝐷} \sqrt{𝐿}$ → cut $𝐿$ by $\frac{1}{4}$ , cut SS by $\frac{1}{2}$ .

2. Less variable lead time: $𝜎_{𝐿}$ falls toward zero. The $𝜇_{𝐷}^{2} 𝜎_{𝐿}^{2}$ term shrinks. Big effect when demand is fast and lead-time variability dominated the formula.

Often both effects compound — fast & reliable.

435.3. Numerical example

Demand: $𝜇_{𝐷} = 100$ /week, $𝜎_{𝐷} = 30$ /week.

Scenario	$𝐿$	$𝜎_{𝐿}$	LT-demand $𝜎$	SS at $𝑧 = 1.65$
Slow, variable	8 wk	2 wk	$\sqrt{8 \cdot 900 + 10000 \cdot 4} = \sqrt{47200} \approx 217$	$358$
Fast, variable	2 wk	1 wk	$\sqrt{2 \cdot 900 + 10000 \cdot 1} = \sqrt{11800} \approx 109$	$179$
Slow, stable	8 wk	0	$\sqrt{8 \cdot 900} = \sqrt{7200} \approx 85$	$140$
Fast, stable	2 wk	0	$\sqrt{2 \cdot 900} \approx 42$	$69$

Going from “slow, variable” to “fast, stable” cuts safety stock by 80%.

435.4. How to shrink lead times

Air freight vs ocean — pay premium for time
Domestic / near-shore — vs offshore production
Vendor-managed inventory — supplier holds inventory at your door
Just-in-time / Kanban — pull-based replenishment shortens effective lead time
Direct-store delivery — bypass DCs

435.5. How to stabilize lead times

Multi-sourcing — backup suppliers smooth out individual variability
Vendor service-level agreements — explicit, monitored commitments
Production buffers at vendor — they hold the variability, not you
Premium expedited service — pay for guaranteed times

435.6. Trade-offs

Faster / more reliable lead times cost more:

Higher unit cost (premium shipping, near-shoring)
Higher per-order fixed cost (smaller batches → more orders)
Supplier relationship investment
Reduced negotiating leverage

This is one of the core cost-vs-responsiveness axes in supply-chain strategy (Fisher’s framework: efficient vs responsive supply chains).

435.7. When lead-time pooling beats location pooling

If demand correlates strongly across regions (so location pooling gains little), but lead-time variability dominates safety stock, lead-time pooling is the bigger win.

Common in:

Fashion / seasonal goods — short selling season, high demand uncertainty
Consumer electronics — new-product launches
Spare parts — slow movers where SS is dominated by lead-time variance