Product Pooling

434. Product Pooling

Reducing inventory by sharing parts / components across product variants rather than holding stock for each finished SKU separately. Two main mechanisms:

Component commonality — products share common parts
Postponement (delayed differentiation) — defer customization until late in the supply chain

Both convert several high-variance finished-good demands into one lower-variance component demand — a textbook application of risk pooling.

434.1. Postponement: the HP DeskJet case

Classic Lee-Tang (1996) example. HP shipped printers configured for North America, Europe, Asia from a Singapore factory. Each region got its own SKU (different power supplies, manuals, plugs). Region-specific safety stocks per SKU.

Postponement: ship generic printers to regional DCs. Final regional configuration (adding power supply, labeling) done at the DC, right before delivery.

Effect:

3 finished SKUs → 1 generic + 3 small customization kits
Safety stock for the generic stage uses aggregate demand across regions
Customization kits have very fast lead time → minimal safety stock

Variance accounting:

	Per-region	Aggregate
Mean demand	$𝜇_{𝑖}$	$\sum 𝜇_{𝑖}$
Variance	$𝜎_{𝑖}^{2}$	$\sum 𝜎_{𝑖}^{2}$ (independent)
Coefficient of variation	$\frac{𝜎_{𝑖}}{𝜇_{𝑖}}$	$\frac{\sqrt{\sum 𝜎_{𝑖}^{2}}}{\sum} 𝜇_{𝑖}$

The aggregate CV is smaller — pooling effect for the generic. Total safety stock falls by a factor $\frac{\sqrt{𝑁}}{𝑁}$ for the components that get postponed.

434.2. Component commonality (Baker-Magazine-Nuttle 1986)

Two end products $𝐴$ and $𝐵$ use:

Some shared components — commonality
Some unique components

For the shared component, demand is $𝐷_{𝐴} + 𝐷_{𝐵}$ — pooled. For unique components, demand is each product’s own — not pooled.

Trade-off:

More commonality → more pooling savings, but each product is harder to differentiate
More uniqueness → more product differentiation, more inventory cost

434.3. Variance math

Let product demands $𝐷_{𝐴}, 𝐷_{𝐵}$ be independent with $𝜎_{𝐴}, 𝜎_{𝐵}$ . The shared component (used in both) sees:

𝜎_{shared} = \sqrt{𝜎_{𝐴}^{2} + 𝜎_{𝐵}^{2}}

vs separate components:

𝜎_{separate, A} + 𝜎_{separate, B} = 𝜎_{𝐴} + 𝜎_{𝐵}

By the triangle inequality $\sqrt{𝜎_{𝐴}^{2} + 𝜎_{𝐵}^{2}} \leq 𝜎_{𝐴} + 𝜎_{𝐵}$ (and strict inequality when both $𝜎_{𝑖} > 0$ ). Equality only when one variance is zero.

So sharing strictly reduces required safety stock for the shared component.

434.4. Practical examples

Auto industry — Toyota uses common platforms across models (Corolla, Camry, RAV4 share many parts)
Electronics — Apple uses common batteries, chargers, screens across product lines
Apparel — DKNY makes generic shirts in white, dyes them to color at distribution centers
PC manufacturing — Dell assemble-to-order from common components
Pharmacy — generic drug → repackaged for retail / hospital channels

434.5. Limitations