429. Location Pooling
Holding inventory at one central location (or fewer central locations) instead of at every demand point. The simplest and most direct application of risk pooling.
429.1. Setup
You serve markets / regions / stores. Demand at each is random with mean and standard deviation . Two extremes:
- Decentralized: each region holds its own safety stock — independent inventories totalling
- Centralized: one warehouse holds aggregate safety stock (for independent demands), then ships on demand
Centralized cuts safety stock by (the square-root law).
429.2. Numerical illustration
regions, each per week, for 95% service.
| Decentralized | Centralized | |
|---|---|---|
| Mean demand | ||
| Std dev | (sum) | (pool) |
| Safety stock at 95% | ||
| Savings | — |
429.3. The trade-offs
Centralization isn’t free:
- Transport cost — central → customer distance increases (more outbound shipping)
- Response time — last-mile lead time grows
- Demand visibility — aggregated demand loses regional / time-of-day texture
- Customer experience — same-day delivery may be impossible from central locations
- Single point of failure — central warehouse outage hits all customers
Some industries (Amazon, parts distribution) trade off these costs explicitly via partial pooling — multiple regional DCs rather than one central or stores.
429.4. Optimal degree of pooling
The trade-off is a facility-location problem:
- More facilities → less safety stock pooling savings, but lower transport costs
- Fewer facilities → more safety stock pooling savings, but higher transport costs
The classical square-root facility-location model (Daganzo continuous approximation; covered in facility location) computes the optimal number of facilities for a given demand density and cost structure.
429.5. Other forms
- Inventory pooling: physical centralization (one warehouse)
- Virtual pooling: separate physical inventories that share via inter-location transfers (transshipments)
- Substitution-based pooling: customer accepts a different but similar product
- Lead-time pooling: covered separately at lead-time pooling
429.6. Real-world examples
- Walmart regional DCs — centralized 1980s; revolutionized big-box retail
- Amazon fulfillment centers — now mostly partially pooled with last-mile depots
- Spare parts depots — defense, automotive
- Hospital networks — central pharmacy for slow-moving / expensive drugs