318. Facility Location
A family of combinatorial optimization problems: where should warehouses / stores / hospitals / cell towers be located to best serve known demand?
318.1. Variants
The variants differ by:
- Objective: minimize total cost, minimize maximum distance, maximize coverage
- Constraints: facility capacity, customer assignment rules
- Discrete vs continuous: candidate locations are finite (-median) or anywhere in space (center of gravity)
| Variant | Objective | Constraint |
|---|---|---|
| UFLP | min | uncapacitated |
| CFLP | same | capacity per facility |
| -median | min total assigned distance | exactly facilities |
| -center | min max distance | exactly facilities |
| Set covering | min number of facilities | every demand covered |
| Max covering | max demand covered | exactly facilities |
| Center of gravity | min weighted sum of distances | single facility, continuous |
318.2. Common decision variables
For discrete location problems:
318.3. Trade-offs
- Many facilities: low transport cost, high fixed cost, less risk pooling
- Few facilities: high transport cost, low fixed cost, more pooling benefit
- Capacity-constrained: forces some demand to nearer facilities even when distant ones are cheaper
318.4. Where it shows up
- Supply chain network design — DC placement
- Public service — fire stations, ambulances, schools (-center for response time)
- Telecom — cell tower placement (set covering)
- Retail — store location (max covering under budget)
- Hub-and-spoke logistics — depots, airports
318.5. See also
- UFLP / CFLP — fixed-charge formulations
- -median / -center
- Set Covering / Max Covering
- Center of Gravity — continuous case
- Daganzo Continuous — strategic scale