Location-Allocation Models
Also known as: facility location, p-median problem, maximal covering location problem, yer-tahsis modelleri
Location-allocation models decide where to place a set of facilities and simultaneously assign demand points to them so as to optimize an objective such as total travel cost, worst-case distance, or population covered. Rooted in the operations-research work of Cooper (1963) and Hakimi (1964) and central to network GIS, they answer questions like where to site warehouses, hospitals, fire stations, or schools to best serve a spatially distributed population.
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The neighbourhood of related methods — select a node to explore.
When to use it
Use location-allocation for siting public or private facilities — hospitals, clinics, fire/EMS stations, schools, warehouses, retail outlets, charging stations — when you must choose locations and service assignments to optimize access, cost, coverage, or equity over a real network. Pick the model to match the goal: p-median for efficiency (minimize total travel), p-center for equity (protect the worst-served), maximal covering for service within a standard. It needs a good network/cost model and demand weights, and results are sensitive to candidate-site definitions and the cost metric. For multi-criteria suitability (combining many map layers rather than a single travel objective), GIS-MCDA is complementary; for routing once facilities exist, use shortest-path/vehicle-routing methods.
Strengths & limitations
- Optimizes facility siting and demand assignment jointly over a real network.
- Multiple objectives (efficiency, equity, coverage) via p-median/p-center/covering.
- Produces actionable outputs: chosen sites plus their service areas.
- Well-grounded in operations research with mature solution methods.
- Large instances are NP-hard, needing heuristics rather than exact solutions.
- Requires an accurate network cost model and demand weighting.
- Sensitive to the set of candidate sites and the chosen cost metric.
- Static: typically ignores future demand change unless modelled explicitly.
Frequently asked
What is the difference between p-median and p-center?
The p-median minimizes the total (population-weighted) travel cost to facilities — an efficiency objective. The p-center minimizes the maximum distance any demand point travels — an equity/worst-case objective. They can yield very different solutions, so the choice should reflect whether you care about average access or protecting the worst-served.
Does it use straight-line or network distance?
Properly, network distance or travel time, computed over the road network, because real access follows routes, not crow-flight lines. Using Euclidean distance is a simplification that can misplace facilities, especially where the network is irregular.
How is this different from GIS-MCDA suitability?
Location-allocation optimizes a single network objective (cost/coverage) and assigns demand. GIS-MCDA combines many weighted criteria layers into a suitability surface for siting. They are complementary: MCDA can screen suitable areas, and location-allocation can then optimize exact sites and service assignment.
Sources
- Cooper, L. (1963). Location-allocation problems. Operations Research, 11(3), 331–343. DOI: 10.1287/opre.11.3.331 ↗
- Hakimi, S. L. (1964). Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research, 12(3), 450–459. DOI: 10.1287/opre.12.3.450 ↗
How to cite this page
ScholarGate. (2026, June 2). Location-Allocation Models. ScholarGate. https://scholargate.app/en/spatial-analysis/location-allocation
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- GIS-MCDASpatial analysis↔ compare
- Integer ProgrammingOptimization↔ compare
- Least-Cost PathSpatial analysis↔ compare
- Linear ProgrammingOptimization↔ compare