Facility Location Model¶
Method — instantiates Discrete Commitment Optimization
Chooses which whole sites to open so that demand is covered at acceptable cost and distance.
A Facility Location Model decides where to plant a set of indivisible facilities — depots, stations, hubs, service points — so that every demand point is served under limits on cost, distance, or capacity. Its decision object is the whole site: you either open a location or you don't, and each opened site then "serves" some region of demand. What makes it this mechanism and not a generic selection is the tension it uniquely balances: an opening cost tied to sites and a service relationship tying each demand point back to an open site. Add too few sites and some demand is stranded or too far away; add too many and the opening cost balloons. The model finds the set of whole placements that resolves that geographic coverage-versus-cost tension.
Example¶
A metro transportation authority is planning a public EV fast-charging network across a sprawling city. It has 60 candidate locations — transit lots, curb segments, a few municipal garages — and a fixed capital budget. The requirement is that no resident should be more than a ten-minute drive from a charger, and dense corridors need chargers within a shorter radius. Each candidate site, once opened, "covers" the blocks that fall inside its service radius.
The model treats each of the 60 candidates as open-or-not and commits a subset such that every block is covered by at least one open site, high-demand corridors get their tighter coverage, and total capital cost stays within budget. A visually attractive downtown site might be left unopened because two cheaper sites nearby already blanket the same blocks — the model refuses to pay twice for the same coverage. The output is a map of which sites to build, chosen as a coherent network rather than one appealing location at a time.
How it works¶
- Enumerate candidate sites as whole options. Each is a binary open/closed commitment; there is no half-open facility.
- Define the service relation. Specify which demand points a site can cover if opened (within a distance radius, a travel time, or a capacity limit).
- Couple demand to open sites. Impose that each demand point is served by at least one — or exactly one — open facility; a demand point may only be served by a site that is actually open.
- Optimize coverage against opening cost. Minimize total cost (or maximize covered demand for a fixed budget), classic p-median / set-covering structures.[1]
The signature is the linkage between the open-site decision and the coverage it unlocks; without that linkage it would collapse into a plain shopping list of sites.
Tuning parameters¶
- Coverage radius / standard — how far a site may reach. Tightening it improves service quality but forces more sites open and raises cost.
- Capacity per site — whether an open facility can absorb unlimited demand or a capped amount. Capacities add realism but can strand demand and force additional openings.
- Budget vs. coverage framing — minimize cost to hit full coverage, or maximize coverage under a fixed budget. The two framings can select very different networks.
- Single- vs. multi-source service — whether each demand point is tied to exactly one site or may split across several. Single-source is cleaner to operate; multi-source hedges against a site's failure.
When it helps, and when it misleads¶
It is the tool for siting decisions where placement is discrete and the payoff is spatial coverage — warehouses, clinics, cell towers, ambulance bases, charging stations. It exposes redundant candidates and stops a team from over-building appealing but duplicative sites.
Its failure mode is that the demand map and the coverage radius drive everything, and both are modeling choices that can quietly encode bias. A radius calibrated to average conditions understates coverage gaps in the hardest-to-serve pockets; a demand estimate built from current usage bakes in the very access inequities a public network was meant to fix. The classic misuse is optimizing aggregate coverage while a few peripheral neighborhoods fall permanently outside every radius. The guarding discipline is to inspect who is left uncovered, not just how much demand is covered in total, and to test the network against demand scenarios rather than a single point estimate.
How it implements the components¶
indivisible_option_set— its core representation: each candidate site is a whole, all-or-nothing placement.objective_function— minimizes opening-plus-service cost (or maximizes covered demand under budget).coupling_constraint— the rule that a demand point may be served only by an open site, and must be covered by at least one, links the site decisions to the coverage they produce.
It does not implement binary_decision_variable or integer_constraint as a general modeling layer — the formal open/closed variable declaration and whole-number quantities are the province of Integer Programming Model; this method owns the siting pattern and hands the formalism off. Nor does it own the cardinality_limit-plus-fairness_guardrail staffing logic of Crew Scheduling Model.
Related¶
- Instantiates: Discrete Commitment Optimization — it is the siting/placement variant.
- Consumes: Integer Programming Solver to solve the resulting covering formulation.
- Sibling mechanisms: Assignment Model · Constraint Satisfaction Search · Crew Scheduling Model · Integer Programming Model · Integer Programming Solver · Project Selection Matrix · Selection Review Board · Solver Dashboard
Editorial Notes¶
Form Classification¶
Form family: Analysis, Modeling & Optimization
Rationale: The model optimizes binary site openings and demand assignments against service-distance, capacity, coverage, and cost constraints.
Nearest alternative: Decision, Gate & Allocation — The solution recommends sites to open, but the operative mechanism is the optimization calculation rather than a separate authority's final allocation.
Review outcome: Adjudicated after independent review; high confidence.
Origin Attribution¶
Primary origin: Operations Research
Origin pattern: Single lineage
Present-day reach: Specialized
Rationale: Facility-location models are canonical operations-research optimization formulations for selecting sites under cost and coverage constraints.
Related originating lineages:
- Logistics & Supply Chain Management — Distribution network design materially supplies their dominant applied formulation.
Review outcome: Independent reviewer agreement; high confidence.
References¶
[1] The p-median and set-covering location models (ReVelle & Swain, 1970; and the covering-location literature) formalize siting as choosing which facilities to open so demand is served within a distance standard — the canonical discrete facility-location formulations. withdrawn registry ↩