How Banks Optimise Branch and ATM Locations: Facility-Location Models, p-Median, Coverage, Demand, Cannibalisation and Access

Quick answer: bank network design is a facility-location problem. A bank has demand distributed across geography and several possible service points—full branches, ATMs, cash-deposit machines, shared hubs or other facilities. The algorithm decides which candidate locations to open or retain and which demand areas each location should serve. A p-median model minimises demand-weighted travel distance. A maximal-covering model maximises the population or demand served within a chosen travel threshold. Real systems add opening and operating cost, capacity, competition, cannibalisation, accessibility, cash needs, resilience and uncertainty. The mathematically cheapest network is not automatically the socially or operationally acceptable network.

A bank can reduce the number of facilities and reduce cost while making the network mathematically worse for the people who are hardest to serve.

Boundary: this article explains public operations-research concepts. It does not disclose or infer any bank’s private site-selection model, future branch plans, cash-security arrangements or commercially sensitive location strategy.

Page role: where facilities should be, not how they run once open

Bukit Timah Tutor already has an article on branch queueing and staffing and another on ATM cash demand and replenishment.

Those pages assume the facility already exists. This page owns the earlier strategic question:

Which locations should exist at all, what type should each location be, and which demand areas should they cover?

1. Turn geography into demand nodes and candidate sites

Suppose a city is divided into demand nodes i = 1,…,n. Each node has weight w_i, representing a chosen measure such as expected transactions, customers, cash need, business deposits or population requiring access.

The bank also has candidate facility locations j = 1,…,m. For every pair (i,j), calculate distance or travel time d_ij.

The core data objects are therefore:

• demand location;
• demand weight;
• candidate site;
• travel-time/distance matrix;
• facility type and capacity;
• site cost;
• existing competitor and own-network facilities;
• accessibility and policy constraints.

The model cannot optimise what the demand weights fail to represent. If digital-heavy customers dominate the dataset, cash-dependent or mobility-constrained communities can disappear mathematically even while they remain socially important.

2. p-Median: minimise weighted distance

The classic p-median model chooses p facilities so that total demand-weighted distance to the assigned facility is minimised.

Let y_j=1 if site j is open and x_ij=1 if demand node i is assigned to facility j. A simplified objective is:

Minimise Σ_iΣ_j w_id_ijx_ij

subject to:

• each demand node is assigned to one open facility;
• x_ij ≤ y_j;
• Σy_j = p.

This is a mixed-integer optimisation problem. It is easy to state and can become computationally difficult as locations, facility types and constraints grow.

Banking-specific research has long combined facility-location models with GIS. Miliotis, Dimopoulou and Giannikos showed how demand-covering and geographic criteria can be combined for bank-branch location in a competitive environment. See A Hierarchical Location Model for Locating Bank Branches in a Competitive Environment.

3. The p-median optimum can still leave one community very far away

An average-distance objective is dominated by high-weight demand. It can rationally place facilities near dense urban demand and leave a small rural population with a very long journey.

That is not a mathematical error. It means the objective function did not include a fairness or minimum-access requirement.

One correction is a hard constraint:

d_i,assigned ≤ D_max

for specified communities, or a penalty for excessive travel time. The model then acknowledges that minimising the mean and protecting the tail are different goals.

4. Maximal covering: maximise demand within a service radius

A maximal-covering model starts with an acceptable travel threshold D. Demand node i is considered covered if at least one selected facility lies within that threshold.

Let z_i=1 if node i is covered. Then:

Maximise Σ w_iz_i

subject to the number/cost of facilities and the requirement that z_i can equal 1 only when an open site is within range.

A banking facility study by Xia and colleagues developed a practical maximal-covering model with varied costs, revenues, multiple facility types and flexible coverage for a large banking network problem. See A Hybrid Nested Partitions Algorithm for Banking Facility Location Problems.

5. Distance is often the wrong metric; travel time is better

Two facilities can be 2 km away in straight-line distance but separated by a river, motorway, steep terrain or weak public transport. A realistic matrix d_ij should therefore reflect how customers actually travel:

• walking time;
• public-transport time;
• driving time;
• cost of travel;
• opening-hour compatibility;
• physical accessibility.

This is visible in current public policy. The UK’s Financial Conduct Authority says cash-access reviews should consider where people and businesses are located, travel time and travel cost when assessing local gaps. Its access-to-cash page was updated on 29 July 2026. See Helping People Access Cash.

6. Current access statistics show why coverage metrics matter

As of the FCA’s 29 July 2026 update, it reports that 95.0% of the UK population are within one mile of a free-to-use cash withdrawal point and 99.7% are within three miles. Those are coverage statistics—not average-distance statistics.

The distinction matters. A network can have excellent average proximity while still leaving a small but important tail poorly served. Coverage metrics make the tail visible.

7. Facility type makes the problem multi-layered

A full bank branch, cash-withdrawal ATM, deposit-capable ATM and shared banking hub do not provide the same service.

Let facility type k have:

• opening cost c_jk;
• operating cost;
• capacity;
• service set S_k;
• hours;
• resilience characteristics.

The decision variable becomes y_jk: should facility type k be placed at candidate site j?

The optimiser can then choose a mixed network rather than pretending every demand node requires a full branch.

8. Capacity links location to queueing

A p-median model can assign half a city to one branch if distance is short. In reality, service capacity is finite.

A capacitated constraint is:

Σ_i demand_ix_ij ≤ capacity_jy_j.

Capacity can mean teller appointments, cash withdrawals, deposit volume, advice slots or machine throughput. Once a site is selected, the queueing problem begins. See How Bank Branches Use Queueing Algorithms to Staff Service.

9. Cannibalisation means new facilities can steal demand from your own network

Suppose a bank opens a new ATM beside an existing branch. Some demand is genuinely new; some simply moves from the branch or another ATM.

A naive forecast counts all nearby demand as incremental and overstates network benefit.

A simple demand-allocation model can assign customer i among alternatives according to utility:

U_ij = −α travel time + β service match + γ convenience − δ expected wait + …

Demand share can then depend on relative utility across own and competitor locations. Research on retail banking finds distance affects consumer bank choice and competitive substitution between nearby branches. See Location and Competition in Retail Banking.

10. Competitors can make clustering rational

It may seem obvious that a bank should locate where competitors are absent. Spatial banking research shows the opposite can also occur: branches may cluster where demand is attractive and information/competition effects make established banking locations valuable.

A 2024 Review of Finance study using tens of thousands of branches across multiple countries found that information sharing can encourage banks to establish branches in locations already served by other banks. The lesson is not “always cluster.” It is that competitor proximity can signal demand and alter customer substitution. Location is strategic, not merely geometric.

11. Digital adoption changes demand weights rather than deleting physical demand

As mobile banking grows, some branch transactions migrate online. The weight w_i for a full branch can therefore fall while the weight for cash access, complex advice or business deposits remains.

The error is to replace every physical-service weight with the national average rate of digital adoption. Demand is heterogeneous by age, business type, vulnerability, local connectivity and service need.

The FCA’s current cash-access regime explicitly requires designated firms to assess significant local gaps and provide reasonable additional cash services where needed. Its rules have been in force since 18 September 2024. The network objective therefore cannot always be “minimise private operating cost.” Applicable public-access obligations add constraints.

12. Resilience requires redundancy

A network optimised for ordinary conditions may place all demand behind one highly efficient facility. If that branch, telecom link or ATM cluster fails, the service disappears.

A resilient model can require double coverage for critical demand:

number of independent reachable facilities ≥ 2

for specified communities or services.

The two facilities should not share every critical dependency, or the apparent redundancy is false. This connects to operational resilience.

13. Stochastic location models admit that demand forecasts are uncertain

A branch decision can last years while local demand changes. Instead of optimising one forecast, define scenarios s with probability or stress weight q_s:

Expected objective = Σ_s q_s Cost(network, demand scenario s).

Scenarios can include:

• population growth or decline;
• digital adoption;
• competitor closures;
• public-transport changes;
• new commercial districts;
• cash-demand stress;
• facility outage.

A robust solution may sacrifice a small amount of base-case efficiency to avoid a large failure under plausible demand shifts.

14. ATM location and ATM replenishment are coupled but separate

Placing an ATM changes withdrawal demand and replenishment logistics. A remote ATM can improve access but cost more to service and require a larger safety stock because refill lead time is longer.

The correct architecture is:

location model → predicted demand by site → replenishment model → operating cost feedback → location model.

See How Banks Forecast ATM Cash Demand and Replenishment.

15. Counterexample: the cheapest network can be infeasible

Suppose the unconstrained model closes three low-volume rural facilities and saves S$2 million per year. Average travel time rises only slightly because most customers live in the city.

Now add a minimum-access constraint for vulnerable and cash-dependent communities. The three closures create significant uncovered areas. The original “optimal” network was optimal only for the wrong objective.

Operations research does not remove value choices. It makes them explicit in the objective and constraints.

16. The facility-location pipeline

1. Define the services the network must provide.
2. Map demand nodes and service-specific weights.
3. Generate candidate sites and facility types.
4. Build travel-time/cost matrices.
5. Estimate site cost and capacity.
6. Map current own-network and competitor facilities.
7. Choose objective: distance, coverage, cost, revenue or multiobjective combination.
8. Add capacity, access, policy and resilience constraints.
9. Model cannibalisation and customer substitution.
10. Optimise the integer facility decision.
11. Stress alternative demand and outage scenarios.
12. Feed selected sites into queueing and cash-replenishment models.
13. Compare predicted with realised demand after changes.
14. Reoptimise when population, digital behaviour or access obligations change.

17. Failure modes

• Average-distance worship. Tail communities become invisible.
• Straight-line distance. Roads, transit and accessibility are ignored.
• One-facility-type assumption. Branch, ATM and hub are treated as equivalent.
• Unlimited capacity. A selected branch is assigned more demand than it can serve.
• Cannibalisation blindness. Shifted demand is counted as new demand.
• Digital-average fallacy. National digital adoption is applied uniformly to local communities.
• Single-scenario design. Long-lived facilities are optimised to one fragile forecast.
• False redundancy. Two sites share the same infrastructure dependency.

18. Diagnostics and falsifiers

• What is mean travel time? Median? 95th percentile? Maximum?
• Which communities become uncovered if one facility closes?
• How many demand nodes exceed the chosen travel threshold?
• Which new site mostly cannibalises existing own-network demand?
• Does a p-median solution differ materially from a maximal-covering solution?
• Which candidate facility becomes optimal only under one demand forecast?
• How does the solution change when vulnerable-community demand receives extra weight?
• Are ATM replenishment and branch queue costs consistent with the proposed network?

Suppose someone claims, “This network is optimal because it minimises total travel distance.” A falsifier is a solution with slightly greater total distance that satisfies a binding access, capacity or resilience requirement the first model violates. Optimality is always conditional on the objective and constraints.

19. Verification and update triggers

• compare predicted site demand with realised transactions;
• rebuild travel-time matrices after transport changes;
• measure actual customer switching and cannibalisation;
• monitor coverage metrics by community, not only network averages;
• re-run after major branch/ATM openings or closures;
• update digital-adoption and cash-demand assumptions;
• test outage scenarios and true dependency independence;
• review current access obligations before implementing network changes.

Research anchors

• Miliotis et al. — bank-branch location in a competitive environment.
• Xia et al. — banking facility-location optimisation.
• Ho & Ishii — Location and Competition in Retail Banking.
• FCA — Helping People Access Cash, updated 29 July 2026.
• FCA — PS24/8 Access to Cash.

The deeper lesson

Branch and ATM network design is a lesson in conditional optimality. p-Median minimises weighted distance. Covering models protect reach. Capacity makes geography meet queueing. Cannibalisation makes demand endogenous to the network. Resilience adds redundancy. Access rules add human constraints that a pure cost function can miss. The strongest model therefore does not claim “this is the best location.” It says “this network is best for this declared objective, under these demand assumptions and constraints—and here is the evidence that would make us choose differently.”

Educational note: This article explains public operations-research and banking-network concepts. It is not a recommendation about any bank’s actual branch/ATM network, investment advice, location advice or a statement about future facility closures.