Construction Site Selection
Uncapacitated Facility Location · NP-Hard
Site selection errors account for 15–25% of construction project cost overruns due to logistics inefficiency, labor access issues, and regulatory delays. Every quarter, a regional construction director must decide which candidate sites to activate for upcoming project portfolios. This is the Uncapacitated Facility Location Problem (UFLP) — NP-hard with a best known 1.488-approximation — where opening costs and travel distances to demand zones must be jointly minimized.
The Problem
Optimizing construction staging site placement across a metro region
You have 8 candidate construction staging sites across a metro region. Each site has a fixed annual lease cost ranging from €120K to €450K. You serve 15 demand zones (project clusters) with distance-dependent logistics costs. The question is: which sites to open so that total lease + logistics cost is minimized?
Opening too few sites concentrates risk and increases travel distances; opening too many wastes lease expenditure on underutilized facilities. The UFLP captures this tension precisely: a binary decision for each candidate site, with every demand zone assigned to the nearest open facility.
| Construction Domain | Mathematical Concept | In This Model |
|---|---|---|
| Staging Site | Facility | 8 candidate locations with fixed lease costs |
| Project Cluster | Demand Node | 15 demand zones generating logistics needs |
| Annual Lease | Fixed Cost fi | €120K–€450K per site per year |
| Transport Distance | Assignment Cost cij | Distance-weighted logistics cost |
| Open / Close | Binary Decision xi | yi ∈ {0, 1} for each site |
where S ⊆ {1, …, m} // set of open facilities
yi ∈ {0, 1} // binary open/close decision for each site
// each demand zone j served by nearest open facility in S
Where fi is the fixed cost of opening site i, cij is the cost of serving demand zone j from site i, and yi indicates whether site i is opened.
See full Facility Location theory and all algorithmsTry It Yourself
Select construction staging sites to minimize total cost
Site Selection Optimizer
8 Sites · 15 ZonesReady. Click “Solve & Compare All Algorithms” to run.
| Algorithm | Sites Open | Total Cost | Time |
|---|
The Algorithms
Heuristic and metaheuristic approaches to facility location
Greedy Add
O(m²n)Start with no facilities open. Iteratively evaluate each closed facility and open the one whose addition most reduces total cost (fixed cost increase minus assignment cost decrease). Repeat until no further improvement is possible. Simple and effective for moderate-size instances, but may miss globally optimal combinations.
Greedy Drop
O(m²n)Start with all facilities open. Iteratively evaluate each open facility and close the one whose removal least increases total cost (fixed cost savings minus assignment cost increase). Repeat until no further improvement is possible. Tends to produce solutions with fewer open facilities and can complement Greedy Add results.
Simulated Annealing
O(T · m · n) | T = cooling stepsExplore the solution space by toggling facilities open/closed or swapping an open facility for a closed one. Accept improvements immediately; accept worse solutions with a probability that decreases as the “temperature” cools. This allows escape from local optima and often finds near-optimal solutions for NP-hard location problems.
Key References
Foundational works in facility location
- (1977). “Location of bank accounts to optimize float.” Management Science, 23(8), 789–810.
- (2013). “A 1.488 approximation algorithm for the uncapacitated facility location problem.” Information and Computation, 222, 45–58.
- (1983). “The simple plant location problem: Survey and synthesis.” European Journal of Operational Research, 12(1), 36–81.
Need to optimize your site selection?
From facility location to supply chain design and logistics optimization, mathematical modeling can transform your construction operations. Let’s discuss how Operations Research can work for you.