Network Design: The Facility Location Problem
Where to locate warehouses? The quantitative trade-off between proximity and scale, responsiveness and efficiency.
The Geography of Cost
Every facility in a supply chain network adds cost and reduces distance. More facilities mean higher fixed costs but lower variable costs. Fewer facilities mean economies of scale but longer last-mile delivery.
The facility location problem finds the optimal number, size, and location of facilities to serve demand at minimum total cost.
The Cost Trade-Offs
Fixed Costs (scale with facility count):
- Facility construction or lease
- Equipment and automation
- Management and administrative staff
- Systems and technology
Variable Costs (scale with throughput):
- Labor for receiving, storage, picking, shipping
- Utilities, maintenance, consumables
- Inventory carrying cost
Transportation Costs (scale with distance):
- Inbound from suppliers
- Outbound to customers
- Inter-facility transfers
The Mathematical Formulation
Minimize: Total Cost = Σ(Fixed Costs) + Σ(Variable Costs) + Σ(Transportation Costs)
Subject to:
- Service level constraints (delivery time, coverage)
- Capacity constraints (throughput, storage)
- Demand satisfaction (all demand met)
The problem is NP-hard. Exact solutions are impossible for large networks. Heuristics and optimization solvers find near-optimal solutions.
The Classic Models
Continuous models — facilities can locate anywhere. Center-of-gravity method finds weighted average location by demand.
Discrete models — facilities must locate at candidate sites. Mixed-integer programming selects optimal subset.
Capacitated models — facilities have throughput limits. Multiple facilities serve high-demand regions.
Multi-echelon models — distribution centers feed regional warehouses. Hierarchical optimization by tier.
The Center-of-Gravity Example
Three markets:
- Chicago: 1,000 units, coordinates (41.9, -87.6)
- Dallas: 800 units, coordinates (32.8, -96.8)
- Atlanta: 600 units, coordinates (33.7, -84.4)
Optimal DC location:
- Latitude = (1,000×41.9 + 800×32.8 + 600×33.7) / 2,400 = 36.4
- Longitude = (1,000×-87.6 + 800×-96.8 + 600×-84.4) / 2,400 = -90.3
Near Memphis, Tennessee. The math reveals what intuition misses.
The Impact of Facility Count
| Facilities | Fixed Cost | Transport Cost | Total Cost | Service Level |
|---|---|---|---|---|
| 1 | Low | High | Moderate | Poor |
| 3 | Moderate | Moderate | Low | Good |
| 5 | High | Low | Moderate | Excellent |
| 10 | Very High | Very Low | High | Excellent |
The optimal number balances fixed cost against transportation savings. Diminishing returns set in as facilities proliferate.
Service Level Constraints
Customer expectations limit design options:
Same-day delivery — requires facilities within 50 miles of demand. High facility count, high fixed cost.
Next-day delivery — allows facilities within 300 miles. Moderate count, moderate cost.
2-3 day delivery — national distribution from 2-3 facilities. Low count, low cost, low responsiveness.
The network must deliver the service level profitably. Premium service requires premium pricing or premium efficiency.
Dynamic Network Design
Static optimization assumes stable demand. Reality changes.
Growth markets — add facilities ahead of demand, or serve expensively from distance until volume justifies investment.
Declining markets — consolidate facilities, absorb fixed cost increases, or exit.
Seasonality — temporary capacity through 3PL partnerships, not permanent facilities.
Disruption — redundant capacity, alternative sourcing, flexible network structure.
The Total Cost Equation
Complete network cost includes:
Operating costs — labor, utilities, maintenance, inventory Transportation costs — inbound, outbound, inter-facility Working capital — inventory positioned across network Risk costs — single points of failure, concentration exposure Administrative costs — complexity management, coordination overhead
Optimization minimizes the sum, not any single component.
The Implementation Reality
> The optimal network on paper is not optimal if it cannot be executed.
Labor availability — facilities require workers. Rural locations have land, not labor.
Transportation access — highways, rail, ports, airports. Infrastructure enables or constrains.
Regulatory environment — taxes, incentives, zoning, environmental rules. Location decisions are political.
Supplier proximity — inbound costs matter. Being close to customers far from suppliers is expensive.
The Bottom Line
Network design is strategic. Facilities last decades. Mistakes are expensive to correct.
The quantitative approach:
- Models total cost, not transportation alone
- Optimizes for service level constraints, not despite them
- Tests sensitivity to demand scenarios
- Incorporates execution feasibility
The best networks are not theoretically optimal. They are robust, adaptable, and executable.
The math provides the starting point. Judgment completes the design.
> Proximity costs money. Distance costs money. The optimal network finds the minimum of the sum.
Published by IMI Lab. Exploring technology-driven supply chains.