Facility Location Strategy: Network Design Optimization

Capacitated Facility Location Problem with Coverage and Cost Trade-offs

📚 Learning Objectives

Formulate the capacitated facility location problem (CFLP) as a mixed-integer linear program with fixed and variable costs

Analyze the trade-off between facility fixed costs, transportation costs, and service coverage requirements

Apply greedy and optimization heuristics to determine which facilities to open from a set of candidates

Evaluate network designs using metrics like coverage, utilization, and total cost efficiency

⚙️ Network Parameters

Facility Fixed Cost ($K/year)

$50K $200K $500K

Transport Cost ($/unit-km)

$1 $5 $20

Facility Capacity (units/year)

100 500 units 1000

Max Service Distance (km)

50 150 km 300

CFLP Formulation

min Σⱼ fⱼyⱼ + Σᵢ Σⱼ cᵢⱼxᵢⱼ
s.t. Σⱼ xᵢⱼ = dᵢ, ∀i
Σᵢ xᵢⱼ ≤ Kⱼyⱼ, ∀j
yⱼ ∈ {0,1}, xᵢⱼ ≥ 0

MIP Network Design Capacitated Coverage

Demand Point

Open Facility

Candidate Site

📍

Demand Points

🏭

Open Facilities

📦

Total Demand

✅

Coverage

💰

Total Cost

📊 Facility Utilization

💰 Cost Breakdown

🏭 Facilities

Click "Generate" to create scenario

📊 Network Metrics

Fixed Cost Total $0

Transport Cost Total $0

Avg. Utilization 0%

Uncovered Demand 0

Avg. Service Distance 0 km

💡 Strategic Insights

📌 Generate a scenario or click on the map to add demand points and candidate facilities.

🎯 Key Managerial Insights

Fixed vs. Variable Cost Trade-off

Opening fewer facilities reduces fixed costs but increases transportation costs and may reduce service levels. The optimal network balances these competing factors based on demand density and cost structure.

Coverage vs. Efficiency

100% coverage often requires disproportionate investment in low-demand areas. Strategic under-coverage of marginal customers can significantly reduce total costs while maintaining high average service levels.

Capacity Utilization Balance

High utilization maximizes asset efficiency but leaves no buffer for demand variability. The optimal utilization target depends on demand uncertainty and the cost of stockouts or delayed service.

📚 Academic References

Daskin, M. S. (2013). Network and Discrete Location: Models, Algorithms, and Applications (2nd ed.). Wiley. • Mirchandani, P. B., & Francis, R. L. (1990). Discrete Location Theory. Wiley-Interscience. • Simchi-Levi, D., Chen, X., & Bramel, J. (2014). The Logic of Logistics (3rd ed.). Springer. • Klose, A., & Drexl, A. (2005). Facility location models for distribution system design. European Journal of Operational Research, 162(1), 4-29.