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Spatial Network Optimization

Definition

Spatial network optimization selects routes, locations, or flows on a network to minimize cost or maximize service while respecting capacity, demand, and policy constraints. Problems include shortest paths with time windows, vehicle routing with pickups and deliveries, facility location-allocation, maximum coverage with travel time budgets, and flow assignment that balances congestion. Inputs combine street graphs, travel-time profiles, fleet characteristics, depot hours, and service-level targets. Solvers range from exact mixed-integer programming to heuristics and metaheuristics (savings, tabu search, genetic algorithms) for large instances.

Application

Logistics companies design daily delivery tours; emergency services place ambulances; utilities schedule inspection crews; school districts optimize bus routes; and humanitarian organizations plan last-mile relief distribution in changing road conditions. Because reality is noisy, robust optimization and rapid re-optimization after disruptions are as valuable as the initial plan.

FAQ

How do you incorporate stochastic travel times and service durations?

Use distributions for links and stops, simulate with Monte Carlo or chance constraints, and select plans that meet on-time performance with high probability rather than only in the mean case.

What is the difference between p-median and maximum coverage facility problems?

P-median minimizes average travel distance to facilities; maximum coverage maximizes the population within a service threshold given a fixed number of sites. They answer different policy questions—efficiency versus equity of access.

How do road restrictions and curb rules change optimal routes in dense cities?

Incorporate loading zones, turn restrictions, and time-dependent speeds; add penalties for dwell-time violations. Including curb data often flips the attractiveness of certain corridors compared with speed-only models.

What metrics should be tracked post-implementation?

On-time rate, route adherence, stop sequence deviations, overtime hours, and customer satisfaction. Continuous comparison to the digital plan reveals where assumptions need updating.