What is CVRP?
The Capacitated Vehicle Routing Problem (CVRP) is a combinatorial optimization problem that determines the optimal set of routes for a fleet of vehicles to serve a set of customers. Each vehicle has a limited capacity, and each customer has a known demand.
In practical terms: given a warehouse, a fleet of trucks, and 50+ delivery stops, CVRP finds the cheapest way to deliver everything while respecting truck capacities and time windows.
Why Traditional Routing Falls Short
Many logistics operations still use manual routing or simple "nearest neighbor" heuristics. The problems:
- Suboptimal routes: Manual planners can't evaluate millions of route combinations
- Capacity waste: Trucks leave partially loaded or make unnecessary return trips
- Time window violations: Deliveries arrive outside customer-specified windows
- Driver imbalance: Some drivers are overloaded while others finish early
How AI Solves CVRP
Modern CVRP solvers use a combination of techniques:
Metaheuristics
- Adaptive Large Neighborhood Search (ALNS): Iteratively destroys and repairs portions of the solution
- Genetic Algorithms: Evolve a population of solutions through selection, crossover, and mutation
- Simulated Annealing: Accept worse solutions probabilistically to escape local optima
Constraint Handling
Real-world CVRP includes constraints beyond basic capacity:
- Time windows: Customer-specified delivery windows (e.g., 9am-12pm)
- Vehicle heterogeneity: Different truck types with different capacities and costs
- Multi-depot: Multiple starting warehouses
- Pickup and delivery: Combined pickup and delivery operations
- Driver working hours: Legal limits on driving time and mandatory breaks
Logistica's CVRP Solver
Our solver handles all the above constraints and optimizes for multiple objectives simultaneously:
Minimize: Total distance + Total time + Vehicle count
Subject to:
- Vehicle capacity ≤ max capacity
- Arrival time within customer time window
- Driver working hours ≤ legal limit
- All customers served exactly once
Performance Benchmarks
On standard CVRP benchmarks (Augerat, Christofides):
| Instance | Best Known | Logistica Solution | Gap |
|---|---|---|---|
| A-n32-k5 | 784 | 787 | 0.4% |
| A-n54-k7 | 1167 | 1174 | 0.6% |
| A-n80-k10 | 1763 | 1781 | 1.0% |
On real-world instances with 38 shipments across 5 vehicles, our solver achieved a 31% cost reduction compared to manual routing.
Implementation with Logistica
Step 1: Define Your Fleet
Input vehicle types, capacities, cost per km, and home depots.
Step 2: Import Shipments
Upload delivery addresses, volumes, weights, and time windows.
Step 3: Optimize
Click "Optimize Routes" — the solver runs in under 60 seconds for fleets up to 200 vehicles and 1000 stops.
Step 4: Dispatch
Send optimized routes directly to driver mobile apps with turn-by-turn navigation.
Cost Savings Calculator
A typical fleet of 20 vehicles serving 100 daily stops can expect:
- Distance reduction: 20-30% (less fuel, less wear)
- Vehicle reduction: 15-25% (serve same stops with fewer trucks)
- Time savings: 2-3 hours per driver per day
- Annual savings: $50,000-150,000 depending on fleet size
Getting Started
Route optimization delivers the fastest ROI of any logistics technology investment. Most clients see payback within the first month.
Request a demo to see how CVRP optimization can transform your delivery operations.
