Heterogeneous Fleet VRP (HFVRP)

Unlike the Capacitated VRP (CVRP), where a single capacity limit applies, HFVRP manages a vector of distinct capacities. Each vehicle type k has its own weight limit (e.g., 1,500 kg vs. 3,500 kg) and volumetric constraint.

• Assignment Logic: A route's cumulative demand cannot exceed the specific capacity of the assigned vehicle type.
• Implication: The solver cannot simply fill routes; it must match high-demand clusters to high-capacity vehicles to avoid costly under-utilization.

The objective function in HFVRP is more complex because both fixed acquisition costs and variable distance costs differ per vehicle type.

• Fixed Costs: A heavy goods vehicle incurs a higher daily depreciation or rental cost than a sprinter van.
• Variable Costs: Fuel consumption per kilometer varies significantly. A solver might select a vehicle with a higher fixed cost but lower per-mile cost for a long-distance rural route.
• Trade-off: Optimizing for total cost requires balancing these two competing financial dimensions.

Beyond weight, physical dimensional compatibility becomes a hard constraint. A vehicle's physical dimensions must be compatible with the access restrictions of the delivery points.

• Physical Access: A 40-ton articulated truck cannot legally or physically navigate a narrow residential cul-de-sac.
• Equipment Compatibility: Specific vehicles may lack required equipment like tail lifts, refrigeration units, or hazardous material placards.
• Regulatory Compliance: Vehicle types may have different speed governors or regional access permits, directly impacting feasible travel times.

HFVRP formulations are categorized by fleet availability, which drastically changes the optimization strategy.

• Fixed Fleet (HFVRP-FF): The solver must use exactly the available vehicles in the current yard. This is a pure assignment problem—if a vehicle type is exhausted, routes must adapt to the remaining types.
• Unlimited Fleet (HFVRP-UF): The solver can recommend an ideal fleet composition. This functions as a strategic procurement tool, identifying the optimal mix of vehicle types to lease or purchase for a given demand profile.

In multi-depot extensions (MDHFVRP), not every vehicle type is compatible with every depot. Originating constraints add a spatial dimension to fleet assignment.

• Infrastructure Limits: A depot may lack the maintenance bays or fueling infrastructure (e.g., CNG, electric charging) for specific vehicle types.
• Zoning Restrictions: Certain vehicle types might be restricted to specific geographic zones radiating from a particular depot.
• Deadheading Costs: The solver must account for the non-revenue-generating distance a specialized vehicle must travel from its home depot to the start of its assigned route.

Vehicle types often have distinct average travel speeds due to physical dynamics, not just road limits, which interacts critically with time windows (VRPTW).

• Acceleration Profiles: Heavy trucks accelerate slower than vans, impacting travel times in urban stop-and-go traffic.
• Congestion Interaction: A route feasible for a nimble scooter within a 15-minute window might be impossible for a van due to parking and walking time overhead.
• Unified Constraint: The solver must verify that the arrival time, calculated using the specific vehicle's speed profile, falls within the customer's hard time window.