Vehicle Routing Solver

2. VRP with Time Windows (VRPTW)

def solve_vrptw(distance_matrix, time_matrix, time_windows,
                demands, vehicle_capacities, depot=0):
    """
    Solve VRP with Time Windows
    """
    manager = pywrapcp.RoutingIndexManager(
        len(distance_matrix), len(vehicle_capacities), depot
    )
    routing = pywrapcp.RoutingModel(manager)

    # Distance callback
    def distance_callback(from_index, to_index):
        from_node = manager.IndexToNode(from_index)
        to_node = manager.IndexToNode(to_index)
        return distance_matrix[from_node][to_node]

    transit_callback_index = routing.RegisterTransitCallback(distance_callback)
    routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)

    # Time dimension with time windows
    def time_callback(from_index, to_index):
        from_node = manager.IndexToNode(from_index)
        to_node = manager.IndexToNode(to_index)
        return time_matrix[from_node][to_node]

    time_callback_index = routing.RegisterTransitCallback(time_callback)

    routing.AddDimension(
        time_callback_index,
        30,  # allow waiting time
        480,  # max time per vehicle (8 hours)
        False,
        'Time'
    )

    time_dimension = routing.GetDimensionOrDie('Time')

    # Add time window constraints
    for location_idx, (early, late) in enumerate(time_windows):
        if location_idx == depot:
            continue
        index = manager.NodeToIndex(location_idx)
        time_dimension.CumulVar(index).SetRange(early, late)

    # Minimize total time
    for i in range(len(vehicle_capacities)):
        routing.AddVariableMinimizedByFinalizer(
            time_dimension.CumulVar(routing.Start(i))
        )
        routing.AddVariableMinimizedByFinalizer(
            time_dimension.CumulVar(routing.End(i))
        )

    # Solve
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC
    )

    solution = routing.SolveWithParameters(search_parameters)
    return extract_routes_with_times(manager, routing, solution, time_dimension)

3. Multi-Depot VRP

def solve_multi_depot_vrp(distance_matrix, demands, depots,
                          vehicles_per_depot, vehicle_capacity):
    """
    Solve VRP with multiple depots
    """
    num_vehicles = sum(vehicles_per_depot)

    # Create start and end indices for each vehicle
    starts = []
    ends = []
    for depot_idx, depot in enumerate(depots):
        for _ in range(vehicles_per_depot[depot_idx]):
            starts.append(depot)
            ends.append(depot)

    manager = pywrapcp.RoutingIndexManager(
        len(distance_matrix), num_vehicles, starts, ends
    )
    routing = pywrapcp.RoutingModel(manager)

    # ... add callbacks and constraints

    return routing

4. Pickup and Delivery

def solve_pdp(distance_matrix, pickups_deliveries, vehicle_capacities):
    """
    Solve Pickup and Delivery Problem
    pickups_deliveries: list of (pickup_node, delivery_node)
    """
    manager = pywrapcp.RoutingIndexManager(
        len(distance_matrix), len(vehicle_capacities), 0
    )
    routing = pywrapcp.RoutingModel(manager)

    # Add pickup and delivery constraints
    for pickup, delivery in pickups_deliveries:
        pickup_index = manager.NodeToIndex(pickup)
        delivery_index = manager.NodeToIndex(delivery)
        routing.AddPickupAndDelivery(pickup_index, delivery_index)
        routing.solver().Add(
            routing.VehicleVar(pickup_index) ==
            routing.VehicleVar(delivery_index)
        )
        routing.solver().Add(
            routing.CumulVar(pickup_index, 'Distance') <=
            routing.CumulVar(delivery_index, 'Distance')
        )

    return routing

5. Route Visualization

def visualize_routes(routes, locations, output_file='routes.html'):
    """
    Generate interactive route map
    """
    import folium

    # Create map centered on locations
    center_lat = sum(loc[0] for loc in locations) / len(locations)
    center_lon = sum(loc[1] for loc in locations) / len(locations)

    m = folium.Map(location=[center_lat, center_lon], zoom_start=12)

    colors = ['red', 'blue', 'green', 'purple', 'orange']

    for route_idx, route in enumerate(routes):
        color = colors[route_idx % len(colors)]

        # Add route line
        route_coords = [locations[node] for node in route]
        folium.PolyLine(route_coords, color=color, weight=3).add_to(m)

        # Add markers
        for stop_idx, node in enumerate(route):
            folium.Marker(
                locations[node],
                popup=f"Route {route_idx}, Stop {stop_idx}",
                icon=folium.Icon(color=color)
            ).add_to(m)

    m.save(output_file)
    return output_file

Process Integration

This skill integrates with the following processes:

• transportation-route-optimization.js
• warehouse-layout-slotting-optimization.js

Output Format

{
  "problem_type": "VRPTW",
  "status": "optimal",
  "total_distance": 1523,
  "total_time": 420,
  "routes": [
    {
      "vehicle_id": 0,
      "route": [0, 3, 5, 2, 0],
      "distance": 450,
      "load": 85,
      "arrival_times": [0, 45, 90, 150, 200],
      "departure_times": [0, 55, 105, 165, 200]
    }
  ],
  "unserved_customers": [],
  "metrics": {
    "vehicle_utilization": 0.85,
    "time_window_violations": 0
  }
}

Tools/Libraries

Best Practices

1. Use realistic distances - Consider actual road networks
2. Account for service times - Loading/unloading duration
3. Balance routes - Fair workload distribution
4. Handle uncertainties - Buffer time windows
5. Iterate on solutions - Use warm starts
6. Validate feasibility - Check all constraints

Constraints

• Respect vehicle capacity limits
• Honor customer time windows
• Consider driver regulations (breaks, max hours)
• Document all routing assumptions