I have a distance matrix with first row and column set to zeros. I try to run the code provided on the VRP website (Or-Tools) and it provides me with the following solution. This is obviously not the correct solution since a vehicle cannot hit all the places with a total distance of 0m.

def create_data_model():
    """Stores the data for the problem."""
    data = {}
    data["distance_matrix"] = [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
                                [0.0, 0.0, 14.0, 201.0, 154.0, 154.0],
                                [0.0, 46.0, 0.0, 165.0, 118.0, 118.0],
                                [0.0, 70.0, 54.0, 0.0, 110.0, 110.0],
                                [0.0, 24.0, 26.0, 187.0, 0.0, 140.0],
                                [0.0, 28.0, 0.0, 199.0, 152.0, 0.0]]
    data["num_vehicles"] = 3
    data["depot"] = 0
    return data

def print_solution(data, manager, routing, solution):
    """Prints solution on console."""
    print(f"Objective: {solution.ObjectiveValue()}")
    max_route_distance = 0
    for vehicle_id in range(data["num_vehicles"]):
        index = routing.Start(vehicle_id)
        plan_output = f"Route for vehicle {vehicle_id}:n"
        route_distance = 0
        while not routing.IsEnd(index):
            plan_output += f" {manager.IndexToNode(index)} -> "
            previous_index = index
            index = solution.Value(routing.NextVar(index))
            route_distance += routing.GetArcCostForVehicle(
                previous_index, index, vehicle_id
            )
        plan_output += f"{manager.IndexToNode(index)}n"
        plan_output += f"Distance of the route: {route_distance}mn"
        print(plan_output)
        max_route_distance = max(route_distance, max_route_distance)
    print(f"Maximum of the route distances: {max_route_distance}m")

def main():
    """Entry point of the program."""
    # Instantiate the data problem.
    data = create_data_model()

    # Create the routing index manager.
    manager = pywrapcp.RoutingIndexManager(
        len(data["distance_matrix"]), data["num_vehicles"], data["depot"]
    )

    # Create Routing Model.
    routing = pywrapcp.RoutingModel(manager)

    # Create and register a transit callback.
    def distance_callback(from_index, to_index):
        """Returns the distance between the two nodes."""
        # Convert from routing variable Index to distance matrix NodeIndex.
        from_node = manager.IndexToNode(from_index)
        to_node = manager.IndexToNode(to_index)
        return data["distance_matrix"][from_node][to_node]

    transit_callback_index = routing.RegisterTransitCallback(distance_callback)

    # Define cost of each arc.
    routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)

    # Add Distance constraint.
    dimension_name = "Distance"
    routing.AddDimension(
        transit_callback_index,
        0,  # no slack
        5000,  # vehicle maximum travel distance
        True,  # start cumul to zero
        dimension_name,
    )
    distance_dimension = routing.GetDimensionOrDie(dimension_name)
    distance_dimension.SetGlobalSpanCostCoefficient(100)

    # Setting first solution heuristic.
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC
    )

    # Solve the problem.
    solution = routing.SolveWithParameters(search_parameters)

    # Print solution on console.
    if solution:
        print_solution(data, manager, routing, solution)
    else:
        print("No solution found !")

I tried changing the vehicle maximum travel distance and global span coefficient. I get the following solution.

Objective: 0
Route for vehicle 0:
 0 -> 0
Distance of the route: 0m

Route for vehicle 1:
 0 -> 0
Distance of the route: 0m

Route for vehicle 2:
 0 ->  5 ->  4 ->  3 ->  2 ->  1 -> 0
Distance of the route: 0m

Maximum of the route distances: 0m