i want to add a constraint to the OR-Tools Pickup and delivery problem

Question

I need to modify the sample code on the website so that each delivery must be completed before a new pick up for example for [1,5] [2,6] it should be that 1>5>2>6, how would i add this constraint or modify the code please? this is the available code:

"""Simple Pickup Delivery Problem (PDP)."""

from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp

def create_data_model():
    """Stores the data for the problem."""
    data = {}
    data["distance_matrix"] = [
        # fmt: off
        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
        [0, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016, 868, 1210],
        [0, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788, 1552, 754],
        [0, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164, 560, 1358],
        [0, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050, 674, 1244],
        [0, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514, 1050, 708],
        [0, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514, 1278, 480],
        [0, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662, 742, 856],
        [0, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320, 1084, 514],
        [0, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274, 810, 468],
        [0, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388, 1152, 354],
        [0, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650, 274, 844],
        [0, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536, 388, 730],
        [0, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342, 422, 536],
        [0, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342, 0, 764, 194],
        [0, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388, 422, 764, 0, 798],
        [0, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730, 536, 194, 798, 0],
        # fmt: on
    ]
    data["pickups_deliveries"] = [
        [1, 6],
        [2, 10],
        [4, 3],
        [5, 9],
        [7, 8],
        [15, 11],
        [13, 12],
        [16, 14],
        [1, 6],
    ]
    data["num_vehicles"] = 4
    data["depot"] = 0
    return data

def print_solution(data, manager, routing, solution):
    """Prints solution on console."""
    print(f"Objective: {solution.ObjectiveValue()}")
    total_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}m\n"
        print(plan_output)
        total_distance += route_distance
    print(f"Total Distance of all routes: {total_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)

    # Define cost of each arc.
    def distance_callback(from_index, to_index):
        """Returns the manhattan distance between the two nodes."""
        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)
    routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)

    # Add Distance constraint.
    dimension_name = "TotalDistance"
    routing.AddDimension(
        transit_callback_index,
        0,  # no slack
        3000,  # vehicle maximum travel distance
        True,  # start cumul to zero
        dimension_name,
    )
    distance_dimension = routing.GetDimensionOrDie(dimension_name)

    # Define Transportation Requests.
    for request in data["pickups_deliveries"]:
        pickup_index = manager.NodeToIndex(request[0])
        delivery_index = manager.NodeToIndex(request[1])
        routing.AddPickupAndDelivery(pickup_index, delivery_index)
        routing.solver().Add(
            routing.VehicleVar(pickup_index) == routing.VehicleVar(delivery_index)
        )
        routing.solver().Add(
            distance_dimension.CumulVar(pickup_index)
            <= distance_dimension.CumulVar(delivery_index)
        )

    # Penalty for empty vehicle travel
    empty_vehicle_penalty = 1000
    for vehicle_id in range(data["num_vehicles"]):
        index = routing.Start(vehicle_id)
        empty_travel_var = routing.VehicleVar(index)
        routing.solver().Add(
            distance_dimension.CumulVar(index) + empty_travel_var * empty_vehicle_penalty
            >= distance_dimension.CumulVar(index)
        )

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

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

    # Print solution on console.
    if solution:
        print_solution(data, manager, routing, solution)


if __name__ == "__main__":
    main()

Im stuck and dont know what to do

Answer 1

Just merge pickup and delivery nodes if they must always follow each other.

Answer 2

Another solution would be to limit vehicle capacity to one package.... i.e. :

• Add a new capacity dimension with:
• +1 for pickup, -1 at delivery node and
• and force_start_cumul at zero
• Set vehicle capacity to 1 (i.e. can only carry one package at a time)

e.g. https://github.com/google/or-tools/blob/main/ortools/constraint_solver/samples/vrp_capacity.py

If instead you want the last pickup package to be the first deliver (i.e. stack) you can use PD_LIFO policy e.g.: https://github.com/google/or-tools/blob/main/ortools/constraint_solver/docs/PDP.md https://github.com/google/or-tools/blob/main/ortools/constraint_solver/samples/vrp_pickup_delivery_lifo.py