Định tuyến xe bằng phương thức đến lấy hàng và giao hàng

Trong phần này, chúng tôi mô tả một VRP, trong đó mỗi chiếc xe đến lấy hàng tại vị trí khác nhau và thả chúng tại những địa điểm khác. Vấn đề là chỉ định tuyến đường cho những chiếc xe đến lấy và giao tất cả các mặt hàng, đồng thời giảm thiểu độ dài của tuyến đường dài nhất.

Ví dụ về VRP với hoạt động đến lấy hàng và giao hàng

Sơ đồ dưới đây thể hiện các vị trí đến lấy hàng và giao hàng trên một lưới tương tự với tham số trong ví dụ về VRP trước đó. Đối với mỗi có một cạnh hướng từ vị trí nhận hàng đến vị trí giao hàng.

Giải ví dụ bằng OR-Tools

Các phần sau đây mô tả cách xử lý VRP bằng phương thức đến lấy hàng và giao hàng của Google. Phần lớn mã được vay từ ví dụ về VRP trước đó, vì vậy chúng tôi sẽ tập trung vào những phần mới.

Tạo dữ liệu

Dữ liệu của bài toán này bao gồm cả ma trận khoảng cách từ VRP trước đó ví dụ: cùng với danh sách các cặp địa điểm đến lấy hàng và giao hàng, data['pickups_deliveries'], tương ứng với các cạnh được định hướng trong biểu đồ ở trên. Mã dưới đây xác định vị trí đến lấy hàng và giao hàng.

Python

    data["pickups_deliveries"] = [
        [1, 6],
        [2, 10],
        [4, 3],
        [5, 9],
        [7, 8],
        [15, 11],
        [13, 12],
        [16, 14],
    ]

C++

  const std::vector<std::vector<RoutingIndexManager::NodeIndex>>
      pickups_deliveries{
          {RoutingIndexManager::NodeIndex{1},
           RoutingIndexManager::NodeIndex{6}},
          {RoutingIndexManager::NodeIndex{2},
           RoutingIndexManager::NodeIndex{10}},
          {RoutingIndexManager::NodeIndex{4},
           RoutingIndexManager::NodeIndex{3}},
          {RoutingIndexManager::NodeIndex{5},
           RoutingIndexManager::NodeIndex{9}},
          {RoutingIndexManager::NodeIndex{7},
           RoutingIndexManager::NodeIndex{8}},
          {RoutingIndexManager::NodeIndex{15},
           RoutingIndexManager::NodeIndex{11}},
          {RoutingIndexManager::NodeIndex{13},
           RoutingIndexManager::NodeIndex{12}},
          {RoutingIndexManager::NodeIndex{16},
           RoutingIndexManager::NodeIndex{14}},
      };

Java

    public final int[][] pickupsDeliveries = {
        {1, 6},
        {2, 10},
        {4, 3},
        {5, 9},
        {7, 8},
        {15, 11},
        {13, 12},
        {16, 14},
    };

C#

        public int[][] PickupsDeliveries = {
            new int[] { 1, 6 }, new int[] { 2, 10 },  new int[] { 4, 3 },   new int[] { 5, 9 },
            new int[] { 7, 8 }, new int[] { 15, 11 }, new int[] { 13, 12 }, new int[] { 16, 14 },
        };

Đối với mỗi cặp, mục đầu tiên là chỉ mục của vị trí đến lấy hàng, còn mục thứ hai là chỉ mục của vị trí giao hàng.

Xác định yêu cầu đến lấy hàng và giao hàng

Mã sau đây xác định yêu cầu đến lấy hàng và giao hàng bằng cách sử dụng tính năng đến lấy hàng và địa điểm giao hàng tại data['pickups_deliveries'].

Python

    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)
        )

C++

  Solver* const solver = routing.solver();
  for (const auto& request : data.pickups_deliveries) {
    const int64_t pickup_index = manager.NodeToIndex(request[0]);
    const int64_t delivery_index = manager.NodeToIndex(request[1]);
    routing.AddPickupAndDelivery(pickup_index, delivery_index);
    solver->AddConstraint(solver->MakeEquality(
        routing.VehicleVar(pickup_index), routing.VehicleVar(delivery_index)));
    solver->AddConstraint(
        solver->MakeLessOrEqual(distance_dimension->CumulVar(pickup_index),
                                distance_dimension->CumulVar(delivery_index)));
  }

Java

    Solver solver = routing.solver();
    for (int[] request : data.pickupsDeliveries) {
      long pickupIndex = manager.nodeToIndex(request[0]);
      long deliveryIndex = manager.nodeToIndex(request[1]);
      routing.addPickupAndDelivery(pickupIndex, deliveryIndex);
      solver.addConstraint(
          solver.makeEquality(routing.vehicleVar(pickupIndex), routing.vehicleVar(deliveryIndex)));
      solver.addConstraint(solver.makeLessOrEqual(
          distanceDimension.cumulVar(pickupIndex), distanceDimension.cumulVar(deliveryIndex)));
    }

C#

        Solver solver = routing.solver();
        for (int i = 0; i < data.PickupsDeliveries.GetLength(0); i++)
        {
            long pickupIndex = manager.NodeToIndex(data.PickupsDeliveries[i][0]);
            long deliveryIndex = manager.NodeToIndex(data.PickupsDeliveries[i][1]);
            routing.AddPickupAndDelivery(pickupIndex, deliveryIndex);
            solver.Add(solver.MakeEquality(routing.VehicleVar(pickupIndex), routing.VehicleVar(deliveryIndex)));
            solver.Add(solver.MakeLessOrEqual(distanceDimension.CumulVar(pickupIndex),
                                              distanceDimension.CumulVar(deliveryIndex)));
        }

Đối với mỗi cặp, lệnh routing.AddPickupAndDelivery(pickup_index, delivery_index) tạo một yêu cầu đến lấy hàng và yêu cầu giao hàng cho một mặt hàng.

Dòng sau đây bổ sung yêu cầu rằng bạn phải nhận từng mặt hàng và do chính chiếc xe đó cung cấp.

routing.solver().Add(
            routing.VehicleVar(pickup_index) ==
            routing.VehicleVar(delivery_index))

Cuối cùng, chúng tôi bổ sung một yêu cầu rõ ràng là người dùng phải nhận từng mặt hàng trước khi phân phối. Để làm được điều đó, chúng tôi yêu cầu quãng đường tích luỹ của xe tại vị trí đến lấy hàng của mặt hàng tối đa là quãng đường tích luỹ tại vị trí giao hàng.

routing.solver().Add(
            distance_dimension.CumulVar(pickup_index) <=
            distance_dimension.CumulVar(delivery_index))

Chạy chương trình

Chương trình hoàn chỉnh của VRP (bao gồm cả phương thức đến lấy hàng và giao hàng) được trình bày trong phần tiếp theo. Khi bạn chạy, chương trình sẽ hiển thị các tuyến sau.

Objective: 226116
Route for vehicle 0:
 0 ->  13 ->  15 ->  11 ->  12 -> 0
Distance of the route: 1552m

Route for vehicle 1:
 0 ->  5 ->  2 ->  10 ->  16 ->  14 ->  9 -> 0
Distance of the route: 2192m

Route for vehicle 2:
 0 ->  4 ->  3 -> 0
Distance of the route: 1392m

Route for vehicle 3:
 0 ->  7 ->  1 ->  6 ->  8 -> 0
Distance of the route: 1780m

Total Distance of all routes: 6916m

Biểu đồ dưới đây minh hoạ các tuyến đường:

Hoàn tất chương trình

Dưới đây là các chương trình hoàn chỉnh.

Python

"""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, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354, 468, 776, 662],
      [548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016, 868, 1210],
      [776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788, 1552, 754],
      [696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164, 560, 1358],
      [582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050, 674, 1244],
      [274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514, 1050, 708],
      [502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514, 1278, 480],
      [194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662, 742, 856],
      [308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320, 1084, 514],
      [194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274, 810, 468],
      [536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388, 1152, 354],
      [502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650, 274, 844],
      [388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536, 388, 730],
      [354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342, 422, 536],
      [468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342, 0, 764, 194],
      [776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388, 422, 764, 0, 798],
      [662, 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],
    ]
    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."""
        # 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)
    routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)

    # Add Distance constraint.
    dimension_name = "Distance"
    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)
    distance_dimension.SetGlobalSpanCostCoefficient(100)

    # 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)
        )

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

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

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


if __name__ == "__main__":
    main()

C++

#include <cstdint>
#include <sstream>
#include <vector>

#include "ortools/constraint_solver/routing.h"
#include "ortools/constraint_solver/routing_enums.pb.h"
#include "ortools/constraint_solver/routing_index_manager.h"
#include "ortools/constraint_solver/routing_parameters.h"

namespace operations_research {
struct DataModel {
  const std::vector<std::vector<int64_t>> distance_matrix{
      {0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354, 468,
       776, 662},
      {548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674,
       1016, 868, 1210},
      {776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130,
       788, 1552, 754},
      {696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822,
       1164, 560, 1358},
      {582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708,
       1050, 674, 1244},
      {274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514,
       1050, 708},
      {502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514,
       1278, 480},
      {194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662,
       742, 856},
      {308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320,
       1084, 514},
      {194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274,
       810, 468},
      {536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730,
       388, 1152, 354},
      {502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308,
       650, 274, 844},
      {388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536,
       388, 730},
      {354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342,
       422, 536},
      {468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342,
       0, 764, 194},
      {776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388,
       422, 764, 0, 798},
      {662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730, 536,
       194, 798, 0},
  };
  const std::vector<std::vector<RoutingIndexManager::NodeIndex>>
      pickups_deliveries{
          {RoutingIndexManager::NodeIndex{1},
           RoutingIndexManager::NodeIndex{6}},
          {RoutingIndexManager::NodeIndex{2},
           RoutingIndexManager::NodeIndex{10}},
          {RoutingIndexManager::NodeIndex{4},
           RoutingIndexManager::NodeIndex{3}},
          {RoutingIndexManager::NodeIndex{5},
           RoutingIndexManager::NodeIndex{9}},
          {RoutingIndexManager::NodeIndex{7},
           RoutingIndexManager::NodeIndex{8}},
          {RoutingIndexManager::NodeIndex{15},
           RoutingIndexManager::NodeIndex{11}},
          {RoutingIndexManager::NodeIndex{13},
           RoutingIndexManager::NodeIndex{12}},
          {RoutingIndexManager::NodeIndex{16},
           RoutingIndexManager::NodeIndex{14}},
      };
  const int num_vehicles = 4;
  const RoutingIndexManager::NodeIndex depot{0};
};

//! @brief Print the solution.
//! @param[in] data Data of the problem.
//! @param[in] manager Index manager used.
//! @param[in] routing Routing solver used.
//! @param[in] solution Solution found by the solver.
void PrintSolution(const DataModel& data, const RoutingIndexManager& manager,
                   const RoutingModel& routing, const Assignment& solution) {
  int64_t total_distance{0};
  for (int vehicle_id = 0; vehicle_id < data.num_vehicles; ++vehicle_id) {
    int64_t index = routing.Start(vehicle_id);
    LOG(INFO) << "Route for Vehicle " << vehicle_id << ":";
    int64_t route_distance{0};
    std::stringstream route;
    while (!routing.IsEnd(index)) {
      route << manager.IndexToNode(index).value() << " -> ";
      const int64_t previous_index = index;
      index = solution.Value(routing.NextVar(index));
      route_distance += routing.GetArcCostForVehicle(previous_index, index,
                                                     int64_t{vehicle_id});
    }
    LOG(INFO) << route.str() << manager.IndexToNode(index).value();
    LOG(INFO) << "Distance of the route: " << route_distance << "m";
    total_distance += route_distance;
  }
  LOG(INFO) << "Total distance of all routes: " << total_distance << "m";
  LOG(INFO) << "";
  LOG(INFO) << "Advanced usage:";
  LOG(INFO) << "Problem solved in " << routing.solver()->wall_time() << "ms";
}

void VrpGlobalSpan() {
  // Instantiate the data problem.
  DataModel data;

  // Create Routing Index Manager
  RoutingIndexManager manager(data.distance_matrix.size(), data.num_vehicles,
                              data.depot);

  // Create Routing Model.
  RoutingModel routing(manager);

  // Define cost of each arc.
  const int transit_callback_index = routing.RegisterTransitCallback(
      [&data, &manager](const int64_t from_index,
                        const int64_t to_index) -> int64_t {
        // Convert from routing variable Index to distance matrix NodeIndex.
        const int from_node = manager.IndexToNode(from_index).value();
        const int to_node = manager.IndexToNode(to_index).value();
        return data.distance_matrix[from_node][to_node];
      });
  routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index);

  // Add Distance constraint.
  routing.AddDimension(transit_callback_index,  // transit callback
                       0,                       // no slack
                       3000,  // vehicle maximum travel distance
                       true,  // start cumul to zero
                       "Distance");
  RoutingDimension* distance_dimension =
      routing.GetMutableDimension("Distance");
  distance_dimension->SetGlobalSpanCostCoefficient(100);

  // Define Transportation Requests.
  Solver* const solver = routing.solver();
  for (const auto& request : data.pickups_deliveries) {
    const int64_t pickup_index = manager.NodeToIndex(request[0]);
    const int64_t delivery_index = manager.NodeToIndex(request[1]);
    routing.AddPickupAndDelivery(pickup_index, delivery_index);
    solver->AddConstraint(solver->MakeEquality(
        routing.VehicleVar(pickup_index), routing.VehicleVar(delivery_index)));
    solver->AddConstraint(
        solver->MakeLessOrEqual(distance_dimension->CumulVar(pickup_index),
                                distance_dimension->CumulVar(delivery_index)));
  }

  // Setting first solution heuristic.
  RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters();
  searchParameters.set_first_solution_strategy(
      FirstSolutionStrategy::PARALLEL_CHEAPEST_INSERTION);

  // Solve the problem.
  const Assignment* solution = routing.SolveWithParameters(searchParameters);

  // Print solution on console.
  PrintSolution(data, manager, routing, *solution);
}
}  // namespace operations_research

int main(int /*argc*/, char* /*argv*/[]) {
  operations_research::VrpGlobalSpan();
  return EXIT_SUCCESS;
}

Java

package com.google.ortools.constraintsolver.samples;
import com.google.ortools.Loader;
import com.google.ortools.constraintsolver.Assignment;
import com.google.ortools.constraintsolver.FirstSolutionStrategy;
import com.google.ortools.constraintsolver.RoutingDimension;
import com.google.ortools.constraintsolver.RoutingIndexManager;
import com.google.ortools.constraintsolver.RoutingModel;
import com.google.ortools.constraintsolver.RoutingSearchParameters;
import com.google.ortools.constraintsolver.Solver;
import com.google.ortools.constraintsolver.main;
import java.util.logging.Logger;

/** Minimal Pickup & Delivery Problem (PDP).*/
public class VrpPickupDelivery {
  private static final Logger logger = Logger.getLogger(VrpPickupDelivery.class.getName());

  static class DataModel {
    public final long[][] distanceMatrix = {
        {0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354, 468, 776, 662},
        {548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016, 868, 1210},
        {776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788, 1552, 754},
        {696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164, 560, 1358},
        {582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050, 674, 1244},
        {274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514, 1050, 708},
        {502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514, 1278, 480},
        {194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662, 742, 856},
        {308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320, 1084, 514},
        {194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274, 810, 468},
        {536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388, 1152, 354},
        {502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650, 274, 844},
        {388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536, 388, 730},
        {354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342, 422, 536},
        {468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342, 0, 764, 194},
        {776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388, 422, 764, 0, 798},
        {662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730, 536, 194, 798, 0},
    };
    public final int[][] pickupsDeliveries = {
        {1, 6},
        {2, 10},
        {4, 3},
        {5, 9},
        {7, 8},
        {15, 11},
        {13, 12},
        {16, 14},
    };
    public final int vehicleNumber = 4;
    public final int depot = 0;
  }

  /// @brief Print the solution.
  static void printSolution(
      DataModel data, RoutingModel routing, RoutingIndexManager manager, Assignment solution) {
    // Solution cost.
    logger.info("Objective : " + solution.objectiveValue());
    // Inspect solution.
    long totalDistance = 0;
    for (int i = 0; i < data.vehicleNumber; ++i) {
      long index = routing.start(i);
      logger.info("Route for Vehicle " + i + ":");
      long routeDistance = 0;
      String route = "";
      while (!routing.isEnd(index)) {
        route += manager.indexToNode(index) + " -> ";
        long previousIndex = index;
        index = solution.value(routing.nextVar(index));
        routeDistance += routing.getArcCostForVehicle(previousIndex, index, i);
      }
      logger.info(route + manager.indexToNode(index));
      logger.info("Distance of the route: " + routeDistance + "m");
      totalDistance += routeDistance;
    }
    logger.info("Total Distance of all routes: " + totalDistance + "m");
  }

  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    // Instantiate the data problem.
    final DataModel data = new DataModel();

    // Create Routing Index Manager
    RoutingIndexManager manager =
        new RoutingIndexManager(data.distanceMatrix.length, data.vehicleNumber, data.depot);

    // Create Routing Model.
    RoutingModel routing = new RoutingModel(manager);

    // Create and register a transit callback.
    final int transitCallbackIndex =
        routing.registerTransitCallback((long fromIndex, long toIndex) -> {
          // Convert from routing variable Index to user NodeIndex.
          int fromNode = manager.indexToNode(fromIndex);
          int toNode = manager.indexToNode(toIndex);
          return data.distanceMatrix[fromNode][toNode];
        });

    // Define cost of each arc.
    routing.setArcCostEvaluatorOfAllVehicles(transitCallbackIndex);

    // Add Distance constraint.
    routing.addDimension(transitCallbackIndex, // transit callback index
        0, // no slack
        3000, // vehicle maximum travel distance
        true, // start cumul to zero
        "Distance");
    RoutingDimension distanceDimension = routing.getMutableDimension("Distance");
    distanceDimension.setGlobalSpanCostCoefficient(100);

    // Define Transportation Requests.
    Solver solver = routing.solver();
    for (int[] request : data.pickupsDeliveries) {
      long pickupIndex = manager.nodeToIndex(request[0]);
      long deliveryIndex = manager.nodeToIndex(request[1]);
      routing.addPickupAndDelivery(pickupIndex, deliveryIndex);
      solver.addConstraint(
          solver.makeEquality(routing.vehicleVar(pickupIndex), routing.vehicleVar(deliveryIndex)));
      solver.addConstraint(solver.makeLessOrEqual(
          distanceDimension.cumulVar(pickupIndex), distanceDimension.cumulVar(deliveryIndex)));
    }

    // Setting first solution heuristic.
    RoutingSearchParameters searchParameters =
        main.defaultRoutingSearchParameters()
            .toBuilder()
            .setFirstSolutionStrategy(FirstSolutionStrategy.Value.PARALLEL_CHEAPEST_INSERTION)
            .build();

    // Solve the problem.
    Assignment solution = routing.solveWithParameters(searchParameters);

    // Print solution on console.
    printSolution(data, routing, manager, solution);
  }
}

C#

using System;
using System.Collections.Generic;
using Google.OrTools.ConstraintSolver;

/// <summary>
///   Minimal Pickup & Delivery Problem (PDP).
/// </summary>
public class VrpPickupDelivery
{
    class DataModel
    {
        public long[,] DistanceMatrix = {
            { 0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354, 468, 776, 662 },
            { 548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016, 868, 1210 },
            { 776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788, 1552, 754 },
            { 696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164, 560, 1358 },
            { 582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050, 674, 1244 },
            { 274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514, 1050, 708 },
            { 502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514, 1278, 480 },
            { 194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662, 742, 856 },
            { 308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320, 1084, 514 },
            { 194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274, 810, 468 },
            { 536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388, 1152, 354 },
            { 502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650, 274, 844 },
            { 388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536, 388, 730 },
            { 354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342, 422, 536 },
            { 468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342, 0, 764, 194 },
            { 776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388, 422, 764, 0, 798 },
            { 662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730, 536, 194, 798, 0 }
        };
        public int[][] PickupsDeliveries = {
            new int[] { 1, 6 }, new int[] { 2, 10 },  new int[] { 4, 3 },   new int[] { 5, 9 },
            new int[] { 7, 8 }, new int[] { 15, 11 }, new int[] { 13, 12 }, new int[] { 16, 14 },
        };
        public int VehicleNumber = 4;
        public int Depot = 0;
    };

    /// <summary>
    ///   Print the solution.
    /// </summary>
    static void PrintSolution(in DataModel data, in RoutingModel routing, in RoutingIndexManager manager,
                              in Assignment solution)
    {
        Console.WriteLine($"Objective {solution.ObjectiveValue()}:");

        // Inspect solution.
        long totalDistance = 0;
        for (int i = 0; i < data.VehicleNumber; ++i)
        {
            Console.WriteLine("Route for Vehicle {0}:", i);
            long routeDistance = 0;
            var index = routing.Start(i);
            while (routing.IsEnd(index) == false)
            {
                Console.Write("{0} -> ", manager.IndexToNode((int)index));
                var previousIndex = index;
                index = solution.Value(routing.NextVar(index));
                routeDistance += routing.GetArcCostForVehicle(previousIndex, index, 0);
            }
            Console.WriteLine("{0}", manager.IndexToNode((int)index));
            Console.WriteLine("Distance of the route: {0}m", routeDistance);
            totalDistance += routeDistance;
        }
        Console.WriteLine("Total Distance of all routes: {0}m", totalDistance);
    }

    public static void Main(String[] args)
    {
        // Instantiate the data problem.
        DataModel data = new DataModel();

        // Create Routing Index Manager
        RoutingIndexManager manager =
            new RoutingIndexManager(data.DistanceMatrix.GetLength(0), data.VehicleNumber, data.Depot);


        // Create Routing Model.
        RoutingModel routing = new RoutingModel(manager);

        // Create and register a transit callback.
        int transitCallbackIndex = routing.RegisterTransitCallback((long fromIndex, long toIndex) =>
                                                                   {
                                                                       // Convert from routing variable Index to
                                                                       // distance matrix NodeIndex.
                                                                       var fromNode = manager.IndexToNode(fromIndex);
                                                                       var toNode = manager.IndexToNode(toIndex);
                                                                       return data.DistanceMatrix[fromNode, toNode];
                                                                   });

        // Define cost of each arc.
        routing.SetArcCostEvaluatorOfAllVehicles(transitCallbackIndex);

        // Add Distance constraint.
        routing.AddDimension(transitCallbackIndex, 0, 3000,
                             true, // start cumul to zero
                             "Distance");
        RoutingDimension distanceDimension = routing.GetMutableDimension("Distance");
        distanceDimension.SetGlobalSpanCostCoefficient(100);

        // Define Transportation Requests.
        Solver solver = routing.solver();
        for (int i = 0; i < data.PickupsDeliveries.GetLength(0); i++)
        {
            long pickupIndex = manager.NodeToIndex(data.PickupsDeliveries[i][0]);
            long deliveryIndex = manager.NodeToIndex(data.PickupsDeliveries[i][1]);
            routing.AddPickupAndDelivery(pickupIndex, deliveryIndex);
            solver.Add(solver.MakeEquality(routing.VehicleVar(pickupIndex), routing.VehicleVar(deliveryIndex)));
            solver.Add(solver.MakeLessOrEqual(distanceDimension.CumulVar(pickupIndex),
                                              distanceDimension.CumulVar(deliveryIndex)));
        }

        // Setting first solution heuristic.
        RoutingSearchParameters searchParameters =
            operations_research_constraint_solver.DefaultRoutingSearchParameters();
        searchParameters.FirstSolutionStrategy = FirstSolutionStrategy.Types.Value.PathCheapestArc;

        // Solve the problem.
        Assignment solution = routing.SolveWithParameters(searchParameters);

        // Print solution on console.
        PrintSolution(data, routing, manager, solution);
    }
}