توجيه المركبات باستخدام الشاحنات والتسليمات

نتناول في هذا القسم برنامج VRP الذي تلتقط فيه كل مركبة العناصر من مواقع مختلفة ويسقطونها في أماكن أخرى. تكمن المشكلة في تعيين مسارات لاستلام كل العناصر وتسليمها، مع تقليل طول أطول مسار.

مثال على تنسيق VRP مع عمليات استلام الطلبات وتوصيلها

يوضح الرسم البياني أدناه مواقع الاستلام والتسليم على شبكة متشابهة لتلك الموجودة في مثال VRP السابق. لكل منها تكون هناك حافة موجَّهة من موقع الاستلام إلى موقع التسليم.

حل المثال باستخدام أدوات OR

تصف الأقسام التالية كيفية حل "حملة وصول الفيديو" (VRP) من خلال عمليات استلام الطلبات وتوصيلها. . يتم استعارة جزء كبير من الرمز مثال VRP السابق، لذلك والتركيز على الأجزاء الجديدة.

إنشاء البيانات

تتضمن بيانات المشكلة مصفوفة المسافة من تنسيق VRP السابق. مثال، إلى جانب قائمة بأزواج مواقع الاستلام والتسليم، data['pickups_deliveries']، تتوافق مع الحواف الموجَّهة في المخطّط البياني أعلاه. يحدّد الرمز أدناه المواقع الجغرافية لاستلام الطلب والتسليم.

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}},
      };

لغة 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 },
        };

لكل زوج من الحِزم، الإدخال الأول هو فهرس موقع استلام الطلب، والإدخال الثاني هو هو فهرس موقع التسليم.

تحديد طلبات الاستلام والتوصيل

يحدد الرمز التالي طلبات الاستلام والتوصيل باستخدام الاستلام مواقع التسليم في 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)));
  }

لغة 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)));
        }

لكل زوج، سيؤدي الأمر ينشئ routing.AddPickupAndDelivery(pickup_index, delivery_index) طلب استلام. وطلب تسليم لعنصر.

يضيف السطر التالي شرطًا يجب فيه اختيار كل عنصر تسليمه بواسطة السيارة نفسها.

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

أخيرًا، نضيف المطلب الواضح الذي يقضي أنه يجب استلام كل عنصر قبل تسليمه. لإجراء ذلك، نحتاج إلى المسافة التراكمية للمركبة في الموقع الجغرافي لاستلام السلعة هي المسافة التراكمية إلى أقصى حد في موقع التسليم.

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

تشغيل البرنامج

يتم عرض البرامج الكاملة لمقدّم خدمة الشراء بالجملة (VRP) مع استلام الطلبات وتسليمها القسم التالي. عند تشغيل البرنامج، يعرض المسارات التالية.

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

يوضح الرسم التخطيطي التالي المسارات:

إكمال البرامج

يتم عرض البرامج الكاملة أدناه.

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;
}

لغة 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);
    }
}