ניתוב רכבים עם טנדרים ומשלוחים

בקטע הזה אנחנו מתארים קמפיין VRP שבו כל רכב אוסף פריטים במיקומים שונים ומשחררים אותם אצל אחרים. הבעיה היא להקצות מסלולים כך שכלי הרכב יאספו וישלחו את כל הפריטים, תוך צמצום האורך של המסלול הארוך ביותר.

דוגמה של קמפיין VRP עם איסוף ומשלוחים

בתרשים הבא מוצגים מיקומי האיסוף והמשלוחים ברשת דומה לזה שמופיע בדוגמה הקודמת של VRP. בכל פעם יש קצה מכוון ממיקום האיסוף אל יעד המשלוח.

פתרון הדוגמה באמצעות כלי OR

בקטעים הבאים מוסבר איך לפתור את ה-VRP עם איסוף ומשלוחים הקצר הזה. התשובות שלך יעזרו לנו להשתפר. חלק גדול מהקוד מושאל הדוגמה הקודמת של VRP, להתמקד בחלקים החדשים.

יצירת הנתונים

הנתונים של הבעיה כוללים את מטריצת המרחק של ה-VRP הקודמת לדוגמה, וגם רשימה של צמדים של מיקומי איסוף ומשלוח, data['pickups_deliveries'], בהתאם לקצוות המכוונים בתרשים למעלה. הקוד שבהמשך מגדיר את מיקומי האיסוף והמשלוח.

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 },
        };

לכל צמד, הרשומה הראשונה היא האינדקס של מיקום האיסוף והרשומה השנייה הוא האינדקס של מיקום המשלוח.

הגדרת בקשות לאיסוף ומשלוח

הקוד הבא מגדיר בקשות לאיסוף ומסירה באמצעות איסוף ומסירה מיקומי משלוחים בdata['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)));
        }

לכל צמד, הפקודה routing.AddPickupAndDelivery(pickup_index, delivery_index) יוצר איסוף ובקשת משלוח של פריט.

השורה הבאה מוסיפה את הדרישה לאסוף כל פריט נמסרה על ידי אותו כלי רכב.

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

לסיום, אנחנו מוסיפים את הדרישה הברורה שלפיה צריך לאסוף כל פריט לפני שהוא נמסר. כדי לעשות זאת, אנחנו דורשים המרחק המצטבר של רכב בנקודת האיסוף של הפריט נמצא במרחק המצטבר לכל היותר במיקום המשלוח.

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

הפעלה של התוכנית

התוכניות המלאות של תוכנית VRP עם איסוף ומשלוחים מוצגות במדינות בקטע הבא. כשמפעילים את התוכנית, מוצגים המסלולים הבאים.

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

בתרשים הבא מוצגים המסלולים:

השלמת תוכניות

התוכניות המלאות מוצגות בהמשך.

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);
    }
}