Routing with time windows

Principles learned

  • Add multiple list decision variables
  • Use lambda expression to define a recursive array
  • Define a sequence of expressions

Problem

../_images/vrptw.png

In the capacitated vehicle routing problem with time-windows (CVRPTW), a fleet of delivery vehicles with uniform capacity must service customers with known demand and opening hours for a single commodity. The vehicles start and end their routes at a common depot. Each customer can only be served by one vehicle. The objectives are to minimize the fleet size and assign a sequence of customers to each truck of the fleet minimizing the total distance travelled such that all customers are served and the total demand served by each truck does not exceed its capacity.

Download the example

Data

The instances provided come from the Solomon instances..

The format of the data files is as follows:

  • The first line gives the name of the instance

  • The fifth line contains the number of vehicle and their common capacity

  • From the 10th line, each line contains the integer data associated to each customer, starting with the depot.

    • The index of the customer
    • The x coordinate
    • The y coordinate
    • The demand
    • The earliest arrival
    • The latest arrival
    • The service time.

Program

The LocalSolver model is an extension of the CVRP model. We refer the reader to this model for the routing aspect of problem. The time-windows are handled as a prioritary objective. In case of early arrival, the truck has to wait for the opening hour of the customer. In case of late arrival, the lateness is measured and the total lateness has to be minimized. The solution is feasible when this cumulated lateness is zero.

In the model the ending times of each truck are defined as a recursive array. The arrivaltime is the maximum of:

  • the end time of the previous visit plus the traveling time (equal to the distance in these instances). For the first visit it amounts to the traveling time from the depot (starting at t=0)
  • the earliest allowed arrival at this customer

The ending time is merely this arrival time plus the service time for this customer. The arrival to the depot at the end of the tour occurs at the end time of the last visit plus the traveling time from this point to the depot.

Such a recursive definition is introduced with a function (i, prev) => .... It allows defining the ith element of an array in function of i and of the (i-1)th element of the array. See our documentation on this topic for details.

The lateness at each visit is computed from the difference between the ending time of this visit and the latest allowed end for this customer. For the arrival at the depot, we compare the arrival time to the maximum horizon defined for the problem.

Finally we minimize in lexicographic order: the total lateness, the number of trucks used, and the total distance travelled by all the trucks.

Execution:
localsolver cvrptw.lsp inFileName=instances/R101.25.txt [lsTimeLimit=] [solFileName=]
/********** cvrptw.lsp **********/

use io;

/* The input files follow the "Solomon" format.*/
function input() {
    usage = "\nUsage: localsolver cvrptw.lsp "
    + "inFileName=inputFile [solFileName=outputFile] [lsTimeLimit=timeLimit]\n";

    if (inFileName == nil) throw usage;    

    readInputCvrptw();
    
    // Compute distance matrix
    computeDistanceMatrix();

}
 
/* Declares the optimization model. */
function model() {
    customersSequences[k in 1..nbTrucks] <- list(nbCustomers); 
   
    // All customers must be visited by  the trucks
    constraint partition[k in 1..nbTrucks](customersSequences[k]);
        
    for[k in 1..nbTrucks] {
      local sequence <- customersSequences[k];
      local c <- count(sequence);    
      
      // A truck is used if it visits at least one customer
      truckUsed[k] <- c > 0;
      
      // The quantity needed in each route must not exceed the truck capacity
      routeQuantity[k] <- sum(0..c-1, i => demands[sequence[i]]); 
      constraint routeQuantity[k] <= truckCapacity; 
        
      endTime[k] <- array(0..c-1, (i, prev) => max(earliestStart[sequence[i]], 
                            i == 0 ? 
                            distanceWarehouse[sequence[0]] : 
                            prev + distanceMatrix[sequence[i-1]][sequence[i]]) 
                        + serviceTime[sequence[i]]);
      
      homeLateness[k] <- truckUsed[k] ? 
           max(0, endTime[k][c - 1] + distanceWarehouse[sequence[c - 1]] - maxHorizon) : 
           0;

      // Distance travelled by truck k
      routeDistances[k] <- sum(1..c-1, 
         i => distanceMatrix[sequence[i-1]][sequence[i]])
         + (truckUsed[k] ? 
           (distanceWarehouse[sequence[0]] + distanceWarehouse[sequence[c-1]]) :
           0);

      lateness[k] <- homeLateness[k] + sum(0..c-1, 
                        i => max(0, endTime[k][i] - latestEnd[sequence[i]]));
    }
    
    // Total lateness, must be 0 for a solution to be valid
    totalLateness <- sum[k in 1..nbTrucks](lateness[k]);
    
    nbTrucksUsed <- sum[k in 1..nbTrucks](truckUsed[k]);
    
    // Total distance travelled (convention in Solomon's instances is to round to 2 decimals)
    totalDistance <- round(100*sum[k in 1..nbTrucks](routeDistances[k]))/100;
    
    minimize totalLateness;
    minimize nbTrucksUsed;
    minimize totalDistance;    
}


/* Parameterizes the solver. */
function param() { 
    if(lsTimeLimit == nil) lsTimeLimit = 20;
}

/* Writes the solution in a file with the following format :
   - number of trucks used and total distance
   - for each truck the nodes visited (omitting the start/end at the depot) */
function output() {  
    if (solFileName == nil) return;
    local outfile = io.openWrite(solFileName);

    outfile.println(nbTrucksUsed.value, " ", totalDistance.value);
    for [k in 1..nbTrucks] {
        if (truckUsed[k].value != 1) continue;
        for [customer in customersSequences[k].value] {
            outfile.print(customer + 1, " ");
        }
        outfile.println();
    }
}

function readInputCvrptw() {
    local inFile = io.openRead(inFileName);
    skipLines(inFile, 4);

    //Truck related data
    nbTrucks = inFile.readInt();
    truckCapacity = inFile.readInt();

    skipLines(inFile, 3);
    
    //Warehouse data
    local line = inFile.readln().split();
    warehouseIndex = line[0].toInt();
    warehouseX = line[1].toInt();
    warehouseY = line[2].toInt();
    maxHorizon = line[5].toInt();

    //Customers data
    i = 0;
    while (!inFile.eof()) {
        inLine = inFile.readln();
        line = inLine.split();
        if(count(line) == 0) break;
        if(count(line) != 7) throw "Wrong file format";
        customerIndex[i] = line[0].toInt();
        customerX[i] = line[1].toInt();
        customerY[i] = line[2].toInt();
        demands[i] = line[3].toInt();
        serviceTime[i] = line[6].toInt();    
        earliestStart[i] = line[4].toInt();
        latestEnd[i] = line[5].toInt() + serviceTime[i]; //in input files due date is meant as latest start time        
        i = i + 1;
    }
    nbCustomers = i;

    inFile.close();
}

function skipLines(inFile, nbLines) {
    if (nbLines < 1) return;
    local dump = inFile.readln();
    for[i in 2..nbLines] dump = inFile.readln();
}



function computeDistanceMatrix() {
    for[i in 0..nbCustomers-1]
    {
        distanceMatrix[i][i] = 0;
        for[j in i+1..nbCustomers-1] {        
            local localDistance = computeDist(i, j);
            distanceMatrix[j][i] = localDistance;
            distanceMatrix[i][j] = localDistance;
        }
    }

    for[i in 0..nbCustomers-1] {
        local localDistance = computeDepotDist(i);
        distanceWarehouse[i] = localDistance;
    }
}


function computeDist(i, j) {
    local x1 = customerX[i];
    local x2 = customerX[j];
    local y1 = customerY[i];
    local y2 = customerY[j];
    return computeDistance(x1, x2, y1, y2);
}

function computeDepotDist(i) {
    local x1 = customerX[i];
    local xd = warehouseX;
    local y1 = customerY[i];
    local yd = warehouseY;
    return computeDistance(x1, xd, y1, yd);
}
    

function computeDistance(x1, x2, y1, y2) {
    return sqrt(pow((x1 - x2), 2) + pow((y1 - y2), 2));
}
Execution (Windows)
set PYTHONPATH=%LS_HOME%\bin\python27\
python cvrptw.py instances\R101.25.txt
Execution (Linux)
export PYTHONPATH=/opt/localsolver_XXX/bin/python27/
python cvrptw.py instances/R101.25.txt
########## cvrptw.py ##########

import localsolver
import sys
import math


def read_elem(filename):
    with open(filename) as f:
        return [str(elem) for elem in f.read().split()]


def main(instance_file, str_time_limit, sol_file):

    #
    # Reads instance data
    #
    (nb_customers, nb_trucks, truck_capacity, distance_matrix, distance_warehouses, demands, service_time, earliest_start,latest_end, max_horizon) = read_input_cvrptw(instance_file)
    
    
    with localsolver.LocalSolver() as ls:
        #
        # Declares the optimization model
        #
        model = ls.model

        # Sequence of customers visited by each truck.
        customers_sequences = [model.list(nb_customers) for k in range(nb_trucks)]

        # All customers must be visited by  the trucks
        model.constraint(model.partition(customers_sequences))
        
        # Create demands, earliest, latest and service as arrays to be able to access it with an "at" operator
        demands_array = model.array(demands)
        earliest_array = model.array(earliest_start)
        latest_array = model.array(latest_end)
        service_array = model.array(service_time)
        
        # Create distance as an array to be able to acces it with an "at" operator
        distance_array = model.array()
        for n in range(nb_customers):
            distance_array.add_operand(model.array(distance_matrix[n]))
        distance_warehouse_array = model.array(distance_warehouses)

        route_distances = [None for n in range(nb_trucks)]
        end_time = [None for n in range(nb_trucks)]
        home_lateness = [None for n in range(nb_trucks)]
        lateness = [None for n in range(nb_trucks)]

        # A truck is used if it visits at least one customer
        trucks_used = [(model.count(customers_sequences[k]) > 0) for k in range(nb_trucks)]
        nb_trucks_used = model.sum(trucks_used)

        for k in range(nb_trucks):
            sequence = customers_sequences[k]
            c = model.count(sequence)
                        
            # Quantity in each truck
            demand_selector = model.function(lambda i: model.at(demands_array, sequence[i]))
            route_quantity = model.sum(model.range(0, c), demand_selector) 
            model.constraint(route_quantity <= truck_capacity)
            
            # Distance traveled by each truck
            dist_selector = model.function(lambda i: model.at(distance_array, sequence[i-1], sequence[i]))
            route_distances[k] = model.sum(model.range(1,c), dist_selector) + \
                 model.iif(c > 0, model.at(distance_warehouse_array, sequence[0]) + model.at(distance_warehouse_array, sequence[c-1]),0)   
                 
            # End of each visit
            end_selector = model.function(lambda i, prev: model.max(model.at(earliest_array, sequence[i]), \
                        model.iif(i == 0, \
                                  model.at(distance_warehouse_array,sequence[0]), \
                                  prev + model.at(distance_array,sequence[i-1],sequence[i]))) + \
                        model.at(service_array, sequence[i])) 
            
            end_time[k] = model.array(model.range(0,c), end_selector)
      
            # Arriving home after max_horizon
            home_lateness[k] = model.iif(trucks_used[k], \
               model.max(0,model.at(end_time[k],c-1) + model.at(distance_warehouse_array,sequence[c-1])-max_horizon), \
                0)

            # completing visit after latest_end
            late_selector = model.function(lambda i:  model.max(0,model.at(end_time[k],i) - model.at(latest_array, sequence[i])))
            lateness[k] = home_lateness[k] + model.sum(model.range(0,c),late_selector) 

                        

        # Total lateness
        total_lateness = model.sum(lateness)
       

        # Total distance travelled
        total_distance = model.div(model.round(100 * model.sum(route_distances)),100);


        # Objective: minimize the number of trucks used, then minimize the distance travelled
        model.minimize(total_lateness)
        model.minimize(nb_trucks_used)
        model.minimize(total_distance)

        model.close()

        #
        # Parameterizes the solver
        #
        ls.create_phase().time_limit = int(str_time_limit)

        ls.solve()

        #
        # Writes the solution in a file with the following format :
        #  - number of trucks used and total distance
        #  - for each truck the nodes visited (omitting the start/end at the depot)
        #
        if len(sys.argv) >= 3:
            with open(sol_file, 'w') as f:
                f.write("%d %d\n" % (nb_trucks_used.value, total_distance.value))
                for k in range(nb_trucks):
                    if(trucks_used[k].value != 1): continue
                    # Values in sequence are in [0..nbCustomers-1]. +2 is to put it back in [2..nbCustomers+1]
                    # as in the data files (1 being the depot)
                    for customer in customers_sequences[k].value:
                        f.write("%d " % (customer + 2))
                    f.write("\n")


# The input files follow the "Solomon" format.
def read_input_cvrptw(filename):
    file_it = iter(read_elem(sys.argv[1]))
    
    for i in range(4): file_it.next()
    
    nb_trucks = int(file_it.next())
    truck_capacity = int(file_it.next())

    for i in range(13): file_it.next()
    
    warehouse_x = int(file_it.next())
    warehouse_y = int(file_it.next())

    for i in range(2): file_it.next()
    
    max_horizon = int(file_it.next())

    file_it.next()
    
    customers_x = []
    customers_y = []
    demands = []
    earliest_start = []
    latest_end = []
    service_time = []
    
    while(1):
        val = next(file_it,None)
        if (val is None) : break
        i = int(val) - 1
        customers_x.append(int(file_it.next()))
        customers_y.append(int(file_it.next()))
        demands.append(int(file_it.next()))
        ready = int(file_it.next())
        due = int(file_it.next())
        stime = int(file_it.next())        
        earliest_start.append(ready)
        latest_end.append(due + stime) #in input files due date is meant as latest start time        
        service_time.append(stime)
        
    nb_customers = i + 1

    # Compute distance matrix
    distance_matrix = compute_distance_matrix(customers_x, customers_y)
    distance_warehouses = compute_distance_warehouses(warehouse_x, warehouse_y, customers_x, customers_y)

    return (nb_customers, nb_trucks, truck_capacity, distance_matrix, distance_warehouses, demands, service_time, earliest_start,latest_end, max_horizon)


# Computes the distance matrix
def compute_distance_matrix(customers_x, customers_y):
    nb_customers = len(customers_x)
    distance_matrix = [[None for i in range(nb_customers)] for j in range(nb_customers)]
    for i in range(nb_customers):
        distance_matrix[i][i] = 0
        for j in range(nb_customers):
            dist = compute_dist(customers_x[i], customers_x[j], customers_y[i], customers_y[j])
            distance_matrix[i][j] = dist
            distance_matrix[j][i] = dist
    return distance_matrix


# Computes the distances to warehouse
def compute_distance_warehouses(depot_x, depot_y, customers_x, customers_y):
    nb_customers = len(customers_x)
    distance_warehouses = [None for i in range(nb_customers)]
    for i in range(nb_customers):
        dist = compute_dist(depot_x, customers_x[i], depot_y, customers_y[i])
        distance_warehouses[i] = dist
    return distance_warehouses



def compute_dist(xi, xj, yi, yj):
    return math.sqrt(math.pow(xi - xj, 2) + math.pow(yi - yj, 2))


if __name__ == '__main__':
    if len(sys.argv) < 2:
        print ("Usage: python cvrptw.py input_file [output_file] [time_limit]")
        sys.exit(1)

    instance_file = sys.argv[1];
    sol_file =  sys.argv[2] if len(sys.argv) > 2 else None;
    str_time_limit = sys.argv[3] if len(sys.argv) > 3 else "20";

    main(instance_file, str_time_limit, sol_file)
Compilation / Execution (Windows)
cl /EHsc cvrptw.cpp -I%LS_HOME%\include /link %LS_HOME%\bin\localsolver.dll.lib
cvrp instances\R101.25.txt
Compilation / Execution (Linux)
g++ cvrptw.cpp -I/opt/localsolver_XXX/include -llocalsolver -lpthread -o cvrp
./cvrp instances/R101.25.txt
/********** cvrptw.cpp **********/

#include <iostream>
#include <fstream>
#include <vector>
#include <cstring>
#include <cmath>
#include "localsolver.h"

using namespace localsolver;
using namespace std;

class Cvrptw {
public:
    // LocalSolver
    LocalSolver localsolver;

    // Number of customers
    int nbCustomers;

    // Capacity of the trucks
    int truckCapacity;
    
    // Latest allowed arrival to depot
    int maxHorizon;

    // Demand on each node
    vector<lsint> demands;

    // Earliest arrival on each node
    vector<lsint> earliestStart;

    // Latest departure from each node
    vector<lsint> latestEnd;

    // Service time on each node
    vector<lsint> serviceTime;

    // Distance matrix
    vector<vector<lsdouble> > distanceMatrix;

    // Distance to depot
    vector<lsdouble> distanceWarehouses;

    // Number of trucks
    int nbTrucks;

    // Decision variables
    vector<LSExpression> customersSequences;
    
    // Are the trucks actually used
    vector<LSExpression> trucksUsed;

    // Cumulated lateness in the solution (must be 0 for the solution to be valid)
    LSExpression totalLateness;

    // Number of trucks used in the solution
    LSExpression nbTrucksUsed;

    // Distance travelled by all the trucks
    LSExpression totalDistance;    
    
    // Constructor
    Cvrptw() {        
    }

    // Reads instance data.
    void readInstance(const string& fileName) {
        readInputCvrptw(fileName);
    }

    void solve(int limit) {
            // Declares the optimization model.
            LSModel model = localsolver.getModel();

            // Sequence of customers visited by each truck.
            customersSequences.resize(nbTrucks);
            for (int k = 0; k < nbTrucks; k++) {
                customersSequences[k] = model.listVar(nbCustomers);
            }

            // All customers must be visited by  the trucks
            model.constraint(model.partition(customersSequences.begin(), customersSequences.end()));

            // Create demands, earliest, latest and service as arrays to be able to access it with an "at" operator
            LSExpression demandsArray = model.array(demands.begin(), demands.end());
            LSExpression earliestArray = model.array(earliestStart.begin(), earliestStart.end());
            LSExpression latestArray = model.array(latestEnd.begin(), latestEnd.end());
            LSExpression serviceArray = model.array(serviceTime.begin(), serviceTime.end());


            // Create distance as an array to be able to acces it with an "at" operator
            LSExpression distanceArray = model.array();
            for (int n = 0; n < nbCustomers; n++) {
                distanceArray.addOperand(model.array(distanceMatrix[n].begin(), distanceMatrix[n].end()));
            }
            LSExpression distanceWarehousesArray = model.array(distanceWarehouses.begin(), distanceWarehouses.end());
            
            trucksUsed.resize(nbTrucks);
            vector<LSExpression> routeDistances(nbTrucks), endTime(nbTrucks), homeLateness(nbTrucks), lateness(nbTrucks);
                       
            for (int k = 0; k < nbTrucks; k++) {
                LSExpression sequence = customersSequences[k];
                LSExpression c = model.count(sequence);

                // A truck is used if it visits at least one customer
                trucksUsed[k] = c > 0;
                                
                // The quantity needed in each route must not exceed the truck capacity
                LSExpression demandSelector = model.createFunction([&](LSExpression i) { return demandsArray[sequence[i]]; });
                LSExpression routeQuantity = model.sum(model.range(0, c), demandSelector);
                model.constraint(routeQuantity <= truckCapacity);

                // Distance traveled by truck k
                LSExpression distSelector = model.createFunction([&](LSExpression i) { return model.at(distanceArray, sequence[i - 1], sequence[i]); }); 
                routeDistances[k] = model.sum(model.range(1, c), distSelector) + 
                    model.iif(c > 0, distanceWarehousesArray[sequence[0]] + distanceWarehousesArray[sequence[c - 1]], 0);
                    
                //End of each visit
                LSExpression endSelector = model.createFunction([&](LSExpression i, LSExpression prev) {  
                 return model.max(model.at(earliestArray, sequence[i]), 
                          model.iif(i == 0, 
                                  distanceWarehousesArray[sequence[0]],
                                  prev + model.at(distanceArray,sequence[i-1],sequence[i]))
                                  ) + 
                          model.at(serviceArray, sequence[i]); }); 
                
                endTime[k] = model.array(model.range(0,c), endSelector);  
                
                // Arriving home after max_horizon
                homeLateness[k] = model.iif(trucksUsed[k], 
                                model.max(0,endTime[k][c-1] + distanceWarehousesArray[sequence[c-1]] - maxHorizon),
                                0);

                //completing visit after latest_end
                LSExpression lateSelector = model.createFunction([&](LSExpression i) { return model.max(0,endTime[k][i] - latestArray[sequence[i]]);});
                lateness[k] = homeLateness[k] + model.sum(model.range(0,c),lateSelector); 
            }
            
            // Total lateness
            totalLateness = model.sum(lateness.begin(), lateness.end());

            // Total nb trucks used
            nbTrucksUsed = model.sum(trucksUsed.begin(), trucksUsed.end());

            // Total distance travelled
            totalDistance = model.round(100*model.sum(routeDistances.begin(), routeDistances.end()))/100;

            // Objective: minimize the number of trucks used, then minimize the distance travelled
            model.minimize(totalLateness);
            model.minimize(nbTrucksUsed);
            model.minimize(totalDistance);

            model.close();

            // Parameterizes the solver.
            LSPhase phase = localsolver.createPhase();
            phase.setTimeLimit(limit);
            localsolver.solve();
            
        
    }

    // Writes the solution in a file with the following format :
    //  - number of trucks used and total distance
    //  - for each truck the nodes visited (omitting the start/end at the depot)
    void writeSolution(const string& fileName) {
        ofstream outfile;
        outfile.exceptions(ofstream::failbit | ofstream::badbit);
        outfile.open(fileName.c_str());
        
        outfile << nbTrucksUsed.getValue() << " " << totalDistance.getDoubleValue() << endl;
        for (int k = 0; k < nbTrucks; k++) {
            if (trucksUsed[k].getValue() != 1) continue;
            // Values in sequence are in [0..nbCustomers-1]. +2 is to put it back in [2..nbCustomers+1]
            // as in the data files (1 being the depot)
            LSCollection customersCollection = customersSequences[k].getCollectionValue();
            for (lsint i = 0; i < customersCollection.count(); i++) {
                outfile << customersCollection[i] + 2 << " ";
            }
            outfile << endl;
        }        
    }

private:


    // The input files follow the "Solomon" format.
    void readInputCvrptw(const string& fileName) {
        ifstream infile(fileName.c_str());
        if (!infile.is_open()) {
            throw std::runtime_error("File cannot be opened.");
        }
        
        string str;
        char *pch;
        char* line;
        int nbNodes;
        long dump;
        
        int depotX, depotY;
        vector<int> customersX;
        vector<int> customersY;
        
        getline(infile, str);
        getline(infile, str);
        getline(infile, str);
        getline(infile, str);
        
        infile >> nbTrucks;
        infile >> truckCapacity;
        
        cout << nbTrucks << " " << truckCapacity <<endl;
        
        getline(infile, str);
        getline(infile, str);
        getline(infile, str);
        getline(infile, str);
        
        infile >> dump;
        infile >> depotX;
        infile >> depotY;
        infile >> dump;
        infile >> dump;
        infile >> maxHorizon;        
        infile >> dump;   
       
        int tt = 1;
        while (!infile.eof()) {
            int cx,cy,demand,ready,due,service;
            infile >> dump;
            infile >> cx;
            infile >> cy;
            infile >> demand;
            infile >> ready;
            infile >> due;
            infile >> service;
            
            customersX.push_back(cx);
            customersY.push_back(cy);
            demands.push_back(demand);
            earliestStart.push_back(ready);
            latestEnd.push_back(due+service);//in input files due date is meant as latest start time 
            serviceTime.push_back(service);
        }
        
        nbCustomers = customersX.size();            
            
        // Compute distance matrix
        computeDistanceMatrix(depotX, depotY, customersX, customersY);

        infile.close();
    }

    // Computes the distance matrix
    void computeDistanceMatrix(int depotX, int depotY, const vector<int>& customersX, const vector<int>& customersY) {
        distanceMatrix.resize(nbCustomers);
        for (int i = 0; i < nbCustomers; i++) {
            distanceMatrix[i].resize(nbCustomers);
        }
        for (int i = 0; i < nbCustomers; i++) {
            distanceMatrix[i][i] = 0;
            for (int j = i + 1; j < nbCustomers; j++) {
                lsdouble distance = computeDist(customersX[i], customersX[j], customersY[i], customersY[j]);
                distanceMatrix[i][j] = distance;
                distanceMatrix[j][i] = distance;
            }
        }
        
        distanceWarehouses.resize(nbCustomers);
        for(int i = 0; i < nbCustomers; ++i) {
            distanceWarehouses[i] = computeDist(depotX, customersX[i], depotY, customersY[i]);
        }
    }

    lsdouble computeDist(int xi, int xj, int yi, int yj) {
        return sqrt(pow((double) xi - xj, 2) + pow((double) yi - yj, 2));
    }

};

int main(int argc, char** argv) {
    if (argc < 2) {
        cerr << "Usage: cvrptw inputFile [outputFile] [timeLimit] [nbTrucks]" << endl;
        return 1;
    }

    const char* instanceFile = argv[1];
    const char* solFile = argc > 2 ? argv[2] : NULL;
    const char* strTimeLimit = argc > 3 ? argv[3] : "20";

    try {
        Cvrptw model;
        model.readInstance(instanceFile);
        model.solve(atoi(strTimeLimit));
        if(solFile != NULL) model.writeSolution(solFile);
        return 0;
    } catch (const exception& e){
        cerr << "Error occurred: " << e.what() << endl;
        return 1;
    }
}
Compilation/Execution (Windows)
copy %LS_HOME%\bin\*net.dll .
csc Cvrptw.cs /reference:localsolvernet.dll
Cvrp instances\R101.25.txt
/********** Cvrptw.cs **********/

using System;
using System.IO;
using System.Collections.Generic;
using localsolver;

public class Cvrptw : IDisposable
{
    // Solver
    LocalSolver localsolver;

    // Number of customers (= number of nodes minus 1)
    int nbCustomers;

    // Capacity of the trucks
    int truckCapacity;
    
    // Latest allowed arrival to depot
    int maxHorizon;

    // Demand on each node
    List<int> demands;

    // Earliest arrival on each node
    List<int> earliestStart;

    // Latest departure from each node
    List<int> latestEnd;

    // Service time on each node
    List<int> serviceTime;

    // Distance matrix between customers
    double[][] distanceMatrix;

    // Distances between customers and warehouse
    double[] distanceWarehouses;

    // Number of trucks
    int nbTrucks;

    // Decision variables
    LSExpression[] customersSequences;

    // Are the trucks actually used
    LSExpression[] trucksUsed;

    // Distance travelled by each truck
    LSExpression[] routeDistances;

    // End time array for each truck
    LSExpression[] endTime;

    // Home lateness for each truck
    LSExpression[] homeLateness;

    // Cumulated Lateness for each truck
    LSExpression[] lateness;

    // Cumulated lateness in the solution (must be 0 for the solution to be valid)
    LSExpression totalLateness;

    // Number of trucks used in the solution
    LSExpression nbTrucksUsed;

    // Distance travelled by all the trucks
    LSExpression totalDistance;

    public Cvrptw()
    {
        localsolver = new LocalSolver();
    }
    
    // Reads instance data.
    void ReadInstance(string fileName)
    {
        ReadInputCvrptw(fileName);
    }

    public void Dispose()
    {
        if (localsolver != null)
            localsolver.Dispose();
    }

    void Solve(int limit)
    {
        // Declares the optimization model.
        LSModel model = localsolver.GetModel();

        trucksUsed = new LSExpression[nbTrucks];
        customersSequences = new LSExpression[nbTrucks];
        routeDistances = new LSExpression[nbTrucks];
        endTime = new LSExpression[nbTrucks];
        homeLateness = new LSExpression[nbTrucks];
        lateness = new LSExpression[nbTrucks];
        

        // Sequence of customers visited by each truck.
        for (int k = 0; k < nbTrucks; k++)
            customersSequences[k] = model.List(nbCustomers);

        // All customers must be visited by the trucks
        model.Constraint(model.Partition(customersSequences));

        // Create demands and distances as arrays to be able to access it with an "at" operator
        LSExpression demandsArray = model.Array(demands);
        LSExpression earliestArray = model.Array(earliestStart);
        LSExpression latestArray = model.Array(latestEnd);
        LSExpression serviceArray = model.Array(serviceTime);
        
        LSExpression distanceWarehouseArray = model.Array(distanceWarehouses);
        LSExpression distanceArray = model.Array(distanceMatrix);

        for (int k = 0; k < nbTrucks; k++)
        {
            LSExpression sequence = customersSequences[k];
            LSExpression c = model.Count(sequence);

            // A truck is used if it visits at least one customer
            trucksUsed[k] = c > 0;

            // The quantity needed in each route must not exceed the truck capacity
            LSExpression demandSelector = model.Function(i => demandsArray[sequence[i]]);
            LSExpression routeQuantity = model.Sum(model.Range(0, c), demandSelector);
            model.Constraint(routeQuantity <= truckCapacity);

            // Distance travelled by truck k
            LSExpression distSelector = model.Function(i => distanceArray[sequence[i - 1], sequence[i]]);
            routeDistances[k] = model.Sum(model.Range(1, c), distSelector)
                                + model.If(c > 0, distanceWarehouseArray[sequence[0]] + distanceWarehouseArray[sequence[c - 1]], 0);
                                
            //End of each visit
            LSExpression endSelector = model.Function( (i,prev) => model.Max(earliestArray[sequence[i]],
                          model.If(i == 0, 
                              distanceWarehouseArray[sequence[0]],
                              prev + distanceArray[sequence[i-1],sequence[i]])) + 
                            serviceArray[sequence[i]] );
                
            endTime[k] = model.Array(model.Range(0,c), endSelector);  
                
            // Arriving home after max_horizon
            homeLateness[k] = model.If(trucksUsed[k], 
                                model.Max(0,endTime[k][c-1] + distanceWarehouseArray[sequence[c-1]] - maxHorizon),
                                0);

            //completing visit after latest_end
            LSExpression lateSelector = model.Function( i => model.Max(endTime[k][i] - latestArray[sequence[i]],0));
            lateness[k] = homeLateness[k] + model.Sum(model.Range(0,c),lateSelector);
        }

        totalLateness = model.Sum(lateness);
        nbTrucksUsed = model.Sum(trucksUsed);
        totalDistance = model.Round(100*model.Sum(routeDistances))/100;

        // Objective: minimize the number of trucks used, then minimize the distance traveled
        model.Minimize(totalLateness);
        model.Minimize(nbTrucksUsed);
        model.Minimize(totalDistance);

        model.Close();

        // Parameterizes the solver.
        LSPhase phase = localsolver.CreatePhase();
        phase.SetTimeLimit(limit);

        localsolver.Solve();
    }

    // Writes the solution in a file with the following format :
    //  - number of trucks used and total distance
    //  - for each truck the nodes visited (omitting the start/end at the depot)
    void WriteSolution(string fileName)
    {
        using (StreamWriter output = new StreamWriter(fileName))
        {
            output.WriteLine(nbTrucksUsed.GetValue() + " " + totalDistance.GetDoubleValue());
            for (int k = 0; k < nbTrucks; k++)
            {
                if (trucksUsed[k].GetValue() != 1) continue;
                // Values in sequence are in [0..nbCustomers-1]. +2 is to put it back in [2..nbCustomers+1]
                // as in the data files (1 being the depot)
                LSCollection customersCollection = customersSequences[k].GetCollectionValue();
                for (int i = 0; i < customersCollection.Count(); i++)
                {
                    output.Write((customersCollection[i] + 2) + " ");
                }
                output.WriteLine();
            }
        }
    }

    public static void Main(string[] args)
    {
        if (args.Length < 1)
        {
            Console.WriteLine("Usage: Cvrptw inputFile [solFile] [timeLimit]");
            Environment.Exit(1);
        }
        string instanceFile = args[0];
        string outputFile = args.Length > 1 ? args[1] : null;
        string strTimeLimit = args.Length > 2 ? args[2] : "20";

        using (Cvrptw model = new Cvrptw())
        {
            model.ReadInstance(instanceFile);
            model.Solve(int.Parse(strTimeLimit));
            if (outputFile != null)
                model.WriteSolution(outputFile);
        }
    }

    private string[] SplitInput(StreamReader input) {
        string line = input.ReadLine();
        if (line == null) return new string[0];
        return line.Split(new [] {' '}, StringSplitOptions.RemoveEmptyEntries);
    }

    // The input files follow the "Solomon" format.
    private void ReadInputCvrptw(string fileName)
    {
        using (StreamReader input = new StreamReader(fileName))
        {
            string[] splitted;
            
            input.ReadLine();
            input.ReadLine();
            input.ReadLine();            
            input.ReadLine();            
            
            splitted = SplitInput(input);
            nbTrucks = int.Parse(splitted[0]);
            truckCapacity = int.Parse(splitted[1]);

            input.ReadLine();
            input.ReadLine();
            input.ReadLine();            
            input.ReadLine();            

            splitted = SplitInput(input);
            int depotX = int.Parse(splitted[1]);
            int depotY = int.Parse(splitted[2]);
            maxHorizon = int.Parse(splitted[5]);
            
            List<int> customersX = new List<int>();
            List<int> customersY = new List<int>();
            demands = new List<int>();
            earliestStart = new List<int>();
            latestEnd = new List<int>();
            serviceTime = new List<int>();
             
            while(!input.EndOfStream)
            {
                splitted = SplitInput(input);
                if (splitted.Length < 7) break;
                customersX.Add(int.Parse(splitted[1]));
                customersY.Add(int.Parse(splitted[2]));
                demands.Add(int.Parse(splitted[3])); 
                int ready = int.Parse(splitted[4]);
                int due = int.Parse(splitted[5]);
                int service = int.Parse(splitted[6]);
    
                earliestStart.Add(ready);
                latestEnd.Add(due+service);//in input files due date is meant as latest start time 
                serviceTime.Add(service);
            }
            
            nbCustomers = customersX.Count;
            
            ComputeDistanceMatrix(depotX, depotY, customersX, customersY);
        }
    }

    // Computes the distance matrix
    private void ComputeDistanceMatrix(int depotX, int depotY, List<int> customersX, List<int> customersY)
    {
        distanceMatrix = new double[nbCustomers][];
        for (int i = 0; i < nbCustomers; i++)
            distanceMatrix[i] = new double[nbCustomers];

        for (int i = 0; i < nbCustomers; i++)
        {
            distanceMatrix[i][i] = 0;
            for (int j = i + 1; j < nbCustomers; j++)
            {
                double dist = ComputeDist(customersX[i], customersX[j], customersY[i], customersY[j]);
                distanceMatrix[i][j] = dist;
                distanceMatrix[j][i] = dist;
            }
        }

        distanceWarehouses = new double[nbCustomers];
        for(int i = 0; i < nbCustomers; ++i) {
            distanceWarehouses[i] = ComputeDist(depotX, customersX[i], depotY, customersY[i]);
        }
    }

    private double ComputeDist(int xi, int xj, int yi, int yj)
    {
        return Math.Sqrt(Math.Pow(xi - xj, 2) + Math.Pow(yi - yj, 2));
    }

}
Compilation / Execution (Windows)
javac Cvrptw.java -cp %LS_HOME%\bin\localsolver.jar
java -cp %LS_HOME%\bin\localsolver.jar;. Cvrptw instances\R101.25.txt
Compilation/Execution (Linux)
javac Cvrptw.java -cp /opt/localsolver_XXX/bin/localsolver.jar
java -cp /opt/localsolver_XXX/bin/localsolver.jar:. Cvrptw instances/R101.25.txt
/********** Cvrptw.java **********/

import java.util.*;
import java.io.*;
import localsolver.*;

public class Cvrptw {
    // Solver
    private LocalSolver localsolver;

    // Number of customers (= number of nodes minus 1)
    int nbCustomers;

    // Capacity of the trucks
    private int truckCapacity;

    // Latest allowed arrival to depot
    int maxHorizon;

    // Demand on each node
    List<Integer> demands;

    // Earliest arrival on each node
    List<Integer> earliestStart;

    // Latest departure from each node
    List<Integer> latestEnd;

    // Service time on each node
    List<Integer> serviceTime;

    // Distance matrix
    private double[][] distanceMatrix;
    
    // Distances between customers and warehouse
    private double[] distanceWarehouses;

    // Number of trucks
    private int nbTrucks;

    // Decision variables
    private LSExpression[] customersSequences;

    // Are the trucks actually used
    private LSExpression[] trucksUsed;
    
    // Distance travelled by each truck
    private LSExpression[] routeDistances;

    // End time array for each truck
    private LSExpression[] endTime;

    // Home lateness for each truck
    private LSExpression[] homeLateness;

    // Cumulated Lateness for each truck
    private LSExpression[] lateness;

    // Cumulated lateness in the solution (must be 0 for the solution to be valid)
    private LSExpression totalLateness;

    // Number of trucks used in the solution
    private LSExpression nbTrucksUsed;

    // Distance traveled by all the trucks
    private LSExpression totalDistance;

    private Cvrptw() {
        localsolver = new LocalSolver();
    }

    // Reads instance data.
    private void readInstance(String fileName) throws IOException {
        readInputCvrptw(fileName);
    }

    private void solve(int limit) {
        // Declares the optimization model.
        LSModel model = localsolver.getModel();

        trucksUsed = new LSExpression[nbTrucks];
        customersSequences = new LSExpression[nbTrucks];
        routeDistances = new LSExpression[nbTrucks];
        endTime = new LSExpression[nbTrucks];
        homeLateness = new LSExpression[nbTrucks];
        lateness = new LSExpression[nbTrucks];

        // Sequence of customers visited by each truck.
        for (int k = 0; k < nbTrucks; k++)
            customersSequences[k] = model.listVar(nbCustomers);

        // All customers must be visited by the trucks
        model.constraint(model.partition(customersSequences));

        // Create demands and distances as arrays to be able to access it with an "at" operator
        LSExpression demandsArray = model.array(demands);
        LSExpression earliestArray = model.array(earliestStart);
        LSExpression latestArray = model.array(latestEnd);
        LSExpression serviceArray = model.array(serviceTime);

        LSExpression distanceWarehouseArray = model.array(distanceWarehouses);
        LSExpression distanceArray = model.array(distanceMatrix);

        for (int k = 0; k < nbTrucks; k++)
        {
            LSExpression sequence = customersSequences[k];
            LSExpression c = model.count(sequence);

            // A truck is used if it visits at least one customer
            trucksUsed[k] = model.gt(c, 0);

            // The quantity needed in each route must not exceed the truck capacity
            LSExpression demandSelector = model.function(i -> model.at(demandsArray, model.at(sequence, i)));
            LSExpression routeQuantity = model.sum(model.range(0, c), demandSelector);
            model.constraint(model.leq(routeQuantity, truckCapacity));

            // Distance traveled by truck k
            LSExpression distSelector = model.function(i -> model.at(
                        distanceArray,
                        model.at(sequence, model.sub(i, 1)),
                        model.at(sequence, i)));
            routeDistances[k] = model.sum(model.sum(model.range(1, c), distSelector),
                                    model.iif(model.gt(c, 0), model.sum(
                                        model.at(distanceWarehouseArray, model.at(sequence, 0)),
                                        model.at(distanceWarehouseArray, model.at(sequence, model.sub(c, 1)))),  0));
            
            //End of each visit
            LSExpression endSelector = model.function( (i,prev) -> model.sum(
                         model.max(model.at(earliestArray,model.at(sequence,i)),
                          model.sum(model.iif(model.eq(i,0), 
                              model.at(distanceWarehouseArray,model.at(sequence,0)),
                              model.sum(prev, model.at(distanceArray, model.at(sequence,model.sub(i,1)),model.at(sequence,i)))))), 
                            model.at(serviceArray,model.at(sequence,i)) ));
                
            endTime[k] = model.array(model.range(0,c), endSelector);  

            LSExpression theEnd = endTime[k];
                
            // Arriving home after max_horizon
            homeLateness[k] = model.iif(trucksUsed[k], 
                                model.max(0,model.sum(model.at(theEnd,model.sub(c,1)),
                                                   model.sub( model.at(distanceWarehouseArray, model.at(sequence, model.sub(c,1))) , maxHorizon))),
                                0);

            //completing visit after latest_end
            LSExpression lateSelector = model.function( i -> model.max(model.sub(model.at(theEnd,i), model.at(latestArray,model.at(sequence,i))),0));
            lateness[k] = model.sum(homeLateness[k], model.sum(model.range(0,c),lateSelector));
        }


        totalLateness = model.sum(lateness);
        nbTrucksUsed = model.sum(trucksUsed);
        totalDistance = model.div(model.round(model.prod(100,model.sum(routeDistances))),100);

        // Objective: minimize the number of trucks used, then minimize the distance traveled
        model.minimize(totalLateness);
        model.minimize(nbTrucksUsed);
        model.minimize(totalDistance);

        model.close();

        // Parameterizes the solver.
        LSPhase phase = localsolver.createPhase();
        phase.setTimeLimit(limit);

        localsolver.solve();
    }

    // Writes the solution in a file with the following format :
    // - number of trucks used and total distance
    // - for each truck the nodes visited (omitting the start/end at the depot)
    private void writeSolution(String fileName) throws IOException {
        try(PrintWriter output = new PrintWriter(fileName)) {
            output.println(nbTrucksUsed.getValue() + " " + totalDistance.getDoubleValue());
            for (int k = 0; k < nbTrucks; k++) {
                if (trucksUsed[k].getValue() != 1) continue;
                // Values in sequence are in [0..nbCustomers-1]. +2 is to put it back in [2..nbCustomers+1]
                // as in the data files (1 being the depot)
                LSCollection customersCollection = customersSequences[k].getCollectionValue();
                for (int i = 0; i < customersCollection.count(); i++) {
                    output.print((customersCollection.get(i) + 2) + " ");
                }
                output.println();
            }
        }
    }

    // The input files follow the "Solomon" format.
    private void readInputCvrptw(String fileName) throws IOException {
        try (Scanner input = new Scanner(new File(fileName))) {
            int nbNodes = 0;
            int dump = 0;
            
            input.nextLine();
            input.nextLine();
            input.nextLine();            
            input.nextLine();            

            nbTrucks = input.nextInt();
            truckCapacity = input.nextInt();

            input.nextLine();
            input.nextLine();
            input.nextLine();            
            input.nextLine();            

            
            dump = input.nextInt();
            int depotX = input.nextInt();
            int depotY = input.nextInt();
            dump = input.nextInt();
            dump = input.nextInt();
            maxHorizon = input.nextInt();
            dump = input.nextInt();
            
            List<Integer> customersX = new ArrayList<Integer>();
            List<Integer> customersY = new ArrayList<Integer>();
            demands = new ArrayList<Integer>();
            earliestStart = new ArrayList<Integer>();
            latestEnd = new ArrayList<Integer>();
            serviceTime = new ArrayList<Integer>();
            
            while (input.hasNextInt()) {
                dump = input.nextInt();
                int cx = input.nextInt();
                int cy = input.nextInt();
                int demand = input.nextInt();
                int ready = input.nextInt();
                int due = input.nextInt();
                int service = input.nextInt();
                
                customersX.add(cx);
                customersY.add(cy);
                demands.add(demand);
                earliestStart.add(ready);
                latestEnd.add(due+service);//in input files due date is meant as latest start time 
                serviceTime.add(service);
            }

            nbCustomers = customersX.size(); 
            
            computeDistanceMatrix(depotX, depotY, customersX, customersY);
            
        }
    }

    // Computes the distance matrix
    private void computeDistanceMatrix(int depotX, int depotY, List<Integer> customersX, List<Integer> customersY) {
        distanceMatrix = new double[nbCustomers][nbCustomers];
        for (int i = 0; i < nbCustomers; i++) {
            distanceMatrix[i][i] = 0;
            for (int j = i + 1; j < nbCustomers; j++) {
                double dist = computeDist(customersX.get(i), customersX.get(j), customersY.get(i), customersY.get(j));
                distanceMatrix[i][j] = dist;
                distanceMatrix[j][i] = dist;
            }
        }
        
        distanceWarehouses = new double[nbCustomers];
        for(int i = 0; i < nbCustomers; ++i) {
            distanceWarehouses[i] = computeDist(depotX, customersX.get(i), depotY, customersY.get(i));
        }
    }

    private double computeDist(int xi, int xj, int yi, int yj) {
        return Math.sqrt(Math.pow(xi - xj, 2) + Math.pow(yi - yj, 2));
    }


    public static void main(String[] args) {
        if (args.length < 1) {
            System.err.println("Usage: java Cvrptw inputFile [outputFile] [timeLimit] [nbTrucks]");
            System.exit(1);
        }

        try {
            String instanceFile = args[0];
            String outputFile = args.length > 1 ? args[1] : null;
            String strTimeLimit = args.length > 2 ? args[2] : "20";

            Cvrptw model = new Cvrptw();
            model.readInstance(instanceFile);
            model.solve(Integer.parseInt(strTimeLimit));
            if (outputFile != null) {
                model.writeSolution(outputFile);
            }
        } catch(Exception ex) {
            System.err.println(ex);
            ex.printStackTrace();
            System.exit(1);
        }
    }
}