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• Time Dependent Capacitated Vehicle Routing Problem with Time Windows (TDCVRPTW)

# Time Dependent Capacitated Vehicle Routing Problem with Time Windows (TDCVRPTW)¶

## Principles learned¶

• Add multiple list decision variables

• Use lambda expressions to define a recursive array

• Define a sequence of expressions

## Problem¶

In the time dependent capacitated vehicle routing problem with time-windows (TDCVRPTW), 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. To model real-world traffic information, the travel time between customers depends on when the travel happens. The objectives are to minimize the fleet size and assign a sequence of customers to each truck of the fleet minimizing the total distance traveled such that all customers are served and the total demand served by each truck does not exceed its capacity.

In this example, the time-dependency is modeled using multiple constant travel time matrices. The horizon is divided into several time ranges. Each time range has its own travel time matrix for travel starting during this range.

## Data¶

The instances provided are based on the Solomon CVRPTW 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 vehicles 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

To create TDCVRPTW instances from these CVRPTW instances, we chose to discretize the time horizon into five parts: early morning, morning peak, day, evening peak, and night. For each day part, the travel time between customers is modified according to coefficients depending on distance profiles. The shorter the distance is, the more the travel time is increased. This is a simple way to create non-proportionnal travel time matrices as it would be the case with real data.

## Program¶

The LocalSolver model is an extension of the CVRPTW model. We refer the reader to this model for the routing with time windows aspects of the problem.

To model the time-dependency, we introduce a `timeToMatrixIdx` array which gives for every time step of the horizon the index of the matrix that should be used.

We also have to define a travel time array with 3 dimensions. The first 2 dimensions represent the origin and destination customers. The third one is the index of the matrix. Hence, `travelTime[origin][destination][matrixIdx]` gives the travel time from `origin` to `destination` for the matrix at index `matrixIdx`.

Following the same logic, we define an array that gives the travel time to reach the depot depending on the matrix index. `travelTimeWarehouse[customer][matrixIdx]` is the travel time between `customer` and the depot for the matrix at index `matrixIdx`.

We can then modify the computation of the end times and home lateness defined in the classical CVRPTW. At each step and after doing the last delivery, we use the travel time given by the matrix valid at this time.

Execution:
localsolver tdcvrptw.lsp inFileName=instances/R101.25.txt [lsTimeLimit=] [solFileName=]
```use io;

function input() {
usage = "Usage: localsolver tdcvrptw.lsp "
+ "inFileName=inputFile [solFileName=outputFile] [lsTimeLimit=timeLimit]";

if (inFileName == nil) throw usage;

computeDistanceMatrices();
}

/* Declare the optimization model */
function model() {

// All customers must be visited by exactly one truck

for [k in 0...nbTrucks] {
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(sequence, j => demands[j]);
constraint routeQuantity[k] <= truckCapacity;

// End of each visit according to the traffic
endTime[k] <- array(0...c, (i, prev) => max(earliestStart[sequence[i]],
i == 0 ? travelTimeWarehouse[sequence][timeToMatrixIdx] :
prev + travelTime[sequence[i-1]][sequence[i]][timeToMatrixIdx[round(prev)]])
+ serviceTime[sequence[i]]);

// Arriving home after max horizon
homeLateness[k] <- truckUsed[k] ? max(0, endTime[k][c-1] +
travelTimeWarehouse[sequence[c-1]][timeToMatrixIdx[round(endTime[k][c-1])]] -
maxHorizon) : 0;

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

// Completing visit after latest end
lateness[k] <- homeLateness[k] + sum(0...c,
i => max(0, endTime[k][i] - latestEnd[sequence[i]]));
}

// Total lateness, must be 0 for a solution to be valid
totalLateness <- sum[k in 0...nbTrucks](lateness[k]);

// Total number of trucks used
nbTrucksUsed <- sum[k in 0...nbTrucks](truckUsed[k]);

// Total distance traveled (convention in Solomon's instances is to round to 2 decimals)
totalDistance <- round(100 * sum[k in 0...nbTrucks](routeDistances[k])) / 100;

// Objective: minimize the lateness, then the number of trucks used, then the distance traveled
minimize totalLateness;
minimize nbTrucksUsed;
minimize totalDistance;
}

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

/* Write the solution in a file with the following format:
* - number of trucks used and total distance
* - for each truck the customers 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 0...nbTrucks] {
if (truckUsed[k].value != 1) continue;
outfile.print(customer + 1, " ");
}
outfile.println();
}
}

skipLines(inFile, 4);

// Truck related data

skipLines(inFile, 3);

// Depot data
depotIndex = line.toInt();
depotX = line.toInt();
depotY = line.toInt();
maxHorizon = line.toInt();

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

inFile.close();
}

function skipLines(inFile, nbLines) {
}

// Compute the distance matrices
function computeDistanceMatrices() {
shortDistanceTravelTimeProfile = {1.00, 2.50, 1.75, 2.50, 1.00};
mediumDistanceTravelTimeProfile = {1.00, 2.00, 1.50, 2.00, 1.00};
longDistanceTravelTimeProfile = {1.00, 1.60, 1.10, 1.60, 1.00};
travelTimeProfileMatrix = {
shortDistanceTravelTimeProfile,
mediumDistanceTravelTimeProfile,
longDistanceTravelTimeProfile
};
distanceLevels = {10, 25};
timeIntervalSteps = {0.0, 0.2, 0.4, 0.6, 0.8, 1.0};
nbTimeIntervals = count(timeIntervalSteps)-1;
nbDistanceLevels = count(distanceLevels);

for [i in 0...nbCustomers] {
distanceMatrix[i][i] = 0;

for [k in 0...nbTimeIntervals] {
travelTime[i][i][k] = 0;
}

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

local profileIdx = getProfile(localDistance);
for [k in 0...nbTimeIntervals] {
local localTravelTime = travelTimeProfileMatrix[profileIdx][k] * localDistance;
travelTime[i][j][k] = localTravelTime;
travelTime[j][i][k] = localTravelTime;
}
}
}

for [i in 0...nbTimeIntervals] {
local timeStepStart = round(timeIntervalSteps[i] * maxHorizon);
local timeStepEnd = round(timeIntervalSteps[i+1] * maxHorizon);
for [j in timeStepStart...timeStepEnd+1] {
timeToMatrixIdx[j] = i;
}
}

for [i in 0...nbCustomers] {
local localDistance = computeDepotDist(i);
distanceDepot[i] = localDistance;

local profileIdx = getProfile(localDistance);
for [j in 0...nbTimeIntervals] {
local localTravelTimeWareHouse = travelTimeProfileMatrix[profileIdx][j] * localDistance;
travelTimeWarehouse[i][j] = localTravelTimeWareHouse;
}
}
}

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 = depotX;
local y1 = customerY[i];
local yd = depotY;
return computeDistance(x1, xd, y1, yd);
}

function computeDistance(x1, x2, y1, y2) {
return sqrt(pow((x1 - x2), 2) + pow((y1 - y2), 2));
}

function getProfile(distance) {
local idx = 0;
while (idx < nbDistanceLevels && distance > distanceLevels[idx]) {
idx = idx + 1;
}
return idx;
}
```
Execution (Windows)
set PYTHONPATH=%LS_HOME%\bin\python
python tdcvrptw.py instances\R101.25.txt
Execution (Linux)
export PYTHONPATH=/opt/localsolver_12_0/bin/python
python tdcvrptw.py instances/R101.25.txt
```import localsolver
import sys
import math

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

def main(instance_file, str_time_limit, output_file):
#
#
nb_customers, nb_trucks, truck_capacity, dist_matrix_data, travel_time_data, \
time_to_matrix_idx_data, dist_depot_data, travel_time_warehouse_data,\
demands_data, service_time_data, earliest_start_data, latest_end_data, \

with localsolver.LocalSolver() as ls:
#
# Declare 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 exactly one truck
model.constraint(model.partition(customers_sequences))

# Create LocalSolver arrays to be able to access them with an "at" operator
demands = model.array(demands_data)
earliest = model.array(earliest_start_data)
latest = model.array(latest_end_data)
service_time = model.array(service_time_data)
dist_matrix = model.array()
for n in range(nb_customers):
travel_time = model.array()
for n in range(nb_customers):
time_matrix = model.array()
for m in range(nb_customers):
time_to_matrix_idx = model.array(time_to_matrix_idx_data)
dist_depot = model.array(dist_depot_data)
travel_time_warehouse = model.array()
for n in range(nb_customers):

dist_routes = [None] * nb_trucks
end_time = [None] * nb_trucks
home_lateness = [None] * nb_trucks
lateness = [None] * 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)

# The quantity needed in each route must not exceed the truck capacity
demand_lambda = model.lambda_function(lambda j: demands[j])
route_quantity = model.sum(sequence, demand_lambda)
model.constraint(route_quantity <= truck_capacity)

# Distance traveled by each truck
dist_lambda = model.lambda_function(
lambda i: model.at(dist_matrix, sequence[i - 1], sequence[i]))
dist_routes[k] = model.sum(model.range(1, c), dist_lambda) \
+ model.iif(c > 0, dist_depot[sequence] + dist_depot[sequence[c - 1]], 0)

# End of each visit according to the traffic
end_time_lambda = model.lambda_function(
lambda i, prev:
model.max(
earliest[sequence[i]],
model.iif(
i == 0, model.at(travel_time_warehouse, sequence, time_to_matrix_idx),
prev + model.at(travel_time, sequence[i - 1], sequence[i],
time_to_matrix_idx[model.round(prev)])))
+ service_time[sequence[i]])

end_time[k] = model.array(model.range(0, c), end_time_lambda)

# Arriving home after max horizon
home_lateness[k] = model.iif(
trucks_used[k],
model.max(
0,
end_time[k][c - 1] + model.at(travel_time_warehouse, sequence[c - 1],
time_to_matrix_idx[model.round(end_time[k][c - 1])]) - max_horizon),
0)

# Completing visit after latest end
late_lambda = model.lambda_function(
lambda i: model.max(0, end_time[k][i] - latest[sequence[i]]))
lateness[k] = home_lateness[k] + model.sum(model.range(0, c), late_lambda)

# Total lateness
total_lateness = model.sum(lateness)

# Total distance traveled
total_distance = model.div(model.round(100 * model.sum(dist_routes)), 100)

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

model.close()

# Parameterize the solver
ls.param.time_limit = int(str_time_limit)

ls.solve()

#
# Write the solution in a file with the following format:
#  - number of trucks used and total distance
#  - for each truck the customers visited (omitting the start/end at the depot)
#
if output_file is not None:
with open(output_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 is to put it back in
# 1...nbCustomers+1 as in the data files (0 being the depot)
for customer in customers_sequences[k].value:
f.write("%d " % (customer + 1))
f.write("\n")

# The input files follow the "Solomon" format

for i in range(4):
next(file_it)

nb_trucks = int(next(file_it))
truck_capacity = int(next(file_it))

for i in range(13):
next(file_it)

depot_x = int(next(file_it))
depot_y = int(next(file_it))

for i in range(2):
next(file_it)

max_horizon = int(next(file_it))

next(file_it)

customers_x = []
customers_y = []
demands = []
earliest_start = []
latest_end = []
service_time = []

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

nb_customers = i + 1

short_distance_travel_time_profile = [1.00, 2.50, 1.75, 2.50, 1.00]
medium_distance_travel_time_profile = [1.00, 2.00, 1.50, 2.00, 1.00]
long_distance_travel_time_profile = [1.00, 1.60, 1.10, 1.60, 1.00]
travel_time_profile_matrix = [
short_distance_travel_time_profile,
medium_distance_travel_time_profile,
long_distance_travel_time_profile
]
distance_levels = [10, 25]
time_interval_steps = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0]
nb_time_intervals = len(time_interval_steps) - 1
nb_distance_levels = len(distance_levels)

# Compute distance matrices
distance_matrix, travel_time, time_to_matrix_idx = compute_distance_matrices(
customers_x, customers_y, max_horizon, travel_time_profile_matrix, time_interval_steps, nb_time_intervals,
distance_levels, nb_distance_levels)
distance_depots, travel_time_warehouse = compute_distance_depots(
depot_x, depot_y, customers_x, customers_y, travel_time_profile_matrix, nb_time_intervals, distance_levels,
nb_distance_levels)

return nb_customers, nb_trucks, truck_capacity, distance_matrix, travel_time, time_to_matrix_idx, distance_depots, \
travel_time_warehouse, demands, service_time, earliest_start, latest_end, max_horizon

# Computes the distance matrices
def compute_distance_matrices(customers_x, customers_y, max_horizon, travel_time_profile_matrix,
time_interval_steps, nb_time_intervals, distance_levels, nb_distance_levels):

nb_customers = len(customers_x)
distance_matrix = [[None for _ in range(nb_customers)] for _ in range(nb_customers)]
travel_time = [[[None for _ in range(nb_time_intervals)] for _ in range(nb_customers)] for _ in range(nb_customers)]
time_to_matrix_idx = [None for _ in range(max_horizon)]
for i in range(nb_customers):
distance_matrix[i][i] = 0

for k in range(nb_time_intervals):
travel_time[i][i][k] = 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

profile_idx = get_profile(dist, distance_levels, nb_distance_levels)
for k in range(nb_time_intervals):
local_travel_time = travel_time_profile_matrix[profile_idx][k] * dist
travel_time[i][j][k] = local_travel_time
travel_time[j][i][k] = local_travel_time

for i in range(nb_time_intervals):
time_step_start = int(round(time_interval_steps[i] * max_horizon))
time_step_end = int(round(time_interval_steps[i+1] * max_horizon))
for j in range(time_step_start, time_step_end):
time_to_matrix_idx[j] = i
return distance_matrix, travel_time, time_to_matrix_idx

# Computes the distances to depot
def compute_distance_depots(depot_x, depot_y, customers_x, customers_y, travel_time_profile_matrix,
nb_time_intervals, distance_levels, nb_distance_levels):
nb_customers = len(customers_x)
distance_depots = [None] * nb_customers
travel_time_warehouse = [[None for _ in range(nb_time_intervals)] for _ in range(nb_customers)]
for i in range(nb_customers):
dist = compute_dist(depot_x, customers_x[i], depot_y, customers_y[i])
distance_depots[i] = dist

profile_idx = get_profile(dist, distance_levels, nb_distance_levels)
for j in range(nb_time_intervals):
local_travel_time_warehouse = travel_time_profile_matrix[profile_idx][j] * dist
travel_time_warehouse[i][j] = local_travel_time_warehouse
return distance_depots, travel_time_warehouse

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

def get_profile(dist, distance_levels, nb_distance_levels):
idx = 0
while idx < nb_distance_levels and dist > distance_levels[idx]:
idx += 1
return idx

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

instance_file = sys.argv
output_file = sys.argv if len(sys.argv) > 2 else None
str_time_limit = sys.argv if len(sys.argv) > 3 else "20"

main(instance_file, str_time_limit, output_file)
```
Compilation / Execution (Windows)
cl /EHsc tdcvrptw.cpp -I%LS_HOME%\include /link %LS_HOME%\bin\localsolver120.lib
tdcvrptw instances\R101.25.txt
Compilation / Execution (Linux)
g++ tdcvrptw.cpp -I/opt/localsolver_12_0/include -llocalsolver120 -lpthread -o tdcvrptw
./tdcvrptw instances/R101.25.txt
```#include "localsolver.h"
#include <cmath>
#include <cstring>
#include <fstream>
#include <iostream>
#include <vector>

using namespace localsolver;
using namespace std;

class Tdcvrptw {
public:
// LocalSolver
LocalSolver localsolver;

// Number of customers
int nbCustomers;

// Capacity of the trucks
int truckCapacity;

// Latest allowed arrival to depot
int maxHorizon;

// Demand for each customer
vector<int> demandsData;

// Earliest arrival for each customer
vector<int> earliestStartData;

// Latest departure from each customer
vector<int> latestEndData;

// Service time for each customer
vector<int> serviceTimeData;

// Distance matrix between customers
vector<vector<double>> distMatrixData;

// Distance  between customers and depot
vector<double> distDepotData;

// Travel time coefficients for each profile
vector<double> shortDistanceTravelTimeProfile{1.00, 2.50, 1.75, 2.50, 1.00};
vector<double> mediumDistanceTravelTimeProfile{1.00, 2.00, 1.50, 2.00, 1.00};
vector<double> longDistanceTravelTimeProfile{1.00, 1.60, 1.10, 1.60, 1.00};
vector<vector<double>> travelTimeProfileMatrix{shortDistanceTravelTimeProfile, mediumDistanceTravelTimeProfile,
longDistanceTravelTimeProfile};

// Distance levels
vector<int> distanceLevels{10, 25};

// Intervals of the temporal discretization
vector<double> timeIntervalSteps{0.0, 0.2, 0.4, 0.6, 0.8, 1.0};

// Number of time intervals
int nbTimeIntervals = timeIntervalSteps.size() - 1;

// Number of distance levels
int nbDistanceLevels = distanceLevels.size();

// Travel time between customers for each day part
vector<vector<vector<double>>> travelTimeData;

// Time interval index for each time unit
vector<int> timeToMatrixIdxData;

// Travel time between customers and depot for each day part
vector<vector<double>> travelTimeWarehouseData;

// Number of trucks
int nbTrucks;

// Decision variables

// 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 traveled by all the trucks
LSExpression totalDistance;

Tdcvrptw() {}

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

// Sequence of customers visited by each truck
for (int k = 0; k < nbTrucks; ++k) {
}

// All customers must be visited by exactly one truck

// Create LocalSolver arrays to be able to access them with an "at" operator
LSExpression demands = model.array(demandsData.begin(), demandsData.end());
LSExpression earliest = model.array(earliestStartData.begin(), earliestStartData.end());
LSExpression latest = model.array(latestEndData.begin(), latestEndData.end());
LSExpression serviceTime = model.array(serviceTimeData.begin(), serviceTimeData.end());
LSExpression distMatrix = model.array();
for (int n = 0; n < nbCustomers; ++n) {
}
LSExpression travelTime = model.array();
for (int n = 0; n < nbCustomers; ++n) {
LSExpression timeMatrix = model.array();
for (int m = 0; m < nbCustomers; ++m) {
}
}
LSExpression timeToMatrixIdx = model.array(timeToMatrixIdxData.begin(), timeToMatrixIdxData.end());
LSExpression distDepot = model.array(distDepotData.begin(), distDepotData.end());
LSExpression travelTimeWarehouse = model.array();
for (int n = 0; n < nbCustomers; ++n) {
model.array(travelTimeWarehouseData[n].begin(), travelTimeWarehouseData[n].end()));
}

trucksUsed.resize(nbTrucks);
vector<LSExpression> distRoutes(nbTrucks), endTime(nbTrucks), homeLateness(nbTrucks), lateness(nbTrucks);

for (int k = 0; k < nbTrucks; ++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 demandLambda =
model.createLambdaFunction([&](LSExpression j) { return demands[j]; });
LSExpression routeQuantity = model.sum(sequence, demandLambda);
model.constraint(routeQuantity <= truckCapacity);

// Distance traveled by truck k
LSExpression distLambda = model.createLambdaFunction(
[&](LSExpression i) { return model.at(distMatrix, sequence[i - 1], sequence[i]); });
distRoutes[k] = model.sum(model.range(1, c), distLambda) +
model.iif(c > 0, distDepot[sequence] + distDepot[sequence[c - 1]], 0);

// End of each visit according to the traffic
LSExpression endTimeLambda = model.createLambdaFunction([&](LSExpression i, LSExpression prev) {
return model.max(earliest[sequence[i]],
model.iif(i == 0, model.at(travelTimeWarehouse, sequence, timeToMatrixIdx),
prev + model.at(travelTime, sequence[i - 1], sequence[i],
timeToMatrixIdx[model.round(prev)]))) +
serviceTime[sequence[i]];
});

endTime[k] = model.array(model.range(0, c), endTimeLambda);

// Arriving home after max horizon
homeLateness[k] = model.iif(trucksUsed[k],
model.max(0, endTime[k][c - 1] +
model.at(travelTimeWarehouse, sequence[c - 1],
timeToMatrixIdx[model.round(endTime[k][c - 1])]) -
maxHorizon),
0);

// Completing visit after latest end
LSExpression lateLambda = model.createLambdaFunction(
[&](LSExpression i) { return model.max(0, endTime[k][i] - latest[sequence[i]]); });
lateness[k] = homeLateness[k] + model.sum(model.range(0, c), lateLambda);
}

// Total lateness
totalLateness = model.sum(lateness.begin(), lateness.end());

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

// Total distance traveled (convention in Solomon's instances is to round to 2 decimals)
totalDistance = model.round(100 * model.sum(distRoutes.begin(), distRoutes.end())) / 100;

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

model.close();

// Parameterize the solver
localsolver.getParam().setTimeLimit(limit);

localsolver.solve();
}

/* Write the solution in a file with the following format:
*  - number of trucks used and total distance
*  - for each truck the customers visited (omitting the start/end at the depot) */
void writeSolution(const string& fileName) {
ofstream outfile;
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 is to put it back in 1...nbCustomers+1
// as in the data files (0 being the depot)
for (int i = 0; i < customersCollection.count(); ++i) {
outfile << customersCollection[i] + 1 << " ";
}
outfile << endl;
}
}

private:
// The input files follow the "Solomon" format
ifstream infile(fileName.c_str());
if (!infile.is_open()) {
throw std::runtime_error("File cannot be opened.");
}

string str;
long tmp;

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;

getline(infile, str);
getline(infile, str);
getline(infile, str);
getline(infile, str);

infile >> tmp;
infile >> depotX;
infile >> depotY;
infile >> tmp;
infile >> tmp;
infile >> maxHorizon;
infile >> tmp;

while (infile >> tmp) {
int cx, cy, demand, ready, due, service;
infile >> cx;
infile >> cy;
infile >> demand;
infile >> due;
infile >> service;

customersX.push_back(cx);
customersY.push_back(cy);
demandsData.push_back(demand);
latestEndData.push_back(due + service); // in input files due date is meant as latest start time
serviceTimeData.push_back(service);
}

nbCustomers = customersX.size();

computeDistanceMatrix(depotX, depotY, customersX, customersY);

infile.close();
}

// Compute the distance matrix
void computeDistanceMatrix(int depotX, int depotY, const vector<int>& customersX, const vector<int>& customersY) {
distMatrixData.resize(nbCustomers);
travelTimeData.resize(nbCustomers);
timeToMatrixIdxData.resize(maxHorizon);
travelTimeWarehouseData.resize(nbCustomers);
for (int i = 0; i < nbCustomers; ++i) {
distMatrixData[i].resize(nbCustomers);
travelTimeData[i].resize(nbCustomers);
for (int j = 0; j < nbCustomers; ++j) {
travelTimeData[i][j].resize(nbTimeIntervals);
}
}
for (int i = 0; i < nbCustomers; ++i) {
travelTimeWarehouseData[i].resize(nbTimeIntervals);
}
for (int i = 0; i < nbCustomers; ++i) {
distMatrixData[i][i] = 0;
for (int k = 0; k < nbTimeIntervals; ++k) {
travelTimeData[i][i][k] = 0;
}
for (int j = i + 1; j < nbCustomers; ++j) {
double distance = computeDist(customersX[i], customersX[j], customersY[i], customersY[j]);
distMatrixData[i][j] = distance;
distMatrixData[j][i] = distance;

int profileIdx = getProfile(distance);
for (int k = 0; k < nbTimeIntervals; ++k) {
double localTravelTime = travelTimeProfileMatrix[profileIdx][k] * distance;
travelTimeData[i][j][k] = localTravelTime;
travelTimeData[j][i][k] = localTravelTime;
}
}
}

for (int i = 0; i < nbTimeIntervals; ++i) {
int timeStepStart = (int)round(timeIntervalSteps[i] * maxHorizon);
int timeStepEnd = (int)round(timeIntervalSteps[i + 1] * maxHorizon);
for (int j = timeStepStart; j < timeStepEnd; ++j) {
timeToMatrixIdxData[j] = i;
}
}

distDepotData.resize(nbCustomers);
for (int i = 0; i < nbCustomers; ++i) {
double distance = computeDist(depotX, customersX[i], depotY, customersY[i]);
distDepotData[i] = distance;

int profileIdx = getProfile(distance);
for (int j = 0; j < nbTimeIntervals; ++j) {
double localTravelTimeWarehouse = travelTimeProfileMatrix[profileIdx][j] * distance;
travelTimeWarehouseData[i][j] = localTravelTimeWarehouse;
}
}
}

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

int getProfile(double distance) {
int idx = 0;
while (idx < nbDistanceLevels && distance > distanceLevels[idx]) {
idx += 1;
}
return idx;
}
};

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

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

try {
Tdcvrptw model;
model.solve(atoi(strTimeLimit));
if (solFile != NULL)
model.writeSolution(solFile);
return 0;
} catch (const exception& e) {
cerr << "An error occurred: " << e.what() << endl;
return 1;
}
}
```
Compilation / Execution (Windows)
copy %LS_HOME%\bin\localsolvernet.dll .
csc Tdcvrptw.cs /reference:localsolvernet.dll
Tdcvrptw instances\R101.25.txt
```using System;
using System.IO;
using System.Collections.Generic;
using localsolver;

public class Tdcvrptw : IDisposable
{
// LocalSolver
LocalSolver localsolver;

// Number of customers
int nbCustomers;

// Capacity of the trucks
int truckCapacity;

// Latest allowed arrival to depot
int maxHorizon;

// Demand for each customer
List<int> demandsData;

// Earliest arrival for each customer
List<int> earliestStartData;

// Latest departure from each customer
List<int> latestEndData;

// Service time for each customer
List<int> serviceTimeData;

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

// Distances between customers and depot
double[] distDepotData;

// Travel time coefficients for each profile
static double[] shortDistanceTravelTimeProfile = { 1.00, 2.50, 1.75, 2.50, 1.00 };
static double[] mediumDistanceTravelTimeProfile = { 1.00, 2.00, 1.50, 2.00, 1.00 };
static double[] longDistanceTravelTimeProfile = { 1.00, 1.60, 1.10, 1.60, 1.00 };
static double[][] travelTimeProfileMatrix =
{
shortDistanceTravelTimeProfile,
mediumDistanceTravelTimeProfile,
longDistanceTravelTimeProfile
};

// Distance levels
static int[] distanceLevels = { 10, 25 };

// Intervals of the temporal discretization
static double[] timeIntervalSteps = { 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 };

// Number of time intervals
static int nbTimeIntervals = timeIntervalSteps.Length - 1;

// Number of distances levels
static int nbDistanceLevels = distanceLevels.Length;

// Travel time between customers for each day part
double[][][] travelTimeData;

// Time interval index for each time unit
int[] timeToMatrixIdxData;

// Travel time between customers and depot for each day part
double[][] travelTimeWarehouseData;

// Number of trucks
int nbTrucks;

// Decision variables

// Are the trucks actually used
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 traveled by all the trucks
LSExpression totalDistance;

public Tdcvrptw()
{
localsolver = new LocalSolver();
}

{
}

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

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

trucksUsed = new LSExpression[nbTrucks];
LSExpression[] distRoutes = new LSExpression[nbTrucks];
LSExpression[] endTime = new LSExpression[nbTrucks];
LSExpression[] homeLateness = new LSExpression[nbTrucks];
LSExpression[] lateness = new LSExpression[nbTrucks];

// Sequence of customers visited by each truck
for (int k = 0; k < nbTrucks; ++k)

// All customers must be visited by exactly one truck

// Create LocalSolver arrays to be able to access them with an "at" operator
LSExpression demands = model.Array(demandsData);
LSExpression earliest = model.Array(earliestStartData);
LSExpression latest = model.Array(latestEndData);
LSExpression serviceTime = model.Array(serviceTimeData);
LSExpression distDepot = model.Array(distDepotData);
LSExpression distMatrix = model.Array(distMatrixData);
LSExpression travelTime = model.Array(travelTimeData);
LSExpression timeToMatrixIdx = model.Array(timeToMatrixIdxData);
LSExpression travelTimeWarehouse = model.Array(travelTimeWarehouseData);

for (int k = 0; k < nbTrucks; ++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 demandLambda = model.LambdaFunction(j => demands[j]);
LSExpression routeQuantity = model.Sum(sequence, demandLambda);
model.Constraint(routeQuantity <= truckCapacity);

// Distance traveled by truck k
LSExpression distLambda = model.LambdaFunction(
i => distMatrix[sequence[i - 1], sequence[i]]
);
distRoutes[k] =
model.Sum(model.Range(1, c), distLambda)
+ model.If(c > 0, distDepot[sequence] + distDepot[sequence[c - 1]], 0);

// End of each visit according to the traffic
LSExpression endTimeLambda = model.LambdaFunction(
(i, prev) =>
model.Max(
earliest[sequence[i]],
model.If(
i == 0,
travelTimeWarehouse[sequence, timeToMatrixIdx],
prev
+ model.At(
travelTime,
sequence[i - 1],
sequence[i],
timeToMatrixIdx[model.Round(prev)]
)
)
) + serviceTime[sequence[i]]
);

endTime[k] = model.Array(model.Range(0, c), endTimeLambda);

// Arriving home after max_horizon
homeLateness[k] = model.If(
trucksUsed[k],
model.Max(
0,
endTime[k][c - 1]
+ travelTimeWarehouse[
sequence[c - 1],
timeToMatrixIdx[model.Round(endTime[k][c - 1])]
]
- maxHorizon
),
0
);

// Completing visit after latest_end
LSExpression lateLambda = model.LambdaFunction(
i => model.Max(endTime[k][i] - latest[sequence[i]], 0)
);
lateness[k] = homeLateness[k] + model.Sum(model.Range(0, c), lateLambda);
}

// Total lateness
totalLateness = model.Sum(lateness);

// Total number of trucks used
nbTrucksUsed = model.Sum(trucksUsed);

// Total distance traveled (convention in Solomon's instances is to round to 2 decimals)
totalDistance = model.Round(100 * model.Sum(distRoutes)) / 100;

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

model.Close();

// Parameterize the solver
localsolver.GetParam().SetTimeLimit(limit);

localsolver.Solve();
}

/* Write the solution in a file with the following format:
*  - number of trucks used and total distance
*  - for each truck the customers 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 is to put it back in 1...nbCustomers+1
// as in the data files (0 being the depot)
for (int i = 0; i < customersCollection.Count(); ++i)
output.Write((customersCollection[i] + 1) + " ");
output.WriteLine();
}
}
}

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

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

{
if (line == null)
return new string;
return line.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
}

// The input files follow the "Solomon" format
{
{
string[] splitted;

splitted = SplitInput(input);
nbTrucks = int.Parse(splitted);
truckCapacity = int.Parse(splitted);

splitted = SplitInput(input);
int depotX = int.Parse(splitted);
int depotY = int.Parse(splitted);
maxHorizon = int.Parse(splitted);

List<int> customersX = new List<int>();
List<int> customersY = new List<int>();
demandsData = new List<int>();
earliestStartData = new List<int>();
latestEndData = new List<int>();
serviceTimeData = new List<int>();

while (!input.EndOfStream)
{
splitted = SplitInput(input);
if (splitted.Length < 7)
break;
int due = int.Parse(splitted);
int service = int.Parse(splitted);

latestEndData.Add(due + service); // in input files due date is meant as latest start time
}

nbCustomers = customersX.Count;

ComputeDistanceMatrix(depotX, depotY, customersX, customersY);
}
}

// Compute the distance matrix
void ComputeDistanceMatrix(int depotX, int depotY, List<int> customersX, List<int> customersY)
{
distMatrixData = new double[nbCustomers][];
travelTimeData = new double[nbCustomers][][];
timeToMatrixIdxData = new int[maxHorizon];
travelTimeWarehouseData = new double[nbCustomers][];

for (int i = 0; i < nbCustomers; ++i)
{
distMatrixData[i] = new double[nbCustomers];
double[][] timeMatrix = new double[nbCustomers][];
for (int j = 0; j < nbCustomers; ++j)
timeMatrix[j] = new double[nbTimeIntervals];
travelTimeData[i] = timeMatrix;
}

for (int i = 0; i < nbCustomers; ++i)
travelTimeWarehouseData[i] = new double[nbTimeIntervals];

for (int i = 0; i < nbCustomers; ++i)
{
distMatrixData[i][i] = 0;
for (int k = 0; k < nbTimeIntervals; ++k)
travelTimeData[i][i][k] = 0;
for (int j = i + 1; j < nbCustomers; ++j)
{
double dist = ComputeDist(
customersX[i],
customersX[j],
customersY[i],
customersY[j]
);
distMatrixData[i][j] = dist;
distMatrixData[j][i] = dist;

int profileIdx = GetProfile(dist);
for (int k = 0; k < nbTimeIntervals; ++k)
{
double localTravelTime = travelTimeProfileMatrix[profileIdx][k] * dist;
travelTimeData[i][j][k] = localTravelTime;
travelTimeData[j][i][k] = localTravelTime;
}
}
}

for (int i = 0; i < nbTimeIntervals; ++i)
{
int timeStepStart = (int)Math.Round(timeIntervalSteps[i] * maxHorizon);
int timeStepEnd = (int)Math.Round(timeIntervalSteps[i + 1] * maxHorizon);
for (int j = timeStepStart; j < timeStepEnd; ++j)
timeToMatrixIdxData[j] = i;
}

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

int profileIdx = GetProfile(dist);
for (int j = 0; j < nbTimeIntervals; ++j)
{
double localTravelTimeWarehouse = travelTimeProfileMatrix[profileIdx][j] * dist;
travelTimeWarehouseData[i][j] = localTravelTimeWarehouse;
}
}
}

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

int GetProfile(double dist)
{
int idx = 0;
while (idx < nbDistanceLevels && dist > distanceLevels[idx])
idx += 1;
return idx;
}
}
```
Compilation / Execution (Windows)
javac Tdcvrptw.java -cp %LS_HOME%\bin\localsolver.jar
java -cp %LS_HOME%\bin\localsolver.jar;. Tdcvrptw instances\R101.25.txt
Compilation / Execution (Linux)
javac Tdcvrptw.java -cp /opt/localsolver_12_0/bin/localsolver.jar
java -cp /opt/localsolver_12_0/bin/localsolver.jar:. Tdcvrptw instances/R101.25.txt
```import java.util.*;
import java.io.*;
import localsolver.*;

public class Tdcvrptw {
// LocalSolver
private final LocalSolver localsolver;

// Number of customers
int nbCustomers;

// Capacity of the trucks
private int truckCapacity;

// Latest allowed arrival to depot
int maxHorizon;

// Demand for each customer
List<Integer> demandsData;

// Earliest arrival for each customer
List<Integer> earliestStartData;

// Latest departure from each customer
List<Integer> latestEndData;

// Service time for each customer
List<Integer> serviceTimeData;

// Distance matrix
private double[][] distMatrixData;

// Distances between customers and depot
private double[] distDepotData;

// Travel time coefficients for each profile
private static double shortDistanceTravelTimeProfile[] = { 1.00, 2.50, 1.75, 2.50, 1.00 };
private static double mediumDistanceTravelTimeProfile[] = { 1.00, 2.00, 1.50, 2.00, 1.00 };
private static double longDistanceTravelTimeProfile[] = { 1.00, 1.60, 1.10, 1.60, 1.00 };
private static double[] travelTimeProfileMatrix[] = {
shortDistanceTravelTimeProfile,
mediumDistanceTravelTimeProfile,
longDistanceTravelTimeProfile
};

// Distance levels
private static int distanceLevels[] = { 10, 25 };

// Intervals of the temporal discretization
private static double timeIntervalSteps[] = { 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 };

// Number of time intervals
private static int nbTimeIntervals = timeIntervalSteps.length - 1;

// Number of distances levels
private static int nbDistanceLevels = distanceLevels.length;

// Travel time between customers for each day part
private double[][][] travelTimeData;

// Time interval index for each time unit
private int[] timeToMatrixIdxData;

// Travel time between customers and depot for each day part
private double[][] travelTimeWarehouseData;

// Number of trucks
private int nbTrucks;

// Decision variables

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

// Distance traveled by each truck
private LSExpression[] distRoutes;

// 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 Tdcvrptw(LocalSolver localsolver) {
this.localsolver = localsolver;
}

private void readInstance(String fileName) throws IOException {
}

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

trucksUsed = new LSExpression[nbTrucks];
distRoutes = 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)

// All customers must be visited by exactly one truck

// Create LocalSolver arrays to be able to access them with an "at" operator
LSExpression demands = m.array(demandsData);
LSExpression earliest = m.array(earliestStartData);
LSExpression latest = m.array(latestEndData);
LSExpression serviceTime = m.array(serviceTimeData);
LSExpression distDepot = m.array(distDepotData);
LSExpression distMatrix = m.array(distMatrixData);
LSExpression travelTime = m.array(travelTimeData);
LSExpression timeToMatrixIdx = m.array(timeToMatrixIdxData);
LSExpression travelTimeWarehouse = m.array(travelTimeWarehouseData);

for (int k = 0; k < nbTrucks; ++k) {
LSExpression c = m.count(sequence);

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

// The quantity needed in each route must not exceed the truck capacity
LSExpression demandLambda = m.lambdaFunction(j -> m.at(demands, j));
LSExpression routeQuantity = m.sum(sequence, demandLambda);
m.constraint(m.leq(routeQuantity, truckCapacity));

// Distance traveled by truck k
LSExpression distLambda = m
.lambdaFunction(i -> m.at(distMatrix, m.at(sequence, m.sub(i, 1)), m.at(sequence, i)));
distRoutes[k] = m.sum(m.sum(m.range(1, c), distLambda), m.iif(m.gt(c, 0),
m.sum(m.at(distDepot, m.at(sequence, 0)), m.at(distDepot, m.at(sequence, m.sub(c, 1)))), 0));

// End of each visit according to the traffic
LSExpression endTimeLambda = m.lambdaFunction((i, prev) -> m.sum(
m.max(m.at(earliest, m.at(sequence, i)),
m.sum(m.iif(m.eq(i, 0),
m.at(travelTimeWarehouse, m.at(sequence, 0), m.at(timeToMatrixIdx, 0)),
m.sum(prev, m.at(travelTime, m.at(sequence, m.sub(i, 1)), m.at(sequence, i),
m.at(timeToMatrixIdx, m.round(prev))))))),
m.at(serviceTime, m.at(sequence, i))));

endTime[k] = m.array(m.range(0, c), endTimeLambda);

LSExpression theEnd = endTime[k];

// Arriving home after max_horizon
homeLateness[k] = m.iif(trucksUsed[k],
m.max(0,
m.sum(m.at(theEnd, m.sub(c, 1)),
m.sub(m.at(m.at(travelTimeWarehouse, m.at(sequence, m.sub(c, 1))),
m.at(timeToMatrixIdx, m.round(m.at(theEnd, m.sub(c, 1))))), maxHorizon))),
0);

// Completing visit after latest_end
LSExpression lateLambda = m
.lambdaFunction(i -> m.max(m.sub(m.at(theEnd, i), m.at(latest, m.at(sequence, i))), 0));
lateness[k] = m.sum(homeLateness[k], m.sum(m.range(0, c), lateLambda));
}

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

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

m.close();

// Parameterize the solver
localsolver.getParam().setTimeLimit(limit);

localsolver.solve();
}

// Write the solution in a file with the following format:
// - number of trucks used and total distance
// - for each truck the customers 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 is to put it back in 1...nbCustomers+1
// as in the data files (0 being the depot)
for (int i = 0; i < customersCollection.count(); ++i) {
output.print((customersCollection.get(i) + 1) + " ");
}
output.println();
}
}
}

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

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

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

input.nextInt();
int depotX = input.nextInt();
int depotY = input.nextInt();
input.nextInt();
input.nextInt();
maxHorizon = input.nextInt();
input.nextInt();

List<Integer> customersX = new ArrayList<Integer>();
List<Integer> customersY = new ArrayList<Integer>();
demandsData = new ArrayList<Integer>();
earliestStartData = new ArrayList<Integer>();
latestEndData = new ArrayList<Integer>();
serviceTimeData = new ArrayList<Integer>();

while (input.hasNextInt()) {
input.nextInt();
int cx = input.nextInt();
int cy = input.nextInt();
int demand = input.nextInt();
int due = input.nextInt();
int service = input.nextInt();

latestEndData.add(due + service);// in input files due date is meant as latest start time
}

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) {
distMatrixData = new double[nbCustomers][nbCustomers];
travelTimeData = new double[nbCustomers][nbCustomers][nbTimeIntervals];
timeToMatrixIdxData = new int[maxHorizon];
travelTimeWarehouseData = new double[nbCustomers][nbTimeIntervals];
for (int i = 0; i < nbCustomers; ++i) {
distMatrixData[i][i] = 0;
for (int k = 0; k < nbTimeIntervals; ++k) {
travelTimeData[i][i][k] = 0;
}
for (int j = i + 1; j < nbCustomers; ++j) {
double dist = computeDist(customersX.get(i), customersX.get(j), customersY.get(i), customersY.get(j));
distMatrixData[i][j] = dist;
distMatrixData[j][i] = dist;

int profileIdx = getProfile(dist);
for (int k = 0; k < nbTimeIntervals; ++k) {
double localTravelTime = travelTimeProfileMatrix[profileIdx][k] * dist;
travelTimeData[i][j][k] = localTravelTime;
travelTimeData[j][i][k] = localTravelTime;
}
}
}

for (int i = 0; i < nbTimeIntervals; ++i) {
int timeStepStart = (int) Math.round(timeIntervalSteps[i] * maxHorizon);
int timeStepEnd = (int) Math.round(timeIntervalSteps[i + 1] * maxHorizon);
for (int j = timeStepStart; j < timeStepEnd; ++j) {
timeToMatrixIdxData[j] = i;
}
}

distDepotData = new double[nbCustomers];
for (int i = 0; i < nbCustomers; ++i) {
double dist = computeDist(depotX, customersX.get(i), depotY, customersY.get(i));
distDepotData[i] = dist;

int profileIdx = getProfile(dist);
for (int j = 0; j < nbTimeIntervals; ++j) {
double localTravelTimeWarehouse = travelTimeProfileMatrix[profileIdx][j] * dist;
travelTimeWarehouseData[i][j] = localTravelTimeWarehouse;
}
}
}

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

private int getProfile(double dist) {
int idx = 0;
while (idx < nbDistanceLevels && dist > distanceLevels[idx]) {
idx += 1;
}
return idx;
}

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

try (LocalSolver localsolver = new LocalSolver()) {
String instanceFile = args;
String outputFile = args.length > 1 ? args : null;
String strTimeLimit = args.length > 2 ? args : "20";

Tdcvrptw model = new Tdcvrptw(localsolver);