Flexible Resource-Constrained Project Scheduling Problem

import hexaly.optimizer
import sys


def read_instance(filename):
    with open(filename) as f:
        lines = f.readlines()

    first_line = lines[0].split()

    # Number of tasks
    nb_tasks = int(first_line[0])

    # Number of resources
    nb_resources = int(first_line[1])

    # Maximum capacity of each resource
    capacity = [int(lines[1].split()[r]) for r in range(nb_resources)]

    # Duration of task i if task i is done by resource r
    task_processing_time_data = [[] for i in range(nb_tasks)]

    # Resource weight of resource r required for task i
    weight = [[] for r in range(nb_resources)]

    # Number of successors
    nb_successors = [0 for i in range(nb_tasks)]

    # Successors of each task i
    successors = [[] for i in range(nb_tasks)]

    for i in range(nb_tasks):
        line_d_w = lines[i + 2].split()
        for r in range(nb_resources):
            task_processing_time_data[i].append(int(line_d_w[2 * r]))
            weight[r].append(int(line_d_w[2 * r + 1]))

        line_succ = lines[i + 2 + nb_tasks].split()
        nb_successors[i] = int(line_succ[0])
        successors[i] = [int(elm) for elm in line_succ[1::]]

    # Trivial upper bound for the start times of the tasks
    horizon = sum(max(task_processing_time_data[i][r] for r in range(nb_resources)) for i in range(nb_tasks))

    return (nb_tasks, nb_resources, capacity, task_processing_time_data, weight, nb_successors, successors, horizon)


def main(instance_file, output_file, time_limit):
    nb_tasks, nb_resources, capacity, task_processing_time_data, weight,\
        nb_successors, successors, horizon = read_instance(instance_file)

    with hexaly.optimizer.HexalyOptimizer() as optimizer:
        #
        # Declare the optimization model
        #
        model = optimizer.model

        # Set of tasks done by each resource
        resources_tasks = [model.set(nb_tasks) for r in range(nb_resources)]
        resources = model.array(resources_tasks)

        # Only compatible resources can be selected for a task
        for i in range(nb_tasks):
            for r in range(nb_resources):
                if task_processing_time_data[i][r] == 0 and weight[r][i] == 0:
                    model.constraint(model.contains(resources_tasks[r], i) == 0)

        # For each task, the selected resource
        task_resource = [model.find(resources, t) for t in range(nb_tasks)]

        # All tasks are scheduled on the resources
        model.constraint(model.partition(resources))

        # Interval decisions: time range of each task
        tasks = [model.interval(0, horizon) for i in range(nb_tasks)]

        # Create Hexaly arrays to be able to access them with an "at" operator
        tasks_array = model.array(tasks)
        task_processing_time = model.array(task_processing_time_data)
        weight_array = model.array(weight)

        # Task duration constraints
        for i in range(nb_tasks):
            model.constraint(model.length(tasks[i]) == task_processing_time[i][task_resource[i]])

        # Precedence constraints between the tasks
        for i in range(nb_tasks):
            for s in range(nb_successors[i]):
                model.constraint(tasks[i] < tasks[successors[i][s]])

        # Makespan: end of the last task
        makespan = model.max([model.end(tasks[i]) for i in range(nb_tasks)])

        # Cumulative resource constraints
        for r in range(nb_resources):
            capacity_respected = model.lambda_function(
                lambda t: model.sum(resources_tasks[r], model.lambda_function(
                    lambda i: model.at(weight_array, r, i) * model.contains(tasks_array[i], t)))
                <= capacity[r])
            model.constraint(model.and_(model.range(makespan), capacity_respected))

        # Minimize the makespan
        model.minimize(makespan)

        model.close()

        # Parameterize the optimizer
        optimizer.param.time_limit = time_limit

        optimizer.solve()

        #
        # Write the solution in a file with the following format:
        # - total makespan
        # - for each task, the task id, the selected resource, the start and end times
        #
        if output_file != None:
            with open(output_file, "w") as f:
                print("Solution written in file", output_file)
                f.write(str(makespan.value) + "\n")
                for i in range(nb_tasks):
                    f.write(
                        str(i) + " " + str(task_resource[i].value) + " " + str(tasks[i].value.start()) + " " +
                        str(tasks[i].value.end()))
                    f.write("\n")


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

    instance_file = sys.argv[1]
    output_file = sys.argv[2] if len(sys.argv) >= 3 else None
    time_limit = int(sys.argv[3]) if len(sys.argv) >= 4 else 60
    main(instance_file, output_file, time_limit)

#include "optimizer/hexalyoptimizer.h"
#include <algorithm>
#include <fstream>
#include <iostream>
#include <limits>
#include <numeric>
#include <vector>

using namespace hexaly;

class FlexibleCumulative {
private:
    // Number of tasks
    int nbTasks;
    // Number of resources
    int nbResources;
    // Maximum capacity of each resource
    std::vector<int> capacity;
    // Duration of task i if task i is done by resource r
    std::vector<std::vector<int>> taskProcessingTimeData;
    // Resource weight of resource r required for task i
    std::vector<std::vector<int>> weightData;
    // Number of successors
    std::vector<int> nbSuccessors;
    // Successors for each task i
    std::vector<std::vector<int>> successors;
    // Trivial upper bound for the start times of the tasks
    int horizon = 0;

    // Hexaly Optimizer
    HexalyOptimizer optimizer;
    // Decision variables: set of tasks done by each resource
    std::vector<HxExpression> resourcesTasks;
    // Decision variables: time range of each task
    std::vector<HxExpression> tasks;
    // For each task, the selected resource
    std::vector<HxExpression> taskResource;
    // Objective = minimize the makespan: end of the last task
    HxExpression makespan;

public:
    FlexibleCumulative(const std::string& fileName) : optimizer() {}

    void readInstance(const std::string& fileName) {
        std::ifstream infile;
        infile.exceptions(std::ifstream::failbit | std::ifstream::badbit);
        infile.open(fileName.c_str());

        infile >> nbTasks;
        infile >> nbResources;

        capacity.resize(nbResources);
        for (int r = 0; r < nbResources; ++r) {
            infile >> capacity[r];
        }

        taskProcessingTimeData.resize(nbTasks);
        weightData.resize(nbResources);

        for (int i = 0; i < nbTasks; ++i) {
            taskProcessingTimeData[i].resize(nbResources);
        }

        for (int r = 0; r < nbResources; ++r) {
            weightData[r].resize(nbTasks);
        }

        for (int i = 0; i < nbTasks; ++i) {
            for (int r = 0; r < nbResources; ++r) {
                infile >> taskProcessingTimeData[i][r];
                std::cout << i << " " << r << " " << taskProcessingTimeData[i][r] << std::endl;
                infile >> weightData[r][i];
            }
        }

        nbSuccessors.resize(nbTasks);
        successors.resize(nbTasks);

        for (int i = 0; i < nbTasks; ++i) {
            infile >> nbSuccessors[i];
            successors[i].resize(nbSuccessors[i]);
            for (int s = 0; s < nbSuccessors[i]; ++s) {
                infile >> successors[i][s];
            }
            horizon += *(std::max_element(taskProcessingTimeData[i].begin(), taskProcessingTimeData[i].end()));
        }

        infile.close();
    }

    void solve(int TimeLimit) {
        // Declare the optimization model
        HxModel model = optimizer.getModel();

        resourcesTasks.resize(nbResources);
        HxExpression resources = model.array();
        for (int r = 0; r < nbResources; ++r) {
            resourcesTasks[r] = model.setVar(nbTasks);
            resources.addOperand(resourcesTasks[r]);
        }

        // Create Hexaly arrays to be able to access them with "at" operators
        HxExpression weight = model.array();
        for (int r = 0; r < nbResources; ++r) {
            weight.addOperand(model.array(weightData[r].begin(), weightData[r].end()));
        }
        HxExpression taskProcessingTime = model.array();
        for (int i = 0; i < nbTasks; ++i) {
            taskProcessingTime.addOperand(
                model.array(taskProcessingTimeData[i].begin(), taskProcessingTimeData[i].end()));
        }

        // Only compatible resources can be selected for a task
        for (int i = 0; i < nbTasks; ++i) {
            for (int r = 0; r < nbResources; ++r) {
                if (taskProcessingTimeData[i][r] == 0 && weightData[r][i] == 0) {
                    model.constraint(model.contains(resourcesTasks[r], i) == 0);
                }
            }
        }

        // All tasks are scheduled on the resources
        model.constraint(model.partition(resources));

        taskResource.resize(nbTasks);
        for (int i = 0; i < nbTasks; ++i) {
            // For each task, the selected resource
            taskResource[i] = model.find(resources, i);
        }

        tasks.resize(nbTasks);
        std::vector<HxExpression> duration(nbTasks);
        for (int i = 0; i < nbTasks; ++i) {
            // Interval decisions: time range of each task
            tasks[i] = model.intervalVar(0, horizon);

            // Task duration constraints
            model.constraint(model.eq(model.length(tasks[i]), taskProcessingTime[i][taskResource[i]]));
        }

        // Precedence constraints between the tasks
        for (int i = 0; i < nbTasks; ++i) {
            for (int s = 0; s < nbSuccessors[i]; ++s) {
                model.constraint(tasks[i] < tasks[successors[i][s]]);
            }
        }

        // Makespan: end of the last task
        makespan = model.max();
        for (int i = 0; i < nbTasks; ++i) {
            makespan.addOperand(model.end(tasks[i]));
        }

        // Create an Hexaly array to be able to access it with "at" operator
        HxExpression tasksArray = model.array();
        for (int i = 0; i < nbTasks; ++i) {
            tasksArray.addOperand(tasks[i]);
        }

        // Cumulative resource constraints
        for (int r = 0; r < nbResources; ++r) {
            HxExpression capacityRespected = model.createLambdaFunction([&](HxExpression t) {
                HxExpression taskWeight = model.createLambdaFunction([&](HxExpression i) {
                    return model.at(weight, r, i) * model.contains(tasksArray[i], t);
                });
                HxExpression totalWeight = model.sum(resourcesTasks[r], taskWeight);
                return model.leq(totalWeight, capacity[r]);
            });
            model.constraint(model.and_(model.range(0, makespan), capacityRespected));
        }

        // Minimize the makespan
        model.minimize(makespan);

        model.close();

        // Parameterize the optimizer
        optimizer.getParam().setTimeLimit(TimeLimit);

        optimizer.solve();
    }

    /* Write the solution in a file with the following format:
     *  - total makespan
     *  - for each task, the task id, the selected resource, the start and end times */
    void writeSolution(const std::string& fileName) {
        std::ofstream outfile(fileName.c_str());
        if (!outfile.is_open()) {
            std::cerr << "File " << fileName << " cannot be opened." << std::endl;
            exit(1);
        }
        std::cout << "Solution written in file " << fileName << std::endl;

        outfile << makespan.getValue() << std::endl;
        for (int i = 0; i < nbTasks; ++i) {
            outfile << i << " " << taskResource[i].getValue() << " " << tasks[i].getIntervalValue().getStart() << " "
                    << tasks[i].getIntervalValue().getEnd() << std::endl;
        }
        outfile.close();
    }
};

int main(int argc, char** argv) {
    if (argc < 2) {
        std::cout << "Usage: flexible_cumulative instanceFile [outputFile] [timeLimit]" << std::endl;
        exit(1);
    }

    const char* instanceFile = argv[1];
    const char* outputFile = argc > 2 ? argv[2] : NULL;
    const char* strTimeLimit = argc > 3 ? argv[3] : "60";

    FlexibleCumulative model(instanceFile);
    try {
        model.readInstance(instanceFile);
        const int timeLimit = atoi(strTimeLimit);
        model.solve(timeLimit);
        if (outputFile != NULL)
            model.writeSolution(outputFile);
        return 0;
    } catch (const std::exception& e) {
        std::cerr << "An error occurred: " << e.what() << std::endl;
        return 1;
    }
}

using System;
using System.IO;
using System.Linq;
using Hexaly.Optimizer;

public class FlexibleCumulative : IDisposable
{
    // Number of tasks
    private int nbTasks;

    // Number of resources
    private int nbResources;

    // Maximum capacity of each resource
    private int[] capacity;

    // Duration of task i if task i is done by resource r
    private int[][] taskProcessingTimeData;

    // Resource weight of resource r required for task i
    private int[][] weightData;

    // Number of successors
    private int[] nbSuccessors;

    // Successors for each task i
    private int[][] successors;

    // Trivial upper bound for the start times of the tasks
    private int horizon = 0;

    // Hexaly Optimizer
    private HexalyOptimizer optimizer;

    // Decision variables: set of tasks done by each resource
    private HxExpression[] resourcesTasks;

    // Decision variables: time range of each task
    private HxExpression[] tasks;

    // For each task, the selected resource
    private HxExpression[] taskResource;

    // Objective = minimize the makespan: end of the last task
    private HxExpression makespan;

    public FlexibleCumulative(string fileName)
    {
        optimizer = new HexalyOptimizer();
    }

    private static string[] ReadNextLine(StreamReader input) {
        return input.ReadLine().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
    }

    private void ReadInstance(string fileName)
    {
        using (StreamReader input = new StreamReader(fileName))
        {
            string[] splitted = ReadNextLine(input);
            if (splitted.Length == 0)
                splitted = ReadNextLine(input);
            nbTasks = int.Parse(splitted[0]);
            nbResources = int.Parse(splitted[1]);

            capacity = new int[nbResources];
            splitted = ReadNextLine(input);
            for (int r = 0; r < nbResources; ++r)
                capacity[r] = int.Parse(splitted[r]);

            taskProcessingTimeData = new int[nbTasks][];
            for (int i = 0; i < nbTasks; i++)
                taskProcessingTimeData[i] = new int[nbResources];

            weightData = new int[nbResources][];
            for (int r = 0; r < nbResources; r++)
                weightData[r] = new int[nbTasks];

            for (int i = 0; i < nbTasks; ++i)
            {
                splitted = ReadNextLine(input);
                if (splitted.Length == 0)
                    splitted = ReadNextLine(input);
                for (int r = 0; r < nbResources; ++r)
                {
                    taskProcessingTimeData[i][r] = int.Parse(splitted[2 * r]);
                    weightData[r][i] = int.Parse(splitted[2 * r + 1]);
                }
            }

            nbSuccessors = new int[nbTasks];
            successors = new int[nbTasks][];

            for (int i = 0; i < nbTasks; ++i)
            {
                splitted = ReadNextLine(input);
                if (splitted.Length == 0)
                    splitted = ReadNextLine(input);
                nbSuccessors[i] = int.Parse(splitted[0]);
                successors[i] = new int[nbSuccessors[i]];
                for (int s = 0; s < nbSuccessors[i]; ++s)
                    successors[i][s] = int.Parse(splitted[s + 1]);
                horizon += (taskProcessingTimeData[i]).Max();
            }
        }
    }

    public void Dispose()
    {
        optimizer.Dispose();
    }

    public void Solve(int timeLimit)
    {
        // Declare the optimization model
        HxModel model = optimizer.GetModel();

        resourcesTasks = new HxExpression[nbResources];

        for (int r = 0; r < nbResources; ++r)
            resourcesTasks[r] = model.Set(nbTasks);

        // Create HexalyOptimizer arrays to be able to access them with "at" operators
        HxExpression resources = model.Array(resourcesTasks);
        HxExpression weight = model.Array(weightData);
        HxExpression taskProcessingTime = model.Array(taskProcessingTimeData);

        // Only compatible resources can be selected for a task
        for (int i = 0; i < nbTasks; ++i)
        {
            for (int r = 0; r < nbResources; ++r)
            {
                if (taskProcessingTimeData[i][r] == 0 && weightData[r][i] == 0)
                {
                    model.Constraint(model.Contains(resourcesTasks[r], i) == 0);
                }
            }
        }

        // All tasks are scheduled on the resources
        model.Constraint(model.Partition(resources));

        taskResource = new HxExpression[nbTasks];
        for (int i = 0; i < nbTasks; ++i)
        {
            // For each task, the selected resource
            taskResource[i] = model.Find(resources, i);
        }

        tasks = new HxExpression[nbTasks];
        for (int i = 0; i < nbTasks; ++i)
        {
            // Interval decisions: time range of each task
            tasks[i] = model.Interval(0, horizon);

            // Task duration constraints
            HxExpression iExpr = model.CreateConstant(i);
            HxExpression duration = model.At(taskProcessingTime, iExpr, taskResource[i]);
            model.Constraint(model.Length(tasks[i]) == duration);
        }

        // Create a HexalyOptimizer array to be able to access it with "at" operator
        HxExpression tasksArray = model.Array();
        for (int i = 0; i < nbTasks; ++i)
            tasksArray.AddOperand(tasks[i]);

        // Precedence constraints between the tasks
        for (int i = 0; i < nbTasks; ++i)
        {
            for (int s = 0; s < nbSuccessors[i]; ++s)
            {
                model.Constraint(tasks[i] < tasks[successors[i][s]]);
            }
        }

        // Makespan: end of the last task
        makespan = model.Max();
        for (int i = 0; i < nbTasks; ++i)
            makespan.AddOperand(model.End(tasks[i]));

        // Cumulative resource constraints
        for (int r = 0; r < nbResources; ++r)
        {
            HxExpression capacityRespected = model.LambdaFunction(t =>
                {
                    HxExpression taskWeight = model.LambdaFunction(i =>
                    {
                        HxExpression rExpr = model.CreateConstant(r);
                        return model.At(weight, rExpr, i) * model.Contains(tasksArray[i], t);
                    });
                    HxExpression totalWeight = model.Sum(resourcesTasks[r], taskWeight);
                    return totalWeight <= capacity[r];
                });
            model.Constraint(model.And(model.Range(0, makespan), capacityRespected));
        }

        // Minimize the makespan
        model.Minimize(makespan);

        model.Close();

        // Parameterize the optimizer
        optimizer.GetParam().SetTimeLimit(timeLimit);

        optimizer.Solve();
    }

    /* Write the solution in a file with the following format:
     *  - total makespan
     *  - for each task, the task id, the selected resource, the start and end times */
    public void WriteSolution(string fileName)
    {
        using (StreamWriter output = new StreamWriter(fileName))
        {
            Console.WriteLine("Solution written in file " + fileName);
            output.WriteLine(makespan.GetValue());
            for (int i = 0; i < nbTasks; ++i)
            {
                output.Write(i + " " + taskResource[i].GetValue() + " " + tasks[i].GetIntervalValue().Start() + " "
                        + tasks[i].GetIntervalValue().End());
                output.WriteLine();
            }
        }
    }

    public static void Main(string[] args)
    {
        if (args.Length < 1)
        {
            Console.WriteLine("Usage: FlexibleCumulative instanceFile [outputFile] [timeLimit]");
            System.Environment.Exit(1);
        }

        string instanceFile = args[0];
        string outputFile = args.Length > 1 ? args[1] : null;
        string strTimeLimit = args.Length > 2 ? args[2] : "60";

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

import java.util.*;
import java.io.*;
import com.hexaly.optimizer.*;

public class FlexibleCumulative {
    // Number of tasks
    private int nbTasks;
    // Number of resources
    private int nbResources;
    // Maximum capacity of each resource
    private int[] capacity;
    // Duration of task i if task i is done by resource r
    private int[][] taskProcessingTimeData;
    // Resource weight of resource r required for task i
    private int[][] weightData;
    // Number of successors
    private int[] nbSuccessors;
    // Successors for each task i
    private int[][] successors;
    // Trivial upper bound for the start times of the tasks
    private int horizon = 0;

    // Hexaly Optimizer
    final HexalyOptimizer optimizer;
    // Decision variables: set of tasks done by each resource
    private HxExpression[] resourcesTasks;
    // Decision variables: time range of each task
    private HxExpression[] tasks;
    // For each task, the selected resource
    private HxExpression[] taskResource;
    // Objective = minimize the makespan: end of the last task
    private HxExpression makespan;

    public FlexibleCumulative(HexalyOptimizer optimizer, String fileName) throws IOException {
        this.optimizer = optimizer;
    }

    private void readInstance(String fileName) throws IOException {
        try (Scanner input = new Scanner(new File(fileName))) {
            nbTasks = input.nextInt();
            nbResources = input.nextInt();

            capacity = new int[nbResources];
            for (int r = 0; r < nbResources; ++r) {
                capacity[r] = input.nextInt();
            }

            taskProcessingTimeData = new int[nbTasks][nbResources];
            weightData = new int[nbResources][nbTasks];
            nbSuccessors = new int[nbTasks];
            successors = new int[nbTasks][];
            for (int i = 0; i < nbTasks; ++i) {
                for (int r = 0; r < nbResources; ++r) {
                    taskProcessingTimeData[i][r] = input.nextInt();
                    weightData[r][i] = input.nextInt();
                }
            }
            for (int i = 0; i < nbTasks; ++i) {
                nbSuccessors[i] = input.nextInt();
                successors[i] = new int[nbSuccessors[i]];
                for (int s = 0; s < nbSuccessors[i]; ++s) {
                    successors[i][s] = input.nextInt();
                }

                int maxDurationTask = taskProcessingTimeData[i][0];
                for (int r = 0; r < nbResources; ++r) {
                    if (taskProcessingTimeData[i][r] > taskProcessingTimeData[i][0]) {
                        maxDurationTask = taskProcessingTimeData[i][r];
                    }
                }
                horizon += maxDurationTask;
            }
        }
    }

    public void solve(int timeLimit) {
        // Declare the optimization model
        HxModel model = optimizer.getModel();

        resourcesTasks = new HxExpression[nbResources];

        for (int r = 0; r < nbResources; ++r) {
            resourcesTasks[r] = model.setVar(nbTasks);
        }
        // Create HexalyOptimizer arrays to be able to access them with "at" operators
        HxExpression resources = model.array(resourcesTasks);
        HxExpression weight = model.array(weightData);
        HxExpression taskProcessingTime = model.array(taskProcessingTimeData);

        // Only compatible resources can be selected for a task
        for (int i = 0; i < nbTasks; ++i) {
            for (int r = 0; r < nbResources; ++r) {
                if (taskProcessingTimeData[i][r] == 0 && weightData[r][i] == 0) {
                    model.constraint(model.eq(model.contains(resourcesTasks[r], i), 0));
                }
            }
        }
        
        // All tasks are scheduled on the resources
        model.constraint(model.partition(resources));
        
        taskResource = new HxExpression[nbTasks];
        for (int i = 0; i < nbTasks; ++i) {
            // For each task, the selected resource
            taskResource[i] = model.find(resources, i);
        }

        tasks = new HxExpression[nbTasks];
        for (int i = 0; i < nbTasks; ++i) {
            // Interval decisions: time range of each task
            tasks[i] = model.intervalVar(0, horizon);

            // Task duration constraints
            HxExpression iExpr = model.createConstant(i);
            HxExpression duration = model.at(taskProcessingTime, iExpr, taskResource[i]);
            model.constraint(model.eq(model.length(tasks[i]), duration));
        }

        // Create a HexalyOptimizer array to be able to access it with "at" operator
        HxExpression tasksArray = model.array();
        for (int i = 0; i < nbTasks; ++i) {
            tasksArray.addOperand(tasks[i]);
        }

        // Precedence constraints between the tasks
        for (int i = 0; i < nbTasks; ++i) {
            for (int s = 0; s < nbSuccessors[i]; ++s) {
                model.constraint(model.lt(tasks[i], tasks[successors[i][s]]));
            }
        }

        // Makespan: end of the last task
        makespan = model.max();
        for (int i = 0; i < nbTasks; ++i) {
            makespan.addOperand(model.end(tasks[i]));
        }

        // Cumulative resource constraints
        for (int r = 0; r < nbResources; ++r) {
            final int rL = r;
            HxExpression capacityRespected = model.lambdaFunction(t -> {
                HxExpression taskWeight = model.lambdaFunction(i -> {
                    HxExpression rExpr = model.createConstant(rL);
                    return model.prod(
                           model.at(weight, rExpr, i),
                           model.contains(model.at(tasksArray, i), t));
                });
                HxExpression totalWeight = model.sum(resourcesTasks[rL], taskWeight);
                return model.leq(totalWeight, capacity[rL]);
            });
            model.constraint(model.and(model.range(0, makespan), capacityRespected));
        }

        // Minimize the makespan
        model.minimize(makespan);
        model.close();

        // Parameterize the optimizer
        optimizer.getParam().setTimeLimit(timeLimit);

        optimizer.solve();
    }

    /*
     * Write the solution in a file with the following format:
     * - total makespan
     * - for each task, the task id, the selected resource, the start and end times
     */
    public void writeSolution(String fileName) throws IOException {
        try (PrintWriter output = new PrintWriter(fileName)) {
            System.out.println("Solution written in file " + fileName);

            output.println(makespan.getValue());

            for (int i = 0; i < nbTasks; ++i) {
                output.println(i + " " + taskResource[i].getValue() + " " + tasks[i].getIntervalValue().getStart() + " "
                        + tasks[i].getIntervalValue().getEnd());
            }
        }
    }

    public static void main(String[] args) {
        if (args.length < 1) {
            System.out.println("Usage: java FlexibleCumulative instanceFile [outputFile] [timeLimit]");
            System.exit(1);
        }

        String instanceFile = args[0];
        String outputFile = args.length > 1 ? args[1] : null;
        String strTimeLimit = args.length > 2 ? args[2] : "60";

        try (HexalyOptimizer optimizer = new HexalyOptimizer()) {
            FlexibleCumulative model = new FlexibleCumulative(optimizer, instanceFile);
            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);
        }
    }
}