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Flexible Job Shop Scheduling Problem with Sequence-Dependent Setup Times (FJSP-SDST)

Principles learned

  • Add multiple list decision variables

  • Use the find operator

  • Order numeric decision variables by pairing them up with a list variable

Problem

../_images/fjsp_setup.svg

In the flexible job shop scheduling problem with sequence-dependent setup times (FJSP-SDST), a set of jobs has to be processed on the machines in the shop. Each job consists of an ordered sequence of tasks (called operations), and each operation must be performed by one of the machines compatible with that operation. An operation cannot begin until the previous operation in the job is completed. Each operation has a given processing time that depends on the chosen machine. Each machine can only process one operation at a time and must be set up between two consecutive operations. These setup times depend both on the operations and the machine considered.

The goal is to find a sequence of jobs that minimizes the makespan: the time when all jobs have been processed.

Download the example


Data

The format of the data files is as follows:

  • First line: number of jobs, number of machines (+ average number of machines per operations, not needed)

  • From the second line, for each job:

    • Number of operations in that job

    • For each operation:

      • Number of machines compatible with this operation

      • For each compatible machine: a pair of numbers (machine, processing time)

  • For each machine and each operation:

    • Setup time between the first operation and every other operation on the machine considered

Program

The model is an extension from the Flexible Job Shop Problem with the use of the setup times on the machines. The decision variables are the following : we represent the start times of the tasks by integer decision variables and we model the order of the operations performed on each machine by a list decision variable.

Each operation of each job must be processed on one and only one machine, hence the partition operator on the lists.

The disjunctive resource contraints between tasks on a machine guarantee that an operation starts on a machine only after the previous operation is done and the setup between the two operations is completed.

The constraints of compatibility of the machines are modeled in the same way as for the flexible job shop problem, and the makespan to be minimized is the time when all tasks have been processed.

Execution:
localsolver flexible_jobshop_setup.lsp inFileName=instances/Fattahi_setup_01.fjs [outFileName=] [lsTimeLimit=]
use io;

/* Read instance data */
function input() {
    local usage = "Usage: localsolver flexible_jobshop_setup.lsp inFileName=instanceFile"
            + " [outFileName=outputFile] [lsTimeLimit=timeLimit]";

    if (inFileName == nil) throw usage;

    // Constant for incompatible machines
    INFINITE = 1000000;

    inFile = io.openRead(inFileName);
    // Number of jobs
    nbJobs = inFile.readInt();
    // Number of machines
    nbMachines = inFile.readInt();
    inFile.readln(); // skip last number

    // Number of tasks
    nbTasks = 0;
    processingTime = {};
    // Processing time for each task, for each machine
    taskProcessingTime = {};
    // For each job, for each operation, the corresponding task id
    jobOperationTask = {};
    
    for [j in 0..nbJobs-1] {
        // Number of operations for each job
        nbOperations[j] = inFile.readInt();
        for [o in 0..nbOperations[j]-1] {
            local nbMachinesOperation = inFile.readInt();
            for [i in 0..nbMachinesOperation-1] {
                local machine = inFile.readInt() - 1;
                local time = inFile.readInt();
                processingTime[j][o][machine] = time;
                taskProcessingTime[nbTasks][machine] = time;
            }
            jobOperationTask[j][o] = nbTasks;
            nbTasks += 1;
        }
    }

    // Setup time between every two consecutive tasks, for each machine
    taskSetupTime[0..nbMachines-1][0..nbTasks-1][0..nbTasks-1] = inFile.readInt();

    inFile.close();

    // Trivial upper bound for the start times of the tasks
    maxStart = 0;
    for [j in 0..nbJobs-1][o in 0..nbOperations[j]-1] {
        local maxProcessingTime = 0;
        for [m in 0..nbMachines - 1] {
            if (processingTime[j][o][m] == nil) {
                local task = jobOperationTask[j][o];
                taskProcessingTime[task][m] = INFINITE;
            } else if (processingTime[j][o][m] >= maxProcessingTime) {
                maxProcessingTime = processingTime[j][o][m];
            }
        }
        maxStart += maxProcessingTime;
    }
}

/* Declare the optimization model */
function model() {
    // Sequence of tasks on each machine
    jobsOrder[m in 0..nbMachines-1] <- list(nbTasks);

    // Each task is scheduled on a machine
    constraint partition[m in 0..nbMachines-1](jobsOrder[m]);

    // Only compatible machines can be selected for a task
    for [t in 0..nbTasks-1][m in 0..nbMachines-1 : taskProcessingTime[t][m] == INFINITE]
        constraint contains(jobsOrder[m], t) == false;

    // For each task, the selected machine
    taskMachine[t in 0..nbTasks-1] <- find(jobsOrder, t);

    // Integer decisions: start time of each task
    start[t in 0..nbTasks-1] <- int(0, maxStart);

    // The task duration depends on the selected machine
    duration[t in 0..nbTasks-1] <- taskProcessingTime[t][taskMachine[t]];
    end[t in 0..nbTasks-1] <- start[t] + duration[t];

    // Precedence constraints between the operations of a job
    for [j in 0..nbJobs-1][o in 0..nbOperations[j]-2] {
        local t1 = jobOperationTask[j][o];
        local t2 = jobOperationTask[j][o + 1];
        constraint start[t2] >= end[t1];
    }

    // Disjunctive resource constraints between the tasks on a machine
    for [m in 0..nbMachines-1] {
        local sequence <- jobsOrder[m];
        constraint and(0..count(sequence)-2, t =>
        start[sequence[t + 1]] >= end[sequence[t]]
                + taskSetupTime[m][sequence[t]][sequence[t + 1]]);
    }

    // Minimize the makespan: end of the last task
    makespan <- max[t in 0..nbTasks-1](end[t]);
    minimize makespan;
}

/* Parameterize the solver */
function param() {
    if (lsTimeLimit == nil) lsTimeLimit = 60;
}

/* Write the solution in a file with the following format:
 *  - for each operation of each job, the selected machine, the start and end dates */
function output() {
    if (outFileName != nil) {
        outFile = io.openWrite(outFileName);
        println("Solution written in file ", outFileName);
        for [j in 0..nbJobs-1][o in 0..nbOperations[j]-1] {
            local task = jobOperationTask[j][o];
            outFile.println(j + 1, "\t", o + 1, "\t", taskMachine[task].value + 1, 
                    "\t", start[task].value, "\t", end[task].value);
        }
    }
}
Execution (Windows)
set PYTHONPATH=%LS_HOME%\bin\python
python flexible_jobshop_setup.py instances\Fattahi_setup_01.fjs
Execution (Linux)
export PYTHONPATH=/opt/localsolver_11_5/bin/python
python flexible_jobshop_setup.py instances/Fattahi_setup_01.fjs
import localsolver
import sys

# Constant for incompatible machines
INFINITE = 1000000


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

    first_line = lines[0].split()
    # Number of jobs
    nb_jobs = int(first_line[0])
    # Number of machines
    nb_machines = int(first_line[1])

    # Number of operations for each job
    nb_operations = [int(lines[j + 1].split()[0]) for j in range(nb_jobs)]

    # Number of tasks
    nb_tasks = sum(nb_operations[j] for j in range(nb_jobs))

    # Processing time for each task, for each machine
    task_processing_time = [[INFINITE for m in range(nb_machines)] for t in range(nb_tasks)]

    # For each job, for each operation, the corresponding task id
    job_operation_task = [[0 for o in range(nb_operations[j])] for j in range(nb_jobs)]

    # Setup time between every two consecutive tasks, for each machine
    task_setup_time = [[[-1 for r in range(nb_tasks)] for t in range(nb_tasks)] for m in range(nb_machines)]

    id = 0
    for j in range(nb_jobs):
        line = lines[j + 1].split()
        tmp = 0
        for o in range(nb_operations[j]):
            nb_machines_operation = int(line[tmp + o + 1])
            for i in range(nb_machines_operation):
                machine = int(line[tmp + o + 2 * i + 2]) - 1
                time = int(line[tmp + o + 2 * i + 3])
                task_processing_time[id][machine] = time
            job_operation_task[j][o] = id
            id = id + 1
            tmp = tmp + 2 * nb_machines_operation

    id_line = nb_jobs + 2
    for m in range(nb_machines):
        for t1 in range(nb_tasks):
            task_setup_time[m][t1] = list(map(int, lines[id_line].split()))
            id_line += 1

    # Trivial upper bound for the start times of the tasks
    max_start = sum(
        max(task_processing_time[t][m] for m in range(nb_machines) if task_processing_time[t][m] != INFINITE)
        for t in range(nb_tasks))

    return nb_jobs, nb_machines, nb_tasks, task_processing_time, job_operation_task, \
        nb_operations, task_setup_time, max_start


def main(instance_file, output_file, time_limit):
    nb_jobs, nb_machines, nb_tasks, task_processing_time_data, job_operation_task, \
        nb_operations, task_setup_time_data, max_start = read_instance(instance_file)

    with localsolver.LocalSolver() as ls:
        #
        # Declare the optimization model
        #
        model = ls.model

        # Sequence of tasks on each machine
        jobs_order = [model.list(nb_tasks) for _ in range(nb_machines)]
        machines = model.array(jobs_order)

        # Each task is scheduled on a machine
        model.constraint(model.partition(machines))

        # Only compatible machines can be selected for a task
        for t in range(nb_tasks):
            for m in range(nb_machines):
                if task_processing_time_data[t][m] == INFINITE:
                    model.constraint(model.not_(model.contains(jobs_order[m], t)))

        # For each task, the selected machine
        task_machine = [model.find(machines, t) for t in range(nb_tasks)]

        task_processing_time = model.array(task_processing_time_data)
        task_setup_time = model.array(task_setup_time_data)

        # Integer decisions: start time of each task
        start = [model.int(0, max_start) for _ in range(nb_tasks)]

        # The task duration depends on the selected machine
        duration = [model.at(task_processing_time, t, task_machine[t]) for t in range(nb_tasks)]
        end = [start[t] + duration[t] for t in range(nb_tasks)]

        start_array = model.array(start)
        end_array = model.array(end)

        # Precedence constraints between the operations of a job
        for j in range(nb_jobs):
            for o in range(nb_operations[j] - 1):
                t1 = job_operation_task[j][o]
                t2 = job_operation_task[j][o + 1]
                model.constraint(start[t2] >= end[t1])

        # Disjunctive resource constraints between the tasks on a machine
        for m in range(nb_machines):
            sequence = jobs_order[m]
            sequence_lambda = model.lambda_function(
                lambda t: start_array[sequence[t + 1]] >= end_array[sequence[t]]
                        + model.at(task_setup_time, m, sequence[t], sequence[t + 1]))
            model.constraint(model.and_(model.range(0, model.count(sequence) - 1), sequence_lambda))

        # Minimize the makespan: end of the last task
        makespan = model.max(end)
        model.minimize(makespan)

        model.close()

        # Parameterize the solver
        ls.param.time_limit = time_limit

        ls.solve()

        # Write the solution in a file with the following format:
        # - for each operation of each job, the selected machine, the start and end dates
        if output_file != None:
            with open(output_file, "w") as f:
                print("Solution written in file", output_file)
                for j in range(nb_jobs):
                    for o in range(0, nb_operations[j]):
                        task = job_operation_task[j][o]
                        f.write(str(j + 1) + "\t" + str(o + 1) + "\t" + str(task_machine[task].value + 1) 
                            + "\t" + str(start[task].value) + "\t" + str(end[task].value) + "\n")


if __name__ == '__main__':
    if len(sys.argv) < 2:
        print("Usage: python flexible_jobshop_setup.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)
Compilation / Execution (Windows)
cl /EHsc flexible_jobshop.cpp -I%LS_HOME%\include /link %LS_HOME%\bin\localsolver115.lib
flexible_jobshop_setup instances\Fattahi_setup_01.fjs
Compilation / Execution (Linux)
g++ flexible_jobshop.cpp -I/opt/localsolver_11_5/include -llocalsolver115 -lpthread -o flexible_jobshop
./flexible_jobshop_setup instances/Fattahi_setup_01.fjs
#include "localsolver.h"
#include <algorithm>
#include <fstream>
#include <iostream>
#include <limits>
#include <numeric>
#include <vector>

using namespace localsolver;

class FlexibleJobshopSetup {
  private:
    // Number of jobs
    int nbJobs;
    // Number of machines
    int nbMachines;
    // Number of tasks
    int nbTasks;
    // Processing time for each task, for each machine
    std::vector<std::vector<int>> taskProcessingTimeData;
    // Setup time between every two consecutive tasks, for each machine
    std::vector<std::vector<std::vector<int>>> taskSetupTimeData;
    // For each job, for each operation, the corresponding task id
    std::vector<std::vector<int>> jobOperationTask;
    // Number of operations for each job
    std::vector<int> nbOperations;
    // Trivial upper bound for the start times of the tasks
    int maxStart;
    // Constant for incompatible machines
    const int INFINITE = 1000000;

    // LocalSolver
    LocalSolver localsolver;
    // Decision variables: start times of the tasks
    std::vector<LSExpression> start;
    // Decision variables: sequence of tasks on each machine
    std::vector<LSExpression> jobsOrder;
    // For each task, the selected machine
    std::vector<LSExpression> taskMachine;
    // End times of the tasks
    std::vector<LSExpression> end;
    // Objective = minimize the makespan: end of the last task
    LSExpression makespan;

  public:
    FlexibleJobshopSetup() : localsolver() {}

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

        infile >> nbJobs;
        infile >> nbMachines;
        infile.ignore(std::numeric_limits<std::streamsize>::max(), '\n'); // skip last number

        nbTasks = 0;
        std::vector<std::vector<std::vector<int>>> processingTime = std::vector<std::vector<std::vector<int>>>(nbJobs);
        jobOperationTask.resize(nbJobs);
        nbOperations.resize(nbJobs);
        for (unsigned int j = 0; j < nbJobs; ++j) {
            infile >> nbOperations[j];
            jobOperationTask[j].resize(nbOperations[j]);
            processingTime[j].resize(nbOperations[j]);
            for (unsigned int o = 0; o < nbOperations[j]; ++o) {
                int nbMachinesOperation;
                infile >> nbMachinesOperation;
                taskProcessingTimeData.push_back(std::vector<int>(nbMachines, INFINITE));
                processingTime[j][o].resize(nbMachines, INFINITE);
                for (int m = 0; m < nbMachinesOperation; ++m) {
                    int machine;
                    int time;
                    infile >> machine;
                    infile >> time;
                    processingTime[j][o][machine - 1] = time;
                    taskProcessingTimeData[nbTasks][machine - 1] = time;
                }
                jobOperationTask[j][o] = nbTasks;
                nbTasks += 1;
            }
        }

        taskSetupTimeData = std::vector<std::vector<std::vector<int>>>(
            nbMachines, std::vector<std::vector<int>>(nbTasks, std::vector<int>(nbTasks)));
        for (unsigned int m = 0; m < nbMachines; m++) {
            for (unsigned int i = 0; i < nbTasks; i++) {
                for (unsigned int j = 0; j < nbTasks; j++) {
                    infile >> taskSetupTimeData[m][i][j];
                }
            }
        }

        infile.close();

        // Trivial upper bound for the start times of the tasks
        maxStart = 0;
        for (unsigned int j = 0; j < nbJobs; ++j) {
            for (unsigned int o = 0; o < nbOperations[j]; ++o) {
                int maxProcessingTime = 0;
                for (unsigned int m = 0; m < nbMachines; ++m) {
                    if (processingTime[j][o][m] != INFINITE && processingTime[j][o][m] > maxProcessingTime)
                        maxProcessingTime = processingTime[j][o][m];
                }
                maxStart += maxProcessingTime;
            }
        }
    }

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

        // Sequence of tasks on each machine
        jobsOrder.resize(nbMachines);
        LSExpression machines = model.array();
        for (unsigned int m = 0; m < nbMachines; ++m) {
            jobsOrder[m] = model.listVar(nbTasks);
            machines.addOperand(jobsOrder[m]);
        }

        // Each task is scheduled on a machine
        model.constraint(model.partition(machines));

        // Only compatible machines can be selected for a task
        for (int t = 0; t < nbTasks; ++t) {
            for (unsigned int m = 0; m < nbMachines; ++m) {
                if (taskProcessingTimeData[t][m] == INFINITE) {
                    model.constraint(!model.contains(jobsOrder[m], t));
                }
            }
        }

        taskMachine.resize(nbTasks);
        LSExpression taskProcessingTime = model.array();
        for (int t = 0; t < nbTasks; ++t) {
            // For each task, the selected machine
            taskMachine[t] = model.find(machines, t);
            taskProcessingTime.addOperand(model.array(taskProcessingTimeData[t].begin(), taskProcessingTimeData[t].end()));
        }

        LSExpression taskSetupTime = model.array();
        for (int m = 0; m < nbMachines; ++m) {
            LSExpression setupTimeMachine = model.array();
            for (int t = 0; t < nbTasks; ++t) {
                setupTimeMachine.addOperand(
                    model.array(taskSetupTimeData[m][t].begin(), taskSetupTimeData[m][t].end()));
            }
            taskSetupTime.addOperand(setupTimeMachine);
        }

        start.resize(nbTasks);
        std::vector<LSExpression> duration(nbTasks);
        end.resize(nbTasks);
        for (int t = 0; t < nbTasks; ++t) {
            // Integer decisions: start time of each task
            start[t] = model.intVar(0, maxStart);

            // The task duration depends on the selected machine
            duration[t] = model.at(taskProcessingTime, t, taskMachine[t]);
            end[t] = start[t] + duration[t];
        }
        LSExpression startArray = model.array(start.begin(), start.end());
        LSExpression endArray = model.array(end.begin(), end.end());

        // Precedence constraints between the operations of a job
        for (unsigned int j = 0; j < nbJobs; ++j) {
            for (unsigned int o = 0; o < nbOperations[j] - 1; ++o) {
                int t1 = jobOperationTask[j][o];
                int t2 = jobOperationTask[j][o + 1];
                model.constraint(start[t2] >= end[t1]);
            }
        }

        // Disjunctive resource constraints between the tasks on a machine
        for (int m = 0; m < nbMachines; ++m) {
            LSExpression sequence = jobsOrder[m];
            LSExpression sequenceLambda = model.createLambdaFunction([&](LSExpression t) {
                return startArray[sequence[t + 1]] >= endArray[sequence[t]]
                        + model.at(taskSetupTime, m, sequence[t], sequence[t + 1]);
            });
            model.constraint(model.and_(model.range(0, model.count(sequence) - 1), sequenceLambda));
        }

        // Minimize the makespan: end of the last task
        makespan = model.max(end.begin(), end.end());
        model.minimize(makespan);

        model.close();

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

        localsolver.solve();
    }

    /* Write the solution in a file with the following format:
     *  - for each operation of each job, the selected machine, the start and end dates */
    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;

        for (unsigned int j = 0; j < nbJobs; ++j) {
            for (unsigned int o = 0; o < nbOperations[j]; ++o) {
                int task = jobOperationTask[j][o];
                outfile << j + 1 << "\t" << o + 1 << "\t" << taskMachine[task].getValue() + 1 << "\t"
                        << start[task].getValue() << "\t" << end[task].getValue() << std::endl;
            }
        }
        outfile.close();
    }
};

int main(int argc, char** argv) {
    if (argc < 2) {
        std::cout << "Usage: flexible_jobshop_setup 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";

    FlexibleJobshopSetup model;
    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;
    }
}
Compilation / Execution (Windows)
copy %LS_HOME%\bin\localsolvernet.dll .
csc FlexibleJobshopSetup.cs /reference:localsolvernet.dll
FlexibleJobshopSetup instances\Fattahi_setup_01.fjs
using System;
using System.IO;
using System.Linq;
using localsolver;

public class FlexibleJobshopSetup : IDisposable
{
    // Number of jobs
    private int nbJobs;

    // Number of machines
    private int nbMachines;

    // Number of tasks
    private int nbTasks;

    // Processing time for each task, for each machine
    private long[][] taskProcessingTimeData;

    //Setup time between every two consecutive tasks, for each machine
    private int[][][] taskSetupTimeData;

    // For each job, for each operation, the corresponding task id
    private int[][] jobOperationTask;

    // Number of operations for each job;
    private int[] nbOperations;

    // Trivial upper bound for the startData times of the tasks
    private long maxStart;

    // Constant for incompatible machines
    private const long INFINITE = 1000000;

    // LocalSolver
    private LocalSolver localsolver;

    // Decision variables: startData times of the tasks
    private LSExpression[] startData;

    // Decision variables: sequence of tasks on each machine
    private LSExpression[] jobsOrder;

    // For each task, the selected machine
    private LSExpression[] taskMachine;

    // End times of the tasks
    private LSExpression[] endData;

    // Objective = minimize the makespan: endData of the last task
    private LSExpression makespan;

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

    public void ReadInstance(string fileName)
    {
        using (StreamReader input = new StreamReader(fileName))
        {
            char[] separators = new char[] { '\t', ' ' };
            string[] splitted = input
                .ReadLine()
                .Split(separators, StringSplitOptions.RemoveEmptyEntries);
            nbJobs = int.Parse(splitted[0]);
            nbMachines = int.Parse(splitted[1]);

            nbTasks = 0;
            long[][][] processingTime = new long[nbJobs][][];
            jobOperationTask = new int[nbJobs][];
            nbOperations = new int[nbJobs];
            for (int j = 0; j < nbJobs; ++j)
            {
                splitted = input
                    .ReadLine()
                    .Split(separators, StringSplitOptions.RemoveEmptyEntries);
                nbOperations[j] = int.Parse(splitted[0]);
                jobOperationTask[j] = new int[nbOperations[j]];
                processingTime[j] = new long[nbOperations[j]][];
                int k = 1;
                for (int o = 0; o < nbOperations[j]; ++o)
                {
                    int nbMachinesOperation = int.Parse(splitted[k]);
                    k++;
                    processingTime[j][o] = Enumerable.Repeat((long)INFINITE, nbMachines).ToArray();
                    for (int m = 0; m < nbMachinesOperation; ++m)
                    {
                        int machine = int.Parse(splitted[k]) - 1;
                        long time = long.Parse(splitted[k + 1]);
                        processingTime[j][o][machine] = time;
                        k += 2;
                    }
                    jobOperationTask[j][o] = nbTasks;
                    nbTasks++;
                }
            }

            input.ReadLine();
            taskSetupTimeData = new int[nbMachines][][];
            for(int m = 0; m < nbMachines; ++m)
            {
                taskSetupTimeData[m] = new int[nbTasks][];
                for(int i = 0; i < nbTasks; ++i)
                {
                    taskSetupTimeData[m][i] = new int[nbTasks];
                    splitted = input.
                        ReadLine()
                        .Split(separators, StringSplitOptions.RemoveEmptyEntries);
                    for(int j = 0; j < nbTasks; ++j)
                    {
                        taskSetupTimeData[m][i][j] = int.Parse(splitted[j]);
                    }
                }
            }

            // Trivial upper bound for the startData times of the tasks
            maxStart = 0;
            taskProcessingTimeData = new long[nbTasks][];
            for (int j = 0; j < nbJobs; ++j)
            {
                long maxProcessingTime = 0;
                for (int o = 0; o < nbOperations[j]; ++o)
                {
                    int task = jobOperationTask[j][o];
                    taskProcessingTimeData[task] = new long[nbMachines];
                    for (int m = 0; m < nbMachines; ++m)
                    {
                        taskProcessingTimeData[task][m] = processingTime[j][o][m];
                        if (
                            processingTime[j][o][m] != INFINITE
                            && processingTime[j][o][m] > maxProcessingTime
                        )
                        {
                            maxProcessingTime = processingTime[j][o][m];
                        }
                    }
                    maxStart += maxProcessingTime;
                }
            }
        }
    }

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

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

        // Sequence of tasks on each machine
        jobsOrder = new LSExpression[nbMachines];
        LSExpression machines = model.Array();
        for (int m = 0; m < nbMachines; ++m)
        {
            jobsOrder[m] = model.List(nbTasks);
            machines.AddOperand(jobsOrder[m]);
        }

        // Each task is scheduled on a machine
        model.Constraint(model.Partition(machines));

        // Only compatible machines can be selected for a task
        for (int t = 0; t < nbTasks; ++t)
        {
            for (int m = 0; m < nbMachines; ++m)
            {
                if (taskProcessingTimeData[t][m] == INFINITE)
                    model.Constraint(!model.Contains(jobsOrder[m], t));
            }
        }

        taskMachine = new LSExpression[nbTasks];
        LSExpression[] taskProcessingTime = new LSExpression[nbTasks];
        for (int t = 0; t < nbTasks; ++t)
        {
            // For each task, the selected machine
            taskMachine[t] = model.Find(machines, t);
            taskProcessingTime[t] = model.Array(taskProcessingTimeData[t]);
        }

        startData = new LSExpression[nbTasks];
        LSExpression[] duration = new LSExpression[nbTasks];
        endData = new LSExpression[nbTasks];
        for (int t = 0; t < nbTasks; ++t)
        {
            // Integer decisions: start time of each task
            startData[t] = model.Int(0, maxStart);

            // The task duration depends on the selected machine
            duration[t] = model.At(taskProcessingTime[t], taskMachine[t]);
            endData[t] = startData[t] + duration[t];
        }
        LSExpression startArray = model.Array(startData);
        LSExpression endArray = model.Array(endData);

        // Precedence constraints between the operations of a job
        for (int j = 0; j < nbJobs; ++j)
        {
            for (int o = 0; o < nbOperations[j] - 1; ++o)
            {
                int t1 = jobOperationTask[j][o];
                int t2 = jobOperationTask[j][o + 1];
                model.Constraint(startData[t2] >= endData[t1]);
            }
        }

        LSExpression taskSetupTime = model.Array(taskSetupTimeData);

        // Disjunctive resource constraints between the tasks on a machine
        for (int m = 0; m < nbMachines; ++m)
        {
            LSExpression sequence = jobsOrder[m];
            LSExpression mexpr = model.CreateConstant(m);
            LSExpression sequenceLambda = model.LambdaFunction(
                t =>
                    startArray[sequence[t + 1]]
                    >= (endArray[sequence[t]]
                        + model.At(taskSetupTime, mexpr, sequence[t], sequence[t + 1])));
            model.Constraint(model.And(model.Range(0, model.Count(sequence) - 1), sequenceLambda));
        }

        // Minimize the makespan: end of the last task
        makespan = model.Max(endData);
        model.Minimize(makespan);

        model.Close();

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

        localsolver.Solve();
    }

    /* Write the solution in a file with the following format:
     *  - for each operation of each job, the selected machine, the startData and endData dates */
    public void WriteSolution(string fileName)
    {
        using (StreamWriter output = new StreamWriter(fileName))
        {
            Console.WriteLine("Solution written in file " + fileName);
            for (int j = 1; j <= nbJobs; ++j)
            {
                for (int o = 1; o <= nbOperations[j - 1]; ++o)
                {
                    int task = jobOperationTask[j - 1][o - 1];
                    output.WriteLine(
                        j
                            + "\t"
                            + o
                            + "\t"
                            + taskMachine[task].GetValue()
                            + "\t"
                            + startData[task].GetValue()
                            + "\t"
                            + endData[task].GetValue()
                    );
                }
            }
        }
    }

    public static void Main(string[] args)
    {
        if (args.Length < 1)
        {
            Console.WriteLine("Usage: FlexibleJobshopSetup 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 (FlexibleJobshopSetup model = new FlexibleJobshopSetup())
        {
            model.ReadInstance(instanceFile);
            model.Solve(int.Parse(strTimeLimit));
            if (outputFile != null)
                model.WriteSolution(outputFile);
        }
    }
}
Compilation / Execution (Windows)
javac FlexibleJobshopSetup.java -cp %LS_HOME%\bin\localsolver.jar
java -cp %LS_HOME%\bin\localsolver.jar;. FlexibleJobshopSetup instances\Fattahi_setup_01.fjs
Compilation / Execution (Linux)
javac FlexibleJobshopSetup.java -cp /opt/localsolver_11_5/bin/localsolver.jar
java -cp /opt/localsolver_11_5/bin/localsolver.jar:. FlexibleJobshopSetup instances/Fattahi_setup_01.fjs
import java.util.*;
import java.io.*;
import localsolver.*;

public class FlexibleJobshopSetup {
    // Number of jobs
    private int nbJobs;
    // Number of machines
    private int nbMachines;
    // Number of tasks
    private int nbTasks;
    // Processing time for each task, for each machine
    private long[][] taskProcessingTimeData;
    // Setup time between every two consecutive tasks, for each machine
    private int[][][] taskSetupTimeData;
    // For each job, for each operation, the corresponding task id
    private int[][] jobOperationTask;
    // Number of operations for each job;
    private int[] nbOperations;
    // Trivial upper bound for the start times of the tasks
    private long maxStart;
    // Constant for incompatible machines
    private final int INFINITE = 1000000;

    // LocalSolver
    final LocalSolver localsolver;
    // Decision variables: start times of the tasks
    private LSExpression[] start;
    // Decision variables: sequence of tasks on each machine
    private LSExpression[] jobsOrder;
    // For each task, the selected machine
    private LSExpression[] taskMachine;
    // End times of the tasks
    private LSExpression[] end;
    // Objective = minimize the makespan: end of the last task
    private LSExpression makespan;

    public FlexibleJobshopSetup(LocalSolver localsolver) throws IOException {
        this.localsolver = localsolver;
    }

    public void readInstance(String fileName) throws IOException {
        try (Scanner input = new Scanner(new File(fileName))) {
            nbJobs = input.nextInt();
            nbMachines = input.nextInt();
            input.next(); // skip last number

            nbTasks = 0;
            long[][][] processingTime = new long[nbJobs][][];
            jobOperationTask = new int[nbJobs][];
            nbOperations = new int[nbJobs];
            for (int j = 0; j < nbJobs; ++j) {
                nbOperations[j] = input.nextInt();
                jobOperationTask[j] = new int[nbOperations[j]];
                processingTime[j] = new long[nbOperations[j]][nbMachines];
                for (int o = 0; o < nbOperations[j]; ++o) {
                    int nbMachinesOperation = input.nextInt();
                    Arrays.fill(processingTime[j][o], INFINITE);
                    for (int m = 0; m < nbMachinesOperation; ++m) {
                        int machine = input.nextInt() - 1;
                        long time = input.nextLong();
                        processingTime[j][o][machine] = time;
                    }
                    jobOperationTask[j][o] = nbTasks;
                    nbTasks++;
                }
            }
            taskSetupTimeData = new int[nbMachines][nbTasks][nbTasks];
            for (int m = 0; m < nbMachines; ++m) {
                for (int i = 0; i < nbTasks; ++i) {
                    for (int j = 0; j < nbTasks; ++j) {
                        taskSetupTimeData[m][i][j] = input.nextInt();
                    }
                }
            }

            // Trivial upper bound for the start times of the tasks
            maxStart = 0;
            taskProcessingTimeData = new long[nbTasks][];
            for (int j = 0; j < nbJobs; ++j) {
                long maxProcessingTime = 0;
                for (int o = 0; o < nbOperations[j]; ++o) {
                    int task = jobOperationTask[j][o];
                    taskProcessingTimeData[task] = new long[nbMachines];
                    for (int m = 0; m < nbMachines; ++m) {
                        taskProcessingTimeData[task][m] = processingTime[j][o][m];
                        if (processingTime[j][o][m] != INFINITE && processingTime[j][o][m] > maxProcessingTime) {
                            maxProcessingTime = processingTime[j][o][m];
                        }
                    }
                    maxStart += maxProcessingTime;
                }
            }
        }
    }

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

        // Sequence of tasks on each machine
        jobsOrder = new LSExpression[nbMachines];
        LSExpression machines = model.array();
        for (int m = 0; m < nbMachines; ++m) {
            jobsOrder[m] = model.listVar(nbTasks);
            machines.addOperand(jobsOrder[m]);
        }

        // Each task is scheduled on a machine
        model.constraint(model.partition(machines));

        // Only compatible machines can be selected for a task
        for (int t = 0; t < nbTasks; ++t) {
            for (int m = 0; m < nbMachines; ++m) {
                if (taskProcessingTimeData[t][m] == INFINITE) {
                    model.constraint(model.not(model.contains(jobsOrder[m], t)));
                }
            }
        }

        // For each task, the selected machine
        taskMachine = new LSExpression[nbTasks];
        for (int t = 0; t < nbTasks; ++t) {
            taskMachine[t] = model.find(machines, t);
        }

        LSExpression taskProcessingTime = model.array(taskProcessingTimeData);

        start = new LSExpression[nbTasks];
        LSExpression[] duration = new LSExpression[nbTasks];
        end = new LSExpression[nbTasks];
        for (int t = 0; t < nbTasks; ++t) {
            // Integer decisions: start time of each task
            start[t] = model.intVar(0, maxStart);

            // The task duration depends on the selected machine
            LSExpression tExpr = model.createConstant(t);
            duration[t] = model.at(taskProcessingTime, tExpr, taskMachine[t]);
            end[t] = model.sum(start[t], duration[t]);
        }
        LSExpression startArray = model.array(start);
        LSExpression endArray = model.array(end);

        // Precedence constraints between the operations of a job
        for (int j = 0; j < nbJobs; ++j) {
            for (int o = 0; o < nbOperations[j] - 1; ++o) {
                int t1 = jobOperationTask[j][o];
                int t2 = jobOperationTask[j][o + 1];
                model.constraint(model.geq(start[t2], end[t1]));
            }
        }

        LSExpression taskSetupTime = model.array(taskSetupTimeData);

        // Disjunctive resource constraints between the tasks on a machine
        for (int m = 0; m < nbMachines; ++m) {
            LSExpression sequence = jobsOrder[m];
            LSExpression mExpr = model.createConstant(m);
            LSExpression sequenceLambda = model
                    .lambdaFunction(t -> model.geq(model.at(startArray, model.at(sequence, model.sum(t, 1))),
                            model.sum(model.at(endArray, model.at(sequence, t)), model.at(taskSetupTime, mExpr,
                                    model.at(sequence, t), model.at(sequence, model.sum(t, 1))))));
            model.constraint(model.and(model.range(0, model.sub(model.count(sequence), 1)), sequenceLambda));
        }

        // Minimize the makespan: end of the last task
        makespan = model.max(end);
        model.minimize(makespan);

        model.close();

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

        localsolver.solve();
    }

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

            for (int j = 1; j <= nbJobs; ++j) {
                for (int o = 1; o <= nbOperations[j - 1]; ++o) {
                    int task = jobOperationTask[j - 1][o - 1];
                    output.write(j + "\t" + o + "\t" + taskMachine[task].getValue() + "\t" + start[task].getValue()
                            + "\t" + end[task].getValue() + "\n");
                }
            }
        }
    }

    public static void main(String[] args) {
        if (args.length < 1) {
            System.out.println("Usage: java FlexibleJobshopSetup 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 (LocalSolver localsolver = new LocalSolver()) {
            FlexibleJobshopSetup model = new FlexibleJobshopSetup(localsolver);
            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);
        }
    }
}