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Flexible Job Shop Scheduling Problem with Machine-Dependent Changeover Times

Principles learned

  • Add multiple list decision variables

  • Use the find operator

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

Problem

../_images/fjsp_changeover.svg

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. Each operation has a given processing time that depends on the chosen machine, and each machine can only process one operation at a time. An operation cannot begin until the previous operation in the job is completed. Furthermore, there is a changeover time between two consecutive operations in the same job that are not processed by the same machine. This changeover time depends on the machines used for the two operations.

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 pair of machines:

    • Changeover time between these two machines

Program

The model is an extension from the Flexible Job Shop Problem with the use of machine-dependent changeover times between consecutive operations of the same job.. The decision variables are the following: we represent the time ranges of the tasks by interval 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 precedence constraints between the operations of a job ensure that a task can start on a machine only after the previous task of this job is done and the changeover time between the two machines of these operations is completed.

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

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 flexiblejobshop_changeover.lsp inFileName=instances/Mk01.fjsc [outFileName=] [lsTimeLimit=]
use io;

/* Read instance data */
function input() {
    local usage = "Usage: localsolver flexiblejobshop_changeover.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] {
        // Number of operations for each job
        nbOperations[j] = inFile.readInt();
        for [o in 0...nbOperations[j]] {
            local nbMachinesOperation = inFile.readInt();
            for [i in 0...nbMachinesOperation] {
                local machine = inFile.readInt() - 1;
                local time = inFile.readInt();
                processingTime[j][o][machine] = time;
                taskProcessingTime[nbTasks][machine] = time;
            }
            jobOperationTask[j][o] = nbTasks;
            nbTasks += 1;
        }
    }

    // Changeover time between two machines
    for [m1 in 0...nbMachines] {
        for [m2 in 0...nbMachines] {
            machineChangeoverTime[m1][m2] = inFile.readInt();
        }
    }

    inFile.close();

    // Trivial upper bound for the start times of the tasks
    maxStart = 0;
    for [j in 0...nbJobs][o in 0...nbOperations[j]] {
        local maxProcessingTime = 0;
        for [m in 0...nbMachines] {
            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] <- list(nbTasks);

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

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

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

    // Interval decisions: time range of each task
    tasks[i in 0...nbTasks] <- interval(0, maxStart);

    // The task duration depends on the selected machine
    duration[i in 0...nbTasks] <- taskProcessingTime[i][taskMachine[i]];
    for [i in 0...nbTasks]
        constraint length(tasks[i]) == duration[i];

    // Precedence constraints between the operations of a job with machine-dependent changeover times
    for [j in 0...nbJobs][o in 0...nbOperations[j]-1] {
        local i1 = jobOperationTask[j][o];
        local i2 = jobOperationTask[j][o + 1];
        constraint start(tasks[i2]) >= end(tasks[i1]) 
                + machineChangeoverTime[taskMachine[i1]][taskMachine[i2]];
    }

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

    // Minimize the makespan: end of the last task
    makespan <- max[i in 0...nbTasks](end(tasks[i]));
    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][o in 0...nbOperations[j]] {
            local taskIndex = jobOperationTask[j][o];
            outFile.println(j + 1, "\t", o + 1, "\t", taskMachine[taskIndex].value + 1, 
                    "\t", tasks[taskIndex].value.start, "\t", tasks[taskIndex].value.end);
        }
    }
}
Execution (Windows)
set PYTHONPATH=%LS_HOME%\bin\python
python flexiblejobshop_changeover.py instances\Mk01.fjsc
Execution (Linux)
export PYTHONPATH=/opt/localsolver_12_0/bin/python
python flexiblejobshop_changeover.py instances/Mk01.fjsc
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 i 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)]

    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

    # Changeover time between two machines
    machine_changeover_time = [[0 for m2 in range(nb_machines)] for m1 in range(nb_machines)]

    for m1 in range(nb_machines):
        line = lines[nb_jobs + 1 + m1].split()
        for m2 in range(nb_machines):
            machine_changeover_time[m1][m2] = int(line[m2])


    # Trivial upper bound for the start times of the tasks
    max_start = sum(
        max(task_processing_time[i][m] for m in range(nb_machines) if task_processing_time[i][m] != INFINITE)
        for i in range(nb_tasks))
    
    return nb_jobs, nb_machines, nb_tasks, task_processing_time, job_operation_task, nb_operations, max_start, machine_changeover_time


def main(instance_file, output_file, time_limit):
    nb_jobs, nb_machines, nb_tasks, task_processing_time_data, job_operation_task, \
        nb_operations, max_start, machine_changeover_time_data = 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 i in range(nb_tasks):
            for m in range(nb_machines):
                if task_processing_time_data[i][m] == INFINITE:
                    model.constraint(model.not_(model.contains(jobs_order[m], i)))

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

        task_processing_time = model.array(task_processing_time_data)

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

        # The task duration depends on the selected machine
        duration = [model.at(task_processing_time, i, task_machine[i]) for i in range(nb_tasks)]
        for i in range(nb_tasks):
            model.constraint(model.length(tasks[i]) == duration[i])

        task_array = model.array(tasks)

        machine_changeover_time = model.array(machine_changeover_time_data)
        # Precedence constraints between the operations of a job with machine-dependent changeover times
        for j in range(nb_jobs):
            for o in range(nb_operations[j] - 1):
                i1 = job_operation_task[j][o]
                i2 = job_operation_task[j][o + 1]
                model.constraint(model.start(tasks[i2]) >= model.end(tasks[i1]) 
                        + machine_changeover_time[task_machine[i1]][task_machine[i2]])

        # 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 i: task_array[sequence[i]] < task_array[sequence[i + 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([model.end(tasks[i]) for i in range(nb_tasks)])
        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]):
                        taskIndex = job_operation_task[j][o]
                        f.write(str(j + 1) + "\t" + str(o + 1)
                                + "\t" + str(task_machine[taskIndex].value + 1)
                                + "\t" + str(tasks[taskIndex].value.start())
                                + "\t" + str(tasks[taskIndex].value.end()) + "\n")


if __name__ == '__main__':
    if len(sys.argv) < 2:
        print("Usage: python flexiblejobshop_changeover.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 flexiblejobshop_changeover.cpp -I%LS_HOME%\include /link %LS_HOME%\bin\localsolver120.lib
flexiblejobshop_changeover instances\Mk01.fjsc
Compilation / Execution (Linux)
g++ flexiblejobshop_changeover.cpp -I/opt/localsolver_12_0/include -llocalsolver120 -lpthread -o flexiblejobshop_changeover
./flexiblejobshop_changeover instances/Mk01.fjsc
#include "localsolver.h"
#include <algorithm>
#include <fstream>
#include <iostream>
#include <limits>
#include <numeric>
#include <vector>

using namespace localsolver;

class FlexibleJobshop {
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;
    // Changeover time between two machines
    std::vector<std::vector<int>> machineChangeoverTimeData;
    // 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: time range of each task
    std::vector<LSExpression> tasks;
    // Decision variables: sequence of tasks on each machine
    std::vector<LSExpression> jobsOrder;
    // For each task, the selected machine
    std::vector<LSExpression> taskMachine;
    // Objective = minimize the makespan: end of the last task
    LSExpression makespan;

public:
    FlexibleJobshop() : 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;
            }
        }

        machineChangeoverTimeData = std::vector<std::vector<int>>(nbMachines, std::vector<int>(nbMachines));
        for (unsigned int m1 = 0; m1 < nbMachines; ++m1){
            for (unsigned int m2 = 0; m2 < nbMachines; ++m2){
                infile >> machineChangeoverTimeData[m1][m2];
            }
        }
        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 i = 0; i < nbTasks; ++i) {
            for (unsigned int m = 0; m < nbMachines; ++m) {
                if (taskProcessingTimeData[i][m] == INFINITE) {
                    model.constraint(!model.contains(jobsOrder[m], i));
                }
            }
        }

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

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

            // The task duration depends on the selected machine
            duration[i] = model.at(taskProcessingTime, i, taskMachine[i]);
            model.constraint(model.length(tasks[i]) == duration[i]);
        }
        LSExpression taskArray = model.array(tasks.begin(), tasks.end());


        LSExpression machineChangeoverTime = model.array();
        for (int m1 = 0; m1 < nbMachines; ++m1) {
            machineChangeoverTime.addOperand(
                    model.array(machineChangeoverTimeData[m1].begin(), machineChangeoverTimeData[m1].end()));
            }

        // Precedence constraints between the operations of a job with machine-dependent changeover times
        for (unsigned int j = 0; j < nbJobs; ++j) {
            for (unsigned int o = 0; o < nbOperations[j] - 1; ++o) {
                int i1 = jobOperationTask[j][o];
                int i2 = jobOperationTask[j][o + 1];
                model.constraint(model.start(tasks[i2]) >= model.end(tasks[i1])
                        + machineChangeoverTime[taskMachine[i1]][taskMachine[i2]]);
            }
        }

        // 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 i) { return taskArray[sequence[i]] < taskArray[sequence[i + 1]]; });
            model.constraint(model.and_(model.range(0, model.count(sequence) - 1), sequenceLambda));
        }

        // Minimize the makespan: end of the last task
        makespan = model.max();
        for (int i = 0; i < nbTasks; ++i) {
            makespan.addOperand(model.end(tasks[i]));
        }
        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 taskIndex = jobOperationTask[j][o];
                outfile << j + 1 << "\t" << o + 1 << "\t" << taskMachine[taskIndex].getValue() + 1 << "\t"
                        << tasks[taskIndex].getIntervalValue().getStart() << "\t"
                        << tasks[taskIndex].getIntervalValue().getEnd() << std::endl;
            }
        }
        outfile.close();
    }
};

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

    FlexibleJobshop 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 FlexibleJobshopChangeover.cs /reference:localsolvernet.dll
FlexibleJobshopChangeover instances\Mk01.fjsc
using System;
using System.IO;
using System.Linq;
using localsolver;

public class FlexibleJobshopChangeover : 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;

    // Changeover time between two machines
    private int[][] machineChangeoverTimeData;

    // 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 const long INFINITE = 1000000;

    // LocalSolver
    private LocalSolver localsolver;

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

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

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

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

    public FlexibleJobshopChangeover()
    {
        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++;
                }
            }

            machineChangeoverTimeData = new int[nbMachines][];
            for (int m1 = 0; m1 < nbMachines; ++m1)
            {
                machineChangeoverTimeData[m1] = new int[nbTasks];
                    splitted = input.
                        ReadLine()
                        .Split(separators, StringSplitOptions.RemoveEmptyEntries);

                machineChangeoverTimeData[m1] = new int[nbMachines];
                for (int m2 = 0; m2 < nbMachines; ++m2)
                {
                    machineChangeoverTimeData[m1][m2] = int.Parse(splitted[m2]);
                }
            }

            // 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 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 i = 0; i < nbTasks; ++i)
        {
            for (int m = 0; m < nbMachines; ++m)
            {
                if (taskProcessingTimeData[i][m] == INFINITE)
                    model.Constraint(!model.Contains(jobsOrder[m], i));
            }
        }

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

        tasks = new LSExpression[nbTasks];
        LSExpression[] duration = new LSExpression[nbTasks];
        LSExpression taskProcessingTime = model.Array(taskProcessingTimeData);
        for (int i = 0; i < nbTasks; ++i)
        {
            // Interval decisions: time range of each task
            tasks[i] = model.Interval(0, maxStart);

            // The task duration depends on the selected machine
            LSExpression iExpr = model.CreateConstant(i);
            duration[i] = model.At(taskProcessingTime, iExpr, taskMachine[i]);
            model.Constraint(model.Length(tasks[i]) == duration[i]);
        }

        LSExpression taskArray = model.Array(tasks);
        LSExpression machineChangeoverTime = model.Array(machineChangeoverTimeData);
        // Precedence constraints between the operations of a job with machine-dependent changeover times
        for (int j = 0; j < nbJobs; ++j)
        {
            for (int o = 0; o < nbOperations[j] - 1; ++o)
            {
                int i1 = jobOperationTask[j][o];
                int i2 = jobOperationTask[j][o + 1];
                model.Constraint(model.Start(tasks[i2]) >= model.End(tasks[i1])
                        + machineChangeoverTime[taskMachine[i1]][taskMachine[i2]]); 
            }
        }

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

        // Minimize the makespan: end of the last task
        makespan = model.Max();
        for (int i = 0; i < nbTasks; ++i)
        {
            makespan.AddOperand(model.End(tasks[i]));
        }
        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)
    {
        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 taskIndex = jobOperationTask[j - 1][o - 1];
                    output.WriteLine(
                        j
                            + "\t"
                            + o
                            + "\t"
                            + taskMachine[taskIndex].GetValue()
                            + "\t"
                            + tasks[taskIndex].GetIntervalValue().Start()
                            + "\t"
                            + tasks[taskIndex].GetIntervalValue().End()
                    );
                }
            }
        }
    }

    public static void Main(string[] args)
    {
        if (args.Length < 1)
        {
            Console.WriteLine("Usage: FlexibleJobshopChangeover 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 (FlexibleJobshopChangeover model = new FlexibleJobshopChangeover())
        {
            model.ReadInstance(instanceFile);
            model.Solve(int.Parse(strTimeLimit));
            if (outputFile != null)
                model.WriteSolution(outputFile);
        }
    }
}
Compilation / Execution (Windows)
javac FlexibleJobshopChangeover.java -cp %LS_HOME%\bin\localsolver.jar
java -cp %LS_HOME%\bin\localsolver.jar;. FlexibleJobshopChangeover instances\Mk01.fjsc
Compilation / Execution (Linux)
javac FlexibleJobshopChangeover.java -cp /opt/localsolver_12_0/bin/localsolver.jar
java -cp /opt/localsolver_12_0/bin/localsolver.jar:. FlexibleJobshopChangeover instances/Mk01.fjsc
import java.util.*;
import java.io.*;
import localsolver.*;

public class FlexibleJobshopChangeover {
    // 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;
    // Changeover time between two machines
    private int[][] machineChangeoverTimeData;
    // 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: time range of each task
    private LSExpression[] tasks;
    // Decision variables: sequence of tasks on each machine
    private LSExpression[] jobsOrder;
    // For each task, the selected machine
    private LSExpression[] taskMachine;
    // Objective = minimize the makespan: end of the last task
    private LSExpression makespan;

    public FlexibleJobshopChangeover(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++;
                }
            }


            machineChangeoverTimeData = new int[nbMachines][nbMachines];
            for (int m1 = 0; m1 < nbMachines; ++m1) {
                for (int m2 = 0; m2 < nbMachines; ++m2) {
                    machineChangeoverTimeData[m1][m2] = 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 i = 0; i < nbTasks; ++i) {
            for (int m = 0; m < nbMachines; ++m) {
                if (taskProcessingTimeData[i][m] == INFINITE) {
                    model.constraint(model.not(model.contains(jobsOrder[m], i)));
                }
            }
        }

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

        LSExpression taskProcessingTime = model.array(taskProcessingTimeData);

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

            // The task duration depends on the selected machine
            LSExpression iExpr = model.createConstant(i);
            duration[i] = model.at(taskProcessingTime, iExpr, taskMachine[i]);
            model.constraint(model.eq(model.length(tasks[i]), duration[i]));
        }

        LSExpression taskArray = model.array(tasks);
        LSExpression machineChangeoverTime = model.array(machineChangeoverTimeData);
    
        // Precedence constraints between the operations of a job with machine-dependent changeover times
        for (int j = 0; j < nbJobs; ++j) {
            for (int o = 0; o < nbOperations[j] - 1; ++o) {
                int i1 = jobOperationTask[j][o];
                int i2 = jobOperationTask[j][o + 1];
                model.constraint(model.geq(model.start(tasks[i2]), model.sum(model.end(tasks[i1]), 
                        model.at(machineChangeoverTime, taskMachine[i1], taskMachine[i2]))));
            }
        }

        // Disjunctive resource constraints between the tasks on a machine
        for (int m = 0; m < nbMachines; ++m) {
            LSExpression sequence = jobsOrder[m];
            LSExpression sequenceLambda = model.lambdaFunction(i -> model
                    .lt(model.at(taskArray, model.at(sequence, i)),
                            model.at(taskArray, model.at(sequence, model.sum(i, 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();
        for (int i = 0; i < nbTasks; ++i) {
            makespan.addOperand(model.end(tasks[i]));
        }
        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 taskIndex = jobOperationTask[j - 1][o - 1];
                    output.write(j + "\t" + o
                            + "\t" + taskMachine[taskIndex].getValue()
                            + "\t" + tasks[taskIndex].getIntervalValue().getStart()
                            + "\t" + tasks[taskIndex].getIntervalValue().getEnd() + "\n");
                }
            }
        }
    }

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