Flexible Job Shop (FJSP)¶

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

public class FlexibleJobshop : 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;

    // 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;

    // Hexaly Optimizer
    private HexalyOptimizer optimizer;

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

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

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

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

    public FlexibleJobshop()
    {
        optimizer = new HexalyOptimizer();
    }

    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++;
                }
            }

            // 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()
    {
        optimizer.Dispose();
    }

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

        // Sequence of tasks on each machine
        jobsOrder = new HxExpression[nbMachines];
        HxExpression 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 HxExpression[nbTasks];
        for (int i = 0; i < nbTasks; ++i)
        {
            taskMachine[i] = model.Find(machines, i);
        }

        tasks = new HxExpression[nbTasks];
        HxExpression[] duration = new HxExpression[nbTasks];
        HxExpression 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
            HxExpression iExpr = model.CreateConstant(i);
            duration[i] = model.At(taskProcessingTime, iExpr, taskMachine[i]);
            model.Constraint(model.Length(tasks[i]) == duration[i]);
        }
        HxExpression taskArray = model.Array(tasks);

        // 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 i1 = jobOperationTask[j][o];
                int i2 = jobOperationTask[j][o + 1];
                model.Constraint(tasks[i1] < tasks[i2]);
            }
        }

        // Disjunctive resource constraints between the tasks on a machine
        for (int m = 0; m < nbMachines; ++m)
        {
            HxExpression sequence = jobsOrder[m];
            HxExpression 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 optimizer
        optimizer.GetParam().SetTimeLimit(timeLimit);

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