/******************************************************** Xpress-BCL Java Example Problems ================================ file xbexpl1.java ````````````````` BCL user guide example. Definition of variables and constraints, variable arrays and SOS, followed by file output, solving and printing of solutions. (c) 2008 Fair Isaac Corporation author: S.Heipcke, Jan. 2000, rev. Dec. 2011 ********************************************************/ import java.io.*; import com.dashoptimization.*; public class xbexpl1 { /**************************************************************************/ /* Expl 1: This example corresponds to the one printed in the */ /* BCL User Guide. It shows how to define variables and */ /* constraints, and Special Ordered Sets, followed by file output, */ /* solving and printing of solutions. */ /* Set the following parameter to true to try out a problem formulation */ /* using Special Ordered Sets: */ static final boolean SOS = false; /**************************************************************************/ static final int NJ = 4; /* Number of jobs */ static final int NT = 10; /* Time limit */ /**** DATA ****/ static final double[] DUR = {3,4,2,2}; /* Durations of jobs */ static XPRBvar[] start; /* Start times of jobs */ static XPRBvar[][] delta; /* Binaries for start times */ static XPRBvar z; /* Maximum completion time (makespan) */ static XPRBsos[] set; /* Sets regrouping start times for jobs */ /*************************************************************************/ static void jobsModel(XPRBprob p) throws IOException { XPRBexpr le; int j,t; /****VARIABLES****/ start = new XPRBvar[NJ]; /* Create start time variables */ for(j=0;j<NJ;j++) start[j] = p.newVar("start");
        z = p.newVar("z",XPRB.PL,0,NT);  /* Declare the makespan variable */

        delta = new XPRBvar[NJ][NT];
        for(j=0;j<NJ;j++)              /* Declare binaries for each job  */
            for(t=0;t<(NT-DUR[j]+1);t++)
                delta[j][t] = p.newVar("delta"+(j+1)+(t+1), XPRB.BV);

        /****CONSTRAINTS****/
        for(j=0;j<NJ;j++)              /* Calculate maximal completion time */
            p.newCtr("Makespan", start[j].add(DUR[j]).lEql(z) );

        p.newCtr("Prec", start[0].add(DUR[0]).lEql(start[2]) );
        /* Precedence rel. between jobs */

        for(j=0;j<NJ;j++) {               /* Linking start times and binaries  */
            le = new XPRBexpr();
            for(t=0;t<(NT-DUR[j]+1);t++)  le.add(delta[j][t].mul((t+1)));
            p.newCtr("Link_"+(j+1), le.eql(start[j]) );
        }

        for(j=0;j<NJ;j++) {               /* One unique start time for each job  */
            le = new XPRBexpr();
            for(t=0;t<(NT-DUR[j]+1);t++)  le.add(delta[j][t]);
            p.newCtr("One_"+(j+1), le.eql(1));
        }

        /****OBJECTIVE****/
        p.setObj(z);                   /* Define and set objective function */

        /****BOUNDS****/
        for(j=0;j<NJ;j++) start[j].setUB(NT-DUR[j]+1);
        /* Upper bounds on start time variables */

        /****OUTPUT****/
        p.print();                     /* Print out the problem definition */
        p.exportProb(XPRB.MPS,"expl1");   /* Output matrix to MPS file */
    }

    /*************************************************************************/
    static void jobsSolve(XPRBprob p) {
        int j,t,statmip;

        if(!SOS)
            for(j=0;j<NJ;j++)
                for(t=0;t<NT-DUR[j]+1;t++)
                    delta[j][t].setDir(XPRB.PR, 10*(t+1));
        /* Give highest priority to variables for earlier start times */
        else
            for(j=0;j<NJ;j++)
                set[j].setDir(XPRB.DN);       /* First branch downwards on sets */

        p.setSense(XPRB.MINIM);
        p.mipOptimize("");              /* Solve the problem as MIP */
        statmip = p.getMIPStat();       /* Get the MIP problem status */

        if((statmip == XPRB.MIP_SOLUTION) || (statmip == XPRB.MIP_OPTIMAL))
            {             /* An integer solution has been found */
                System.out.println("Objective: "+ p.getObjVal());
                for(j=0;j<NJ;j++)
                    {                              /* Print the solution for all start times */
                        System.out.println(start[j].getName() + ": "+ start[j].getSol());
                        for(t=0;t<NT-DUR[j]+1;t++)
                            System.out.print(delta[j][t].getName() + ": "+ delta[j][t].getSol());
                        System.out.println();
                    }
            }
    }

    /*************************************************************************/

    public static void main(String[] args) throws Exception {
        try (XPRBprob p = new XPRBprob("jobs")) { /* Initialize BCL and create a new problem */

            if(!SOS)
                jobsModel(p);                 /* Basic problem definition */
            else
                jobsModelb(p);                /* Formulation using SOS */

            jobsSolve(p);                   /* Solve and print solution */
        }
    }

    /*************************************************************************/

    static void jobsModelb(XPRBprob p) throws IOException {     /**** SOS-formulation ****/
        XPRBexpr le;
        int j,t;

        /****VARIABLES****/
        start = new XPRBvar[NJ];         /* Create start time variables */
        for(j=0;j<NJ;j++) start[j] = p.newVar("start");
        z = p.newVar("z",XPRB.PL,0,NT);  /* Declare the makespan variable */

        delta = new XPRBvar[NJ][NT];
        for(j=0;j<NJ;j++)             /* Declare binaries for each job  */
            for(t=0;t<(NT-DUR[j]+1);t++)
                delta[j][t] = p.newVar("delta"+(j+1)+(t+1), XPRB.PL, 0,1);

        /****CONSTRAINTS****/
        for(j=0;j<NJ;j++)             /* Calculate maximal completion time */
            p.newCtr("Makespan", start[j].add(DUR[j]).lEql(z));

        p.newCtr("Prec", start[0].add(DUR[0]).lEql(start[2]) );
        /* Precedence rel. betw. jobs */

        for(j=0;j<NJ;j++) {              /* Linking start times and binaries  */
            le = new XPRBexpr();
            for(t=0;t<(NT-DUR[j]+1);t++)  le.add(delta[j][t].mul((t+1)));
            p.newCtr("Link_"+(j+1), le.eql(start[j]) );
        }

        for(j=0;j<NJ;j++) {              /* One unique start time for each job  */
            le = new XPRBexpr();
            for(t=0;t<(NT-DUR[j]+1);t++)  le.add(delta[j][t]);
            p.newCtr("One_"+(j+1), le.eql(1));
        }

        /****OBJECTIVE****/
        p.setObj(z);                  /* Define and set objective function */

        /****BOUNDS****/
        for(j=0;j<NJ;j++) start[j].setUB(NT-DUR[j]+1);
        /* Upper bounds on start time variables */

        /****SETS****/
        set = new XPRBsos[NJ];
        for(j=0;j<NJ;j++) {
            le = new XPRBexpr();
            for(t=0;t<(NT-DUR[j]+1);t++)  le.add(delta[j][t].mul((t+1)));
            set[j] = p.newSos("sosj", XPRB.S1, le);
        }

        /****OUTPUT****/
        p.print();                    /* Print out the problem definition */
        p.exportProb(XPRB.MPS,"expl1");  /* Output matrix to MPS file */
    }
}