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Els - An economic lot-sizing problem solved by cut-and-branch and branch-and-cut heuristics

Description
The version 'xbels' of this example shows how to implement cut-and-branch (= cut generation at the root node of the MIP search) and 'xbelsc' implements a branch-and-cut (= cut generation at the MIP search tree nodes) algorithm using the cut manager.


Source Files
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xbels.java[download]
xbelsc.java[download]





xbels.java

/********************************************************
  Xpress-BCL Java Example Problems
  ================================

  file xbels.java
  ```````````````
  Economic lot sizing, ELS, problem, solved by adding
  (l,S)-inequalities) in several rounds looping over
  the root node.

  ELS considers production planning over a horizon
  of T periods. In period t, t=1,...,T, there is a
  given demand DEMAND[t] that must be satisfied by
  production prod[t] in period t and by inventory
  carried over from previous periods. There is a
  set-up up cost SETUPCOST[t] associated with
  production in period t. The unit production cost
  in period t is PRODCOST[t]. There is no inventory
  or stock-holding cost.

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, 2001, rev. Mar. 2011
********************************************************/

import com.dashoptimization.*;

public class xbels {
    static final double EPS = 1e-6;
    static final int T = 6;                 /* Number of time periods */

    /****DATA****/
    static final int[] DEMAND    = { 1, 3, 5, 3, 4, 2};  /* Demand per period */
    static final int[] SETUPCOST = {17,16,11, 6, 9, 6};  /* Setup cost / period */
    static final int[] PRODCOST  = { 5, 3, 2, 1, 3, 1};  /* Prod. cost / period */
    static int[][] D;                       /* Total demand in periods t1 - t2 */

    static XPRBvar[] prod;                  /* Production in period t */
    static XPRBvar[] setup;                 /* Setup in period t */


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

    static void modEls(XPRBprob p) throws XPRSexception {
        int s,t,k;
        XPRBexpr cobj,le;

        D = new int[T][T];
        for(s=0;s<T;s++)
            for(t=0;t<T;t++)
                for(k=s;k<=t;k++)
                    D[s][t] += DEMAND[k];

        /****VARIABLES****/
        prod = new XPRBvar[T];
        setup = new XPRBvar[T];
        for(t=0;t<T;t++) {
            prod[t]=p.newVar("prod" + (t+1));
            setup[t]=p.newVar("setup" +(t+1), XPRB.BV);
        }

        /****OBJECTIVE****/
        cobj = new XPRBexpr();
        for(t=0;t<T;t++)                      /* Minimize total cost */
            cobj .add(setup[t].mul(SETUPCOST[t]) .add(prod[t].mul(PRODCOST[t])) );
        p.setObj(cobj);

        /****CONSTRAINTS****/
        /* Production in period t must not exceed the total demand for the
           remaining periods; if there is production during t then there
           is a setup in t */
        for(t=0;t<T;t++)
            p.newCtr("Production", prod[t] .lEql(setup[t].mul(D[t][T-1])) );

        /* Production in periods 0 to t must satisfy the total demand
           during this period of time */
        for(t=0;t<T;t++) {
            le = new XPRBexpr();
            for(s=0;s<=t;s++) le .add(prod[s]);
            p.newCtr("Demand", le.gEql(D[0][t]) );
        }
    }

    /**************************************************************************/
    /*  Cut generation loop at the top node:                                  */
    /*    solve the LP and save the basis                                     */
    /*    get the solution values                                             */
    /*    identify and set up violated constraints                            */
    /*    load the modified problem and load the saved basis                  */
    /**************************************************************************/
    static void solveEls(XPRBprob p) throws XPRSexception {
        double objval;               /* Objective value */
        int t,l;
        int starttime;
        int ncut, npass, npcut;      /* Counters for cuts and passes */
        double[] solprod, solsetup;  /* Solution values for var.s prod & setup */
        double ds;
        XPRSprob op;
        XPRBbasis basis;
        XPRBexpr le;

        starttime=XPRB.getTime();
        op=p.getXPRSprob();
        op.setIntControl(XPRS.CUTSTRATEGY, 0);
        /* Disable automatic cuts - we use our own */
        op.setIntControl(XPRS.PRESOLVE, 0);
        /* Switch presolve off */
        ncut = npass = 0;
        solprod = new double[T];
        solsetup = new double[T];

        do {
            npass++;
            npcut = 0;
            p.lpOptimize("p");          /* Solve the LP */
            basis = p.saveBasis();      /* Save the current basis */
            objval = p.getObjVal();     /* Get the objective value */

            /* Get the solution values: */
            for(t=0;t<T;t++) {
                solprod[t]=prod[t].getSol();
                solsetup[t]=setup[t].getSol();
            }

            /* Search for violated constraints: */
            for(l=0;l<T;l++) {
                for(ds=0.0, t=0; t<=l; t++) {
                    if(solprod[t] < D[t][l]*solsetup[t] + EPS)  ds += solprod[t];
                    else  ds += D[t][l]*solsetup[t];
                }

                /* Add the violated inequality: the minimum of the actual production
                   prod[t] and the maximum potential production D[t][l]*setup[t]
                   in periods 0 to l must at least equal the total demand in periods
                   0 to l.
                   sum(t=1:l) min(prod[t], D[t][l]*setup[t]) >= D[0][l]
                */
                if(ds < D[0][l] - EPS) {
                    le = new XPRBexpr();
                    for(t=0;t<=l;t++) {
                        if (solprod[t] < D[t][l]*solsetup[t] + EPS)
                            le .add(prod[t]);
                        else
                            le .add(setup[t].mul(D[t][l]));
                    }
                    p.newCtr("cut" +(ncut+1), le.gEql(D[0][l]) );
                    ncut++;
                    npcut++;
                }
            }

            System.out.println("Pass " +npass + " (" +(XPRB.getTime()-starttime)/1000.0
                               + " sec), objective value " + objval + ", cuts added: " + npcut
                               + " (total " + ncut +")");

            if(npcut==0)
                System.out.println("Optimal integer solution found:");
            else {
                p.loadMat();                 /* Reload the problem */
                p.loadBasis(basis);          /* Load the saved basis */
                basis = null;                /* No need to keep the basis any longer */
            }
        } while(npcut>0);

        /* Print out the solution: */
        for(t=0;t<T;t++)
            System.out.println("Period " + (t+1) + ": prod " + prod[t].getSol()
                               + " (demand: " + DEMAND[t] + ", cost: " + PRODCOST[t] + "), setup "
                               + setup[t].getSol() + " (cost: " + SETUPCOST[t] + ")");
    }

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

    public static void main(String[] args) throws XPRSprobException, XPRSexception {
        try (XPRBprob p = new XPRBprob("Els"); /* Initialize BCL and create a new problem */
             XPRS xprs = new XPRS()) {         /* Initialize Xpress-Optimizer */
            modEls(p);                     /* Model the problem */
            solveEls(p);                   /* Solve the problem */
        }
    }
}

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