/******************************************************** 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) 2008-2024 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++) +=DEMAND[k]; prod=new setup=new prod[t]=p.newVar("prod" setup[t]=p.newVar("setup" cobj=new Minimize total cost Production in period t must not exceed the demand for remaining if there is production during then a periods to satisfy this of time le=new for(s=0;s<=t;s++) Cut generation loop at top node: solve LP and save basis get solution values identify set up violated constraints load modified problem saved static void throws XPRSexception double Objective value int Counters cuts passes Solution var.s XPRSprob XPRBbasis XPRBexpr starttime=XPRB.getTime(); op=p.getXPRSprob(); Disable automatic we use our own Switch presolve off ncut=npass solprod=new solsetup=new do npcut=0; Solve Save current objval=p.getObjVal(); Get objective values: solprod[t]=prod[t].getSol(); solsetup[t]=setup[t].getSol(); Search constraints: for(l=0;l<T;l++) for(ds=0.0, t<=l; ds else Add inequality: minimum actual maximum potential l least equal l. sum(t=1:l)>= 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)/1.000
                               + " 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 */
        }
    }
}