/********************************************************/ /* Xpress-BCL C# Example Problems */ /* ============================== */ /* */ /* file xbels.cs */ /* ````````````` */ /* Example for the use of Xpress-BCL */ /* (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 */ /* authors: S.Heipcke, D.Brett. */ /********************************************************/ using System; using System.Text; using System.IO; using Optimizer; using BCL; namespace Examples { public class TestAdvEls { const double EPS = 1e-6; const int T = 6; /* Number of time periods */ /****DATA****/ int[] DEMAND = { 1, 3, 5, 3, 4, 2}; /* Demand per period */ int[] SETUPCOST = {17,16,11, 6, 9, 6}; /* Setup cost per period */ int[] PRODCOST = { 5, 3, 2, 1, 3, 1}; /* Production cost per period */ int[,] D = new int[T,T]; /* Total demand,periods t1-t2 */ XPRBvar[] prod = new XPRBvar[T]; /* Production in period t */ XPRBvar[] setup = new XPRBvar[T]; /* Setup in period t */ XPRBprob p = new XPRBprob("Els"); /* Initialize a new BCL prob */ /*********************************************************************/ public void modEls() { int s,t,k; XPRBexpr cobj,le; for(s=0;s<T;s++) for(t=0;t<T;t++) for(k=s;k<=t;k++) +=DEMAND[k]; 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 setup <=D[t,T-1]*setup[t]); periods to satisfy this of time le=new for(s=0;s<=t;s++)>= 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             */
        /*********************************************************************/
        public void solveEls()
        {
            double objval;               /* Objective value */
            int t,l;
            int starttime;
            int ncut, npass, npcut;      /* Counters for cuts and passes */

             /* Solution values for var.s prod & setup */
            double[] solprod = new double[T];
            double[] solsetup = new double[T];

            double ds;
            XPRBbasis basis;
            XPRBexpr le;
            XPRSprob xprsp = p.getXPRSprob();

            starttime=XPRB.getTime();

            /* Disable automatic cuts - we use our own */
            xprsp.CutStrategy = 0;

            /* Switch presolve off */
            xprsp.Presolve = 0;

            ncut = npass = 0;

            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++) (ds=0.0, t=0; t<=l; ds +=solprod[t]; else Add the inequality: minimum of actual production and maximum potential in periods to l must at least equal total demand l. sum(t=1:l)>= D[0][l]
                    */
                    if(ds < D[0,l] - EPS)
                    {
                        le = new XPRBexpr(0);
                        for(t=0;t<=l;t++)
                        {
                            if (solprod[t] < D[t,l]*solsetup[t] + EPS)
                                le += prod[t];
                            else
                                le += D[t,l]*setup[t];
                        }
                        p.newCtr("cut" + (ncut+1), le >= D[0,l]);
                        ncut++;
                        npcut++;
                    }
                }

                System.Console.WriteLine("Pass " + npass + " (" +
                    (XPRB.getTime()-starttime)/1.000 +
                	" sec), objective value " + objval + ", cuts added: " +
                	npcut + " (total " + ncut + ")");

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

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

        }

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

        public static void Main()
        {
           XPRB.init();
           TestAdvEls TestInstance = new TestAdvEls();

            TestInstance.modEls();       /* Model the problem */
            TestInstance.solveEls();     /* Solve the problem */

            return;
        }

    }

}