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

  file xbpurch.java
  `````````````````
  Purchasing problem using SOS-2.

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, Jan. 2000, rev. Mar. 2011
********************************************************/

/* WARNING. This model is not for the novice, but it does contain many  *
 * useful ideas.                                                        *
 * The formulation is tricky because the discounts are all-quantity,    *
 * so the graph of cost against quantity purchased is discontinuous.    *
 * To maintain sanity in the special ordered set formulation, we must   *
 * coarsen the discontinuity by stopping purchases just at the break    *
 * point. */

import java.io.*;
import com.dashoptimization.*;

public class xbpurch {
    static final String PARAMSFILE = System.getProperty("XPRBDATA") +
        "/purchase/params.dat";
    static final String MAXPERCFILE= System.getProperty("XPRBDATA") +
        "/purchase/maxperc.dat";
    static final String REQFILE    = System.getProperty("XPRBDATA") +
        "/purchase/required.dat";
    static final String PRICEFILE  = System.getProperty("XPRBDATA") +
        "/purchase/pricebk.dat";

    /****TABLES****/
    static int NS;             /* Number of suppliers */
    static int NB;             /* Number of price breaks */
    static int NB2;            /* Useful parameter */

    static double[][] UC;      /* Unit cost */
    static double[][] BR;      /* Breakpoints (quantities at which unit cost
                                  changes) */
    static double[][] X;       /* Coarsened break points */
    static double[][] C;       /* Total cost at break points */
    static double[] DELTA;     /* Coarsening factors */
    static double[] MAXPERC;   /* Maximum percentage from each supplier */
    static double REQ;         /* Total quantity required */

    static final double delta = 0.10;   /* Base coarsening factor */

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

    static void modPurchase() {
        XPRBexpr lobj, lc;
        XPRBexpr[] lr;
        int s,b;
        XPRBvar[] x;
        XPRBvar[][] lam;

        try (XPRBprob p = new XPRBprob("Purchase")) { /* Initialize BCL and create a new problem */

            /****VARIABLES****/
            x = new XPRBvar[NS];          /* Quantity to purchase from supplier s */
            for(s=0;s<NS;s++)  x[s] = p.newVar("x");

            lam = new XPRBvar[NS][NB2];
            for(s=0;s<NS;s++)
                for(b=0;b<NB2;b++)
                    lam[s][b] = p.newVar("lam_" + (s+1));
            /* Weights at breakpoint b for supplier s */

            /****OBJECTIVE****/
            lobj = new XPRBexpr();
            for(s=0;s<NS;s++)         /* Minimize the sum of costs*weights */
                for(b=0;b<NB2;b++)  lobj.add(lam[s][b].mul(C[s][b]));
            p.setObj(lobj);           /* Set objective function */

            /****CONSTRAINTS****/
            /* Define x and also order the lam variables by breakpoint quantities */
            lr = new XPRBexpr[NS];
            for(s=0;s<NS;s++) {
                lr[s] = new XPRBexpr();
                for(b=0;b<NB2;b++)  lr[s].add(lam[s][b].mul(X[s][b]));
                p.newCtr("DefX", lr[s].eql(x[s]) );
            }

            /* The convexity constraint (lam sum to 1) */
            for(s=0;s<NS;s++) {
                lc = new XPRBexpr();
                for(b=0;b<NB2;b++)  lc.add(lam[s][b]);
                p.newCtr("Conv", lc.eql(1) );
            }

            /* The minimum quantity that must be bought */
            lc = new XPRBexpr();
            for(s=0;s<NS;s++) lc.add(x[s]);
            p.newCtr("MustBuy", lc.gEql(REQ) );

            /****BOUNDS****/
            /* No more than the maximum percentage from each supplier */
            for(s=0;s<NS;s++)  x[s].setUB(MAXPERC[s]*REQ/100.0);

            /****SETS****/
            /* Define the lam as SOS2 as we can linearly interpolate between the
             * breakpoints. The weights are the DefX coefficients augmented by 1
             because BCL does not accept the weight 0. */
            for(s=0;s<NS;s++) {
                for(b=0;b<NB2;b++)  lr[s].add(lam[s][b]);
                p.newSos("SetLam", XPRB.S2, lr[s]);
            }

            /****SOLVING + OUTPUT****/
            try {
                p.exportProb(XPRB.MPS,"purc");   /* Output to MPS file */
            }
            catch(IOException e) {
                System.err.println(e.getMessage());
                System.exit(1);
            }
            p.setSense(XPRB.MINIM);           /* Choose the sense of the optimization */
            p.mipOptimize("");                /* Solve the MIP-problem */

            System.out.println("Objective: " + p.getObjVal());  /* Get objective value */

            for(s=0;s<NS;s++)                 /* Print out the solution values */
                System.out.print(x[s].getName() +":"+ x[s].getSol() +" ");
            System.out.println();
            for(s=0;s<NS;s++)
                for(b=0;b<NB2;b++)
                    System.out.print(lam[s][b].getName() +":"+ lam[s][b].getSol() +" ");
            System.out.println();
        }
    }

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

    /**** Initialize the stream tokenizer ****/
    static StreamTokenizer initST(FileReader file) {
        StreamTokenizer st=null;

        st= new StreamTokenizer(file);   /* Initialize the stream tokenizer */
        st.commentChar('!');             /* Use the character '!' for comments */
        st.eolIsSignificant(true);       /* Return end-of-line character */
        st.ordinaryChar(',');            /* Use ',' as separator */
        st.parseNumbers();               /* Read numbers as numbers (not strings)*/
        return st;
    }

    /**** Read single line data file ****/
    static void readOneLineFile(String filename, double[] data) throws IOException {
        FileReader datafile=null;
        StreamTokenizer st;
        int i=0;

        datafile = new FileReader(filename);
        st = initST(datafile);
        do {
            do {
                st.nextToken();
            } while(st.ttype==st.TT_EOL);    /* Skip empty lines */
            while(st.ttype == st.TT_NUMBER) {
                data[i++] = st.nval;
                if(st.nextToken() != ',') break;
                st.nextToken();
            }
        } while( st.ttype == st.TT_EOL );
        datafile.close();
    }

    /**** Read data from files ****/
    static void readData() throws IOException {
        int s,b;
        double[] val;
        FileReader datafile=null;
        StreamTokenizer st;
        int i=0;

        /* Read the parameter file */
        val = new double[2];
        readOneLineFile(PARAMSFILE,val);
        NS = (int)val[0];
        NB = (int)val[1];
        NB2 = 2*NB;

        /* Now define the tables that we will use, using the sizes we
           have just read. */
        UC= new double[NS][NB];
        BR = new double[NS][NB];
        X=new double[NS][NB2];
        C=new double[NS][NB2];
        DELTA=new double[NB2];
        MAXPERC=new double[NS];

        /* Define coarsening factors */
        DELTA[0]=0;
        DELTA[1] = -1*delta;
        for(b=2;b<NB2;b++) DELTA[b] = -1*DELTA[b-1];

        /* Read the price and breakpoint data file */
        for(s=0;s<NS;s++)
            for(b=0;b<NB;b++) {
                UC[s][b]=0;
                BR[s][b]=0;
            }

        datafile = new FileReader(PRICEFILE);
        st = initST(datafile);
        do {
            do {
                st.nextToken();
            } while(st.ttype==st.TT_EOL);    /* Skip empty lines */
            if(st.ttype != st.TT_NUMBER) break;
            s=(int)st.nval;
            if(st.nextToken() != ',') break;
            if(st.nextToken() != st.TT_NUMBER) break;
            b=(int)st.nval;
            if(st.nextToken() != ',') break;
            if(st.nextToken() != st.TT_NUMBER) break;
            UC[s-1][b-1]=st.nval;
            if(st.nextToken() != ',') break;
            if(st.nextToken() != st.TT_NUMBER) break;
            BR[s-1][b-1]=st.nval;
        } while( st.nextToken() == st.TT_EOL );
        datafile.close();

        /* Read the percentages data file */
        readOneLineFile(MAXPERCFILE,MAXPERC);

        /* Read the required amount data file */
        readOneLineFile(REQFILE,val);
        REQ = val[0];

        /* We now pick out the data from the tables into which they have
           been read. */
        for(s=0;s<NS;s++) {
            C[s][0] = 0;      /* First total cost and (new) breakpoint are (0,0) */
            X[s][0] = 0;
            for(b=1;b<NB2;b++)
                {                          /* Rest calculated... */
                    C[s][b] = UC[s][b/2] * BR[s][(b-1)/2];   /* ...unit price*quantity */
                    X[s][b] = BR[s][(b-1)/2] + DELTA[b];     /* ...coarsened grids */
                }
        }
    }

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

    public static void main(String[] args) {
        try {
            readData();           /* Data input from file */
        }
        catch(IOException e) {
            System.err.println(e.getMessage());
            System.exit(1);
        }
        modPurchase();         /* Formulate and solve the problem */
    }
}