/********************************************************
Xpress-BCL Java Example Problems
================================
file xbpurch.java
`````````````````
Purchasing problem using SOS-2.
(c) 2008-2023 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 */
}
}
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