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Purchase - Definition of SOS-2

Description
A model for optimal purchasing with price-breaks featuring a complex MIP model, data input from file and using SOS-2.

Further explanation of this example: Quick reference guide 'MIP formulations and linearizations', Section 3.3 Price breaks

Source Files
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Data Files

xbpurch.cs

/********************************************************
Xpress-BCL C# Example Problems
==============================

file xbpurch.cs


(c) 2008 Fair Isaac Corporation
authors: S.Heipcke, D.Brett.
********************************************************/

/* 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. */

using System;
using System.Text;
using System.IO;
using BCL;

namespace Examples
{
public class TestProduction
{

//Define XPRBDATAPATH to wherever you have placed the data folder; here we expect it to be same directory as compiled example.
static string XPRBDATAPATH = Directory.GetParent(System.Reflection.Assembly.GetExecutingAssembly().Location).FullName + "/Data";
string PARAMSFILE = XPRBDATAPATH + "/purchase/params.dat";
string MAXPERCFILE = XPRBDATAPATH + "/purchase/maxperc.dat";
string REQFILE = XPRBDATAPATH + "/purchase/required.dat";
string PRICEFILE = XPRBDATAPATH + "/purchase/pricebk.dat";

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

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

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

/* Initialize a new problem in BCL */
XPRBprob p = new XPRBprob("Purchase");

public static void Main()
{
System.Console.WriteLine("Started Production Test.\n");
XPRB.init();

TestProduction InitClassInstance = new TestProduction();

/* Data input from file */

/* Formulate and solve the problem */
InitClassInstance.modPurchase();

return;
}

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

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

/****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++)
{
/* Weights at breakpoint b for supplier s */
for(b=0;b<NB2;b++)
lam[s,b] = p.newVar(("lam_" + (s+1).ToString()));
}

/****OBJECTIVE****/
//Init lobj
lobj = new XPRBexpr();

/* Minimize the sum of costs*weights */
for(s=0;s<NS;s++)
for(b=0;b<NB2;b++)  lobj += C[s,b]*lam[s,b];

/* Set objective function */
p.setObj(p.newCtr("OBJ", lobj));

/****CONSTRAINTS****/
/* Define x, also order the lam variables by breakpoint quantities */
lr = new XPRBexpr[NS];
for(s=0;s<NS;s++)
{
lr[s] = new XPRBexpr(0);
for(b=0;b<NB2;b++)
lr[s] += X[s,b]*lam[s,b];
p.newCtr("DefX", lr[s] == 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 += lam[s, b];
p.newCtr("Conv", lc == 1);
}

/* The minimum quantity that must be bought */
lc = new XPRBexpr();
for(s=0;s<NS;s++) lc += x[s];

/****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] += lam[s,b];
p.newSos("SetLam", BCLconstant.XPRB_S2, lr[s]);
}

/****SOLVING + OUTPUT****/
/* Output to MPS file */
p.exportProb(BCLconstant.XPRB_MPS,"TestResult.matrix");

/* Choose the sense of the optimization */
p.setSense(BCLconstant.XPRB_MINIM);

/* Solve the MIP-problem */
p.mipOptimize();

/* Get objective value */
System.Console.WriteLine("Objective: " + p.getObjVal() + "\n");

/* Print out the solution values */
for(s=0;s<NS;s++)
System.Console.Write(x[s].getName() + ":" + x[s].getSol() + " ");
System.Console.WriteLine("\n");
for(s=0;s<NS;s++)
for(b=0;b<NB2;b++)
System.Console.Write(lam[s,b].getName() + ":" +
lam[s,b].getSol() + " ");
System.Console.WriteLine("\n");

}

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

/**** Read data from files ****
* Need to do this via StreamReader as per XPRBreadline C# method
******************************/
{

//			   string format, out object[] output)
FileStream file = new FileStream(PARAMSFILE, FileMode.Open,

int s,b;

/* Read the parameter file */
//int maxlen, string format, out object[] output)

fileStreamIn.Close();
file.Close();

NB2 = 2*NB;

/* Now define the tables that we will use, using the sizes we
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;
}

file = new FileStream(PRICEFILE, FileMode.Open, FileAccess.Read);
while (p.XPRBreadline(fileStreamIn, 200, "{i}, {i}, {g}, {g}",
{
UC[s - 1, b - 1] = (double)objRead[2];
BR[s - 1, b - 1] = (double)objRead[3];
}
fileStreamIn.Close();
file.Close();

/* Read the percentages data file */
file = new FileStream(MAXPERCFILE, FileMode.Open, FileAccess.Read);
p.XPRBreadarrline(fileStreamIn, 200, "{g}, ", out MAXPERC, NS);
fileStreamIn.Close();
file.Close();

/* Read the required amount data file */
file = new FileStream(REQFILE, FileMode.Open, FileAccess.Read);
fileStreamIn.Close();
file.Close();

/* We now pick out the data from the tables into which they have
for(s=0;s<NS;s++)
{
/* First total cost and (new) breakpoint are (0,0) */
C[s,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 */
}
}
}

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

}

}
`