/******************************************************** Xpress-BCL C++ Example Problems =============================== file xbpurch.cxx ```````````````` Purchasing problem using SOS-2. (c) 2008-2024 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. */ #include <iostream>
#include <cstdio>
#include "xprb_cpp.h"

using namespace std;
using namespace ::dashoptimization;

#define PARAMSFILE  XPRBDATAPATH "/purchase/params.dat"
#define MAXPERCFILE XPRBDATAPATH "/purchase/maxperc.dat"
#define REQFILE     XPRBDATAPATH "/purchase/required.dat"
#define 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 = 0,1;        /* Base coarsening factor */
                    
/***********************************************************************/

void modPurchase(XPRBprob &p)
{
 XPRBexpr lobj, *lr, lc;
 int s,b;
 XPRBvar *x,**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 for(s=0;s<NS;s++) lam[s]=new for(b=0;b<NB2;b++) lam[s][b]=p.newVar(XPRBnewname("lam_%d",s+1)); Weights at breakpoint b for supplier s Minimize the sum of lobj +=C[s][b]*lam[s][b]; Set objective function Define x and also order variables by quantities lr=new lr[s]== The convexity constraint to lc=0; minimum quantity that must be bought>= REQ);

/****BOUNDS****/
    /* No more than the maximum percentage from each supplier */
 for(s=0;s<NS;s++) x[s].setUB(MAXPERC[s]*REQ/100); /****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", XPRB_S2, lr[s]); } /****SOLVING + OUTPUT****/ p.exportProb(XPRB_MPS,"purc"); /* Output to MPS file */ p.setSense(XPRB_MINIM); /* Choose the sense of the optimization */ p.mipOptimize(""); /* Solve the MIP-problem */ cout << "Objective: " << p.getObjVal() << endl; /* Get objective value */ for(s=0;s<NS;s++) /* Print out the solution values */ cout << x[s].getName() << ":" << x[s].getSol() << " "; cout << endl; for(s=0;s<NS;s++) for(b=0;b<NB2;b++) cout << lam[s][b].getName() << ":" << lam[s][b].getSol() << " "; cout << endl; delete [] BR; delete [] UC; delete [] lr; for(s=0;s<NS;s++) delete [] lam[s]; delete [] lam; delete [] x; } /***********************************************************************/ /**** Read data from files ****/ void readData() { FILE *datafile; int s,b; double val1,val2; /* Read the parameter file */ datafile=fopen(PARAMSFILE,"r"); XPRBreadlinecb(XPRB_FGETS, datafile, 200, "i", &NS); XPRBreadlinecb(XPRB_FGETS, datafile, 200, "i", &NB); fclose(datafile); NB2 = 2*NB; /* Now define the tables that we will use, using the sizes we have just read. */ UC= new double*[NS]; for(s=0;s<NS;s++) UC[s]=new double[NB]; BR = new double*[NS]; for(s=0;s<NS;s++) BR[s]=new double[NB]; X=new double*[NS]; for(s=0;s<NS;s++) X[s]=new double[NB2]; C=new double*[NS]; for(s=0;s<NS;s++) C[s]=new double[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=fopen(PRICEFILE,"r"); while(XPRBreadlinecb(XPRB_FGETS, datafile, 200, "i,i,g,g", &s, &b, &val1, &val2)==4) { UC[s-1][b-1]=val1; BR[s-1][b-1]=val2; } fclose(datafile); /* Read the percentages data file */ datafile=fopen(MAXPERCFILE,"r"); XPRBreadarrlinecb(XPRB_FGETS, datafile, 200, "g,", MAXPERC, NS); fclose(datafile); /* Read the required amount data file */ datafile=fopen(REQFILE,"r"); XPRBreadlinecb(XPRB_FGETS, datafile, 200, "g", &REQ); fclose(datafile); /* 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 */ } } } /***********************************************************************/ int main(int argc, char **argv) { XPRBprob p("Purchase"); /* Initialize a new problem in BCL */ readData(); /* Data input from file */ modPurchase(p); /* Formulate and solve the problem */ return 0; }