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

  file xbcutstk.cxx
  `````````````````
  Cutting stock problem, solved by column (= cutting 
  pattern) generation heuristic looping over the
  root node.

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, 2001, rev. Mar. 2014
********************************************************/

#include <iostream>
#include <cmath>
#include "xprb_cpp.h"
#include "xprs.h"

using namespace std;
using namespace ::dashoptimization;

#define NWIDTHS 5
#define MAXWIDTH 94

#define EPS 1e-6
#define MAXCOL 10

/****DATA****/
double WIDTH[] = {17, 21, 22.5,  24, 29,5};  /* Possible widths */
int DEMAND[] =  {150, 96,   48, 108,  227};  /* Demand per width */
int PATTERNS[NWIDTHS][NWIDTHS];              /* (Basic) cutting patterns */

XPRBvar pat[NWIDTHS+MAXCOL];               /* Rolls per pattern */
XPRBctr dem[NWIDTHS];                      /* Demand constraints */
XPRBctr cobj;                              /* Objective function */

double knapsack(int N, double *c, double *a, double R, int *d, int *xbest);

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

void modCutStock(XPRBprob &p)
{
 int i,j;
 XPRBexpr le;

 for(j=0;j<NWIDTHS;j++) PATTERNS[j][j]=(int)floor(MAXWIDTH/WIDTH[j]); for(j=0;j<NWIDTHS;j++) pat[j]=p.newVar(XPRBnewname("pat_%d",j+1), le +=pat[j]; Minimize total number of rolls cobj=p.newCtr("OBJ", for(i=0;i<NWIDTHS;i++) Satisfy the demand per width dem[i]=p.newCtr("Demand",>= DEMAND[i]);
 }
}

/**************************************************************************/
/*  Column generation loop at the top node:                               */
/*    solve the LP and save the basis                                     */
/*    get the solution values                                             */
/*    generate new column(s) (=cutting pattern)                           */
/*    load the modified problem and load the saved basis                  */
/**************************************************************************/
void solveCutStock(XPRBprob &p)
{
 double objval;                  /* Objective value */
 int i,j;
 int starttime;
 int npatt, npass;               /* Counters for columns and passes */
 double solpat[NWIDTHS+MAXCOL];  /* Solution values for variables pat */
 double dualdem[NWIDTHS];        /* Dual values of demand constraints */
 XPRBbasis basis;
 double dw,z;
 int x[NWIDTHS];

 starttime=XPRB::getTime();
 npatt = NWIDTHS;

 for(npass=0;npass<MAXCOL;npass++) Solve the LP basis=p.saveBasis(); Save current objval=p.getObjVal(); Get objective value solution values: for(j=0;j<npatt;j++) solpat[j]=pat[j].getSol(); for(i=0;i<NWIDTHS;i++) dualdem[i]=dem[i].getDual(); integer knapsack problem z=min{cx : ax<=r, x in with r=MAXWIDTH, n=NWIDTHS cout <<="(" endl No need to keep any longer else Print new pattern: z-1 dw=0; +=WIDTH[i]*x[i]; Create a variable for this pat[npatt]=p.newVar(XPRBnewname("pat_%d",npatt+1),XPRB_UI); cobj Add var. demand> EPS)
    {
     dem[i] += x[i]*pat[npatt];
     if((int)ceil((double)DEMAND[i]/x[i]) > dw)
      dw = (int)ceil((double)DEMAND[i]/x[i]);
    }
   pat[npatt].setUB(dw);           /* Change the upper bound on the new var.*/  

   npatt++;

   p.loadMat();                    /* Reload the problem */
   p.loadBasis(basis);             /* Load the saved basis */
   basis.reset();                  /* No need to keep the basis any longer */
  }
 }

 p.mipOptimize("");                /* Solve the MIP */
  
 cout << "(" << (XPRB::getTime()-starttime)/1.000 << " sec) Optimal solution: " << p.getObjVal() << " rolls, " << npatt << " patterns" << endl << "   "; 
 cout << "Rolls per pattern: ";
 for(i=0;i<npatt;i++) cout << pat[i].getSol() << ", ";
 cout << endl;   
}

/**************************************************************************/
/* Integer Knapsack Algorithm for solving the integer knapsack problem    */
/*    z = max{cx : ax <= R, x <= d, x in Z^N}                             */
/*                                                                        */
/* Input data:                                                            */
/*   N:        Number of item types                                       */
/*   c[i]:     Unit profit of item type i, i=1..n                         */
/*   a[i]:     Unit resource use of item type i, i=1..n                   */
/*   R:        Total resource available                                   */
/*   d[i]:     Demand for item type i, i=1..n                             */
/* Return values:                                                         */
/*   xbest[i]: Number of items of type i used in optimal solution         */
/*   zbest:    Value of optimal solution                                  */
/**************************************************************************/
double knapsack(int N, double *c, double *a, double R, int *d, int *xbest)
{
 int j;
 double zbest = 0.0;
 XPRBvar *x;
 XPRBexpr klobj, knap;
 XPRBprob pk("Knapsack");

/*
 cout << "Solving z = max{cx : ax <= b; x in Z^n}\n   c   =";
 for (j = 0; j < N; j++) cout << " " << c[j] << ",";
 cout << "\n   a   =";
 for (j = 0; j < N; j++) cout << " " << a[j] << ",";
 cout << "\n   c/a =";
 for (j = 0; j < N; j++) cout << " " << c[j]/a[j] << ",";
 cout << "\n   b   = " << R << endl;
*/
 
 x = new XPRBvar[N];
 if(x==NULL) cout << "Allocating memory for variables failed." << endl;
 for(j=0;j<N;j++) x[j]=pk.newVar("x", XPRB_UI, 0, d[j]);

 for(j=0;j<N;j++) klobj += c[j]*x[j];
 pk.setObj(pk.newCtr("OBJ",klobj));  
 for(j=0;j<N;j++) knap += a[j]*x[j];
 pk.newCtr("KnapXPRBctr", knap <= R);
 pk.setSense(XPRB_MAXIM);
 pk.mipOptimize("");

 zbest = pk.getObjVal();
 for(j=0;j<N;j++) xbest[j]=(int)floor(x[j].getSol() + 0,5);
/*
 cout << "   z = " << zbest << endl << "   x =";
 for(j=0; j<N; j++) cout << " " << xbest[j] << ",";
 cout << endl;
*/

 delete [] x;
 
 return (zbest);
}

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

int main(int argc, char **argv)
{
 XPRBprob p("CutStock");           /* Initialize a new problem in BCL */
 modCutStock(p);                   /* Model the problem */
 solveCutStock(p);                 /* Solve the problem */
  
 return 0;
}