Contract - Semi-continuous variables, predefined constraint functions, combine BCL with Xpress Optimizer

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

  file xbcontr.cxx
  ````````````````
  Contract allocation example.

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

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

using namespace std;
using namespace ::dashoptimization;

#define District 6                /* Number of districts */
#define Contract 10               /* Number of contracts */

/**** DATA ****/
int OUTPUT[] = {50, 40, 10, 20, 70, 50};    /* Max. output per district */
int COST[]   = {50, 20, 25, 30, 45, 40};    /* Cost per district */
int VOLUME[]   = {20, 10, 30, 15, 20, 30, 10, 50, 10, 20};  
                                  /* Volume of contracts */

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

int main(int argc, char **argv)
{
 int d,c;
 XPRBprob p("Contract");          /* Initialize a new problem in BCL */
 XPRBexpr l1,l2,lobj;
 XPRBvar x[District][Contract];   /* Variables indicating whether a project 
                                     is chosen */
 XPRBvar y[District][Contract];   /* Quantities allocated to contractors */
 
/**** VARIABLES ****/
 for(d=0;d<District;d++)
  for(c=0;c<Contract;c++)
  {
   x[d][c] = p.newVar(XPRBnewname("x_d%dc%d",d+1,c+1),XPRB_BV);
   y[d][c] = p.newVar(XPRBnewname("q_d%dc%d",d+1,c+1),XPRB_SC,0,OUTPUT[d]);
   y[d][c].setLim(5);
  } 

/****OBJECTIVE****/
 for(d=0;d<District;d++)
  for(c=0;c<Contract;c++)
   lobj += COST[d]*y[d][c];   
     
 p.setObj(p.newCtr("OBJ",lobj));  /* Set the objective function */
 
/**** CONSTRAINTS ****/
 for(c=0;c<Contract;c++)
 {
  l1=0;
  l2=0;  
  for(d=0;d<District;d++)
  {
   l1 += y[d][c];
   l2 += x[d][c];
  }
  p.newCtr("Size", l1 >= VOLUME[c]);  /* "Size": cover the required volume */
  p.newCtr("Min", l2 >= 2 ); 	 /* "Min": at least 2 districts per contract */
 }
 
 for(d=0;d<District;d++)         /* Do not exceed max. output of any district */
 {
  l1=0;
  for(c=0;c<Contract;c++)
   l1 += y[d][c];
  p.newCtr("Output", l1 <= OUTPUT[d]);
 } 
 
 for(d=0;d<District;d++)         /* If a contract is allocated to a district,
                                    then at least 1 unit is allocated to it */
  for(c=0;c<Contract;c++)
   p.newCtr("XY", x[d][c] <= y[d][c]);

/****SOLVING + OUTPUT****/
 p.exportProb(XPRB_MPS,"Contract");  /* Output the matrix in MPS format */
 p.setSense(XPRB_MINIM);         /* Choose the sense of the optimization */   
 p.mipOptimize("");              /* Solve the MIP-problem */

 if((p.getMIPStat()==XPRB_MIP_SOLUTION) || (p.getMIPStat()==XPRB_MIP_OPTIMAL)) 
                                 /* Test whether an integer sol. was found */
 {              
  cout << "Objective: " << p.getObjVal() << endl;  /* Get objective value */

  for(d=0;d<District;d++)        /* Print the solution values */
  {
   for(c=0;c<Contract;c++)
    if(x[d][c].getSol()>0)
     cout << y[d][c].getName() << ":" << y[d][c].getSol() << ", ";
   cout << endl;
  }
 } 
 return 0;
}