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

/********************************************************
  BCL Example Problems
  ====================

  file xbcontr.c
  ``````````````
  Contract allocation example.

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

#include <stdio.h>
#include "xprb.h"

#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;
 XPRBctr c1,c2,cobj;
 XPRBvar x[District][Contract];    /* Variables indicating whether a project 
                                      is chosen */
 XPRBvar y[District][Contract];    /* Quantities allocated to contractors */
 XPRBprob prob;

 prob=XPRBnewprob("Contract");     /* Initialize a new problem in BCL */

/**** VARIABLES ****/
 for(d=0;d<District;d++)
  for(c=0;c<Contract;c++)
  {
   x[d][c] = XPRBnewvar(prob,XPRB_BV,XPRBnewname("x_d%dc%d",d+1,c+1),0,1);
   y[d][c] = 
     XPRBnewvar(prob,XPRB_SC,XPRBnewname("q_d%dc%d",d+1,c+1),0,OUTPUT[d]);
   XPRBsetlim(y[d][c],5);
  } 

/****OBJECTIVE****/
 cobj = XPRBnewctr(prob,"OBJ",XPRB_N);  /* Define objective: total cost */
 for(d=0;d<District;d++)
  for(c=0;c<Contract;c++)
   XPRBaddterm(cobj,y[d][c],COST[d]);     
 XPRBsetobj(prob,cobj);                 /* Set objective function */ 
 
/**** CONSTRAINTS ****/
 for(c=0;c<Contract;c++)
 {
  c1=XPRBnewctr(prob,"Size",XPRB_G);  /* Cover the required contract volume */
  c2=XPRBnewctr(prob,"Min",XPRB_G);   /* At least 2 districts per contract */
  for(d=0;d<District;d++)
  {
   XPRBaddterm(c1,y[d][c],1);
   XPRBaddterm(c2,x[d][c],1);
  }
  XPRBaddterm(c1,NULL,VOLUME[c]);
  XPRBaddterm(c2,NULL,2); 
 } 
 
 for(d=0;d<District;d++)        /* Do not exceed max. output of any district */
 {
  c1=XPRBnewctr(prob,"Output",XPRB_L);
  for(c=0;c<Contract;c++)
   XPRBaddterm(c1,y[d][c],1);
  XPRBaddterm(c1,NULL,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++)
   XPRBnewprec(prob,"XY",x[d][c],0,y[d][c]);

/****SOLVING + OUTPUT****/
 XPRBexportprob(prob,XPRB_MPS,"Contract");   /* Output matrix in MPS format */
  
 XPRBsetsense(prob,XPRB_MINIM);      /* Choose the sense of the optimization */
 XPRBmipoptimize(prob,"");           /* Solve the MIP-problem */

 if((XPRBgetmipstat(prob)==XPRB_MIP_SOLUTION) || 
    (XPRBgetmipstat(prob)==XPRB_MIP_OPTIMAL)) 
                                /* Test whether an integer solution was found */
 {              
  printf("Objective: %g\n",XPRBgetobjval(prob));  /* Get objective value */

  for(d=0;d<District;d++)       /* Print the solution values */
  {
   for(c=0;c<Contract;c++)
    if(XPRBgetsol(x[d][c])>0)
     printf("%s:%g, ", XPRBgetvarname(y[d][c]), XPRBgetsol(y[d][c]));
   printf("\n");
  }
 } 
 return 0;
}