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

  file foliomip1.c
  ````````````````
  Modeling a small MIP problem
  to perform portfolio optimization.
   -- Limiting the total number of assets --

  (c) 2008-2023 Fair Isaac Corporation
      author: S.Heipcke, Dec. 2003, rev. Mar. 2011
********************************************************/

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

#define MAXNUM 4                   /* Max. number of different assets */

#define NSHARES 10                 /* Number of shares */
#define NRISK 5                    /* Number of high-risk shares */
#define NNA 4                      /* Number of North-American shares */

double RET[] = {5,17,26,12,8,9,7,6,31,21};  /* Estimated return in investment */
int RISK[] = {1,2,3,8,9};          /* High-risk values among shares */
int NA[] = {0,1,2,3};              /* Shares issued in N.-America */

int main(int argc, char **argv)
{
 int s;
 XPRBprob prob;
 XPRBctr Risk,Na,Return,Cap,Num;
 XPRBvar frac[NSHARES];            /* Fraction of capital used per share */
 XPRBvar buy[NSHARES];             /* 1 if asset is in portfolio, 0 otherwise */
 char *MIPSTATUS[] = {"not loaded", "not optimized", "LP optimized",
                      "unfinished (no solution)",
                      "unfinished (solution found)", "infeasible", "optimal",
                      "unbounded"};

 prob = XPRBnewprob("FolioMIP1");  /* Initialize a new problem in BCL */

/* Create the decision variables (including upper bounds for `frac') */
 for(s=0;s<NSHARES;s++)
 {
  frac[s] = XPRBnewvar(prob, XPRB_PL, "frac", 0, 0,3);
  buy[s] = XPRBnewvar(prob, XPRB_BV, "buy", 0, 1);
 }

/* Objective: total return */
 Return = XPRBnewctr(prob, "Return", XPRB_N);
 for(s=0;s<NSHARES;s++) XPRBaddterm(Return, frac[s], RET[s]);
 XPRBsetobj(prob,Return);          /* Set the objective function */

/* Limit the percentage of high-risk values */
 Risk = XPRBnewctr(prob, "Risk", XPRB_L);
 for(s=0;s<NRISK;s++) XPRBaddterm(Risk, frac[RISK[s]], 1);
 XPRBaddterm(Risk, NULL, 1/3);

/* Minimum amount of North-American values */
 Na = XPRBnewctr(prob, "NA", XPRB_G);
 for(s=0;s<NNA;s++) XPRBaddterm(Na, frac[NA[s]], 1);
 XPRBaddterm(Na, NULL, 0,5);

/* Spend all the capital */
 Cap = XPRBnewctr(prob, "Cap", XPRB_E);
 for(s=0;s<NSHARES;s++) XPRBaddterm(Cap, frac[s], 1);
 XPRBaddterm(Cap, NULL, 1);

/* Limit the total number of assets */
 Num = XPRBnewctr(prob, "Num", XPRB_L);
 for(s=0;s<NSHARES;s++) XPRBaddterm(Num, buy[s], 1);
 XPRBaddterm(Num, NULL, MAXNUM);

/* Linking the variables */
 for(s=0;s<NSHARES;s++) XPRBnewprec(prob, "Link", frac[s], 0, buy[s]);

/* Solve the problem */
 XPRBsetsense(prob, XPRB_MAXIM);
 XPRBmipoptimize(prob, "");

 printf("Problem status: %s\n", MIPSTATUS[XPRBgetmipstat(prob)]);

/* Solution printing */
 printf("Total return: %g\n", XPRBgetobjval(prob));
 for(s=0;s<NSHARES;s++)
  printf(" %d : %g%% (%g)\n", s, XPRBgetsol(frac[s])*100, XPRBgetsol(buy[s]));

 return 0;
}