Try our new documentation site.


facility_c.c


/* Copyright 2019, Gurobi Optimization, LLC */

/* Facility location: a company currently ships its product from 5 plants
   to 4 warehouses. It is considering closing some plants to reduce
   costs. What plant(s) should the company close, in order to minimize
   transportation and fixed costs?

   Based on an example from Frontline Systems:
   http://www.solver.com/disfacility.htm
   Used with permission.
 */

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "gurobi_c.h"


#define opencol(p)         p
#define transportcol(w,p)  nPlants*(w+1)+p
#define MAXSTR             128

int
main(int   argc,
     char *argv[])
{
  GRBenv   *env   = NULL;
  GRBmodel *model = NULL;
  int       error = 0;
  int       p, w, col;
  int      *cbeg = NULL;
  int      *cind = NULL;
  int       idx, rowct;
  double   *cval = NULL;
  double   *rhs = NULL;
  char     *sense = NULL;
  char     vname[MAXSTR];
  int      cnamect = 0;
  char   **cname = NULL;
  double   maxFixed = -GRB_INFINITY, sol, obj;

  /* Number of plants and warehouses */
  const int nPlants = 5;
  const int nWarehouses = 4;

  /* Warehouse demand in thousands of units */
  double Demand[] = { 15, 18, 14, 20 };

  /* Plant capacity in thousands of units */
  double Capacity[] = { 20, 22, 17, 19, 18 };

  /* Fixed costs for each plant */
  double FixedCosts[] =
    { 12000, 15000, 17000, 13000, 16000 };

  /* Transportation costs per thousand units */
  double TransCosts[4][5] = {
                              { 4000, 2000, 3000, 2500, 4500 },
                              { 2500, 2600, 3400, 3000, 4000 },
                              { 1200, 1800, 2600, 4100, 3000 },
                              { 2200, 2600, 3100, 3700, 3200 }
                            };

  /* Create environment */
  error = GRBloadenv(&env, "facility.log");
  if (error) goto QUIT;

  /* Create initial model */
  error = GRBnewmodel(env, &model, "facility", nPlants * (nWarehouses + 1),
                      NULL, NULL, NULL, NULL, NULL);
  if (error) goto QUIT;

  /* Initialize decision variables for plant open variables */
  for (p = 0; p < nPlants; ++p)
  {
    col = opencol(p);
    error = GRBsetcharattrelement(model, "VType", col, GRB_BINARY);
    if (error) goto QUIT;
    error = GRBsetdblattrelement(model, "Obj", col, FixedCosts[p]);
    if (error) goto QUIT;
    sprintf(vname, "Open%i", p);
    error = GRBsetstrattrelement(model, "VarName", col, vname);
    if (error) goto QUIT;
  }

  /* Initialize decision variables for transportation decision variables:
     how much to transport from a plant p to a warehouse w */
  for (w = 0; w < nWarehouses; ++w)
  {
    for (p = 0; p < nPlants; ++p)
    {
      col = transportcol(w, p);
      error = GRBsetdblattrelement(model, "Obj", col, TransCosts[w][p]);
      if (error) goto QUIT;
      sprintf(vname, "Trans%i.%i", p, w);
      error = GRBsetstrattrelement(model, "VarName", col, vname);
      if (error) goto QUIT;
    }
  }

  /* The objective is to minimize the total fixed and variable costs */
  error = GRBsetintattr(model, "ModelSense", GRB_MINIMIZE);
  if (error) goto QUIT;

  /* Make space for constraint data */
  rowct = (nPlants > nWarehouses) ? nPlants : nWarehouses;
  cbeg = malloc(sizeof(int) * rowct);
  if (!cbeg) goto QUIT;
  cind = malloc(sizeof(int) * (nPlants * (nWarehouses + 1)));
  if (!cind) goto QUIT;
  cval = malloc(sizeof(double) * (nPlants * (nWarehouses + 1)));
  if (!cval) goto QUIT;
  rhs = malloc(sizeof(double) * rowct);
  if (!rhs) goto QUIT;
  sense = malloc(sizeof(char) * rowct);
  if (!sense) goto QUIT;
  cname = calloc(rowct, sizeof(char*));
  if (!cname) goto QUIT;

  /* Production constraints
     Note that the limit sets the production to zero if
     the plant is closed */
  idx = 0;
  for (p = 0; p < nPlants; ++p)
  {
    cbeg[p] = idx;
    rhs[p] = 0.0;
    sense[p] = GRB_LESS_EQUAL;
    cname[p] = malloc(sizeof(char) * MAXSTR);
    if (!cname[p]) goto QUIT;
    cnamect++;
    sprintf(cname[p], "Capacity%i", p);
    for (w = 0; w < nWarehouses; ++w)
    {
      cind[idx] = transportcol(w, p);
      cval[idx++] = 1.0;
    }
    cind[idx] = opencol(p);
    cval[idx++] = -Capacity[p];
  }
  error = GRBaddconstrs(model, nPlants, idx, cbeg, cind, cval, sense,
                        rhs, cname);
  if (error) goto QUIT;

  /* Demand constraints */
  idx = 0;
  for (w = 0; w < nWarehouses; ++w)
  {
    cbeg[w] = idx;
    sense[w] = GRB_EQUAL;
    sprintf(cname[w], "Demand%i", w);
    for (p = 0; p < nPlants; ++p)
    {
      cind[idx] = transportcol(w, p);
      cval[idx++] = 1.0;
    }
  }
  error = GRBaddconstrs(model, nWarehouses, idx, cbeg, cind, cval, sense,
                        Demand, cname);
  if (error) goto QUIT;

  /* Guess at the starting point: close the plant with the highest
     fixed costs; open all others */

  /* First, open all plants */
  for (p = 0; p < nPlants; ++p)
  {
    error = GRBsetdblattrelement(model, "Start", opencol(p), 1.0);
    if (error) goto QUIT;
  }

  /* Now close the plant with the highest fixed cost */
  printf("Initial guess:\n");
  for (p = 0; p < nPlants; ++p)
  {
    if (FixedCosts[p] > maxFixed)
    {
      maxFixed = FixedCosts[p];
    }
  }
  for (p = 0; p < nPlants; ++p)
  {
    if (FixedCosts[p] == maxFixed)
    {
      error = GRBsetdblattrelement(model, "Start", opencol(p), 0.0);
      if (error) goto QUIT;
      printf("Closing plant %i\n\n", p);
      break;
    }
  }

  /* Use barrier to solve root relaxation */
  error = GRBsetintparam(GRBgetenv(model),
                         GRB_INT_PAR_METHOD,
                         GRB_METHOD_BARRIER);
  if (error) goto QUIT;

  /* Solve */
  error = GRBoptimize(model);
  if (error) goto QUIT;

  /* Print solution */
  error = GRBgetdblattr(model, "ObjVal", &obj);
  if (error) goto QUIT;
  printf("\nTOTAL COSTS: %f\n", obj);
  printf("SOLUTION:\n");
  for (p = 0; p < nPlants; ++p)
  {
    error = GRBgetdblattrelement(model, "X", opencol(p), &sol);
    if (error) goto QUIT;
    if (sol > 0.99)
    {
      printf("Plant %i open:\n", p);
      for (w = 0; w < nWarehouses; ++w)
      {
        error = GRBgetdblattrelement(model, "X", transportcol(w, p), &sol);
        if (error) goto QUIT;
        if (sol > 0.0001)
        {
          printf("  Transport %f units to warehouse %i\n", sol, w);
        }
      }
    }
    else
    {
      printf("Plant %i closed!\n", p);
    }
  }


QUIT:

  /* Error reporting */

  if (error)
  {
    printf("ERROR: %s\n", GRBgeterrormsg(env));
    exit(1);
  }

  /* Free data */

  free(cbeg);
  free(cind);
  free(cval);
  free(rhs);
  free(sense);
  for (p = 0; p < cnamect; ++p) {
    free(cname[p]);
  }
  free(cname);

  /* Free model */

  GRBfreemodel(model);

  /* Free environment */

  GRBfreeenv(env);

  return 0;
}

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search