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### facility_c.c

/* Copyright 2023, 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;
}


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