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### diet_c.c

/* Copyright 2019, Gurobi Optimization, LLC */

/* Solve the classic diet model, showing how to add constraints
to an existing model. */

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

int printSolution(GRBmodel* model, int nCategories, int nFoods);

int
main(int   argc,
char *argv[])
{
GRBenv   *env   = NULL;
GRBmodel *model = NULL;
int       error = 0;
int       i, j;
int      *cbeg, *cind, idx;
double   *cval, *rhs;
char     *sense;

/* Nutrition guidelines, based on
USDA Dietary Guidelines for Americans, 2005
http://www.health.gov/DietaryGuidelines/dga2005/ */

const int nCategories = 4;
char *Categories[] =
{ "calories", "protein", "fat", "sodium" };
double minNutrition[] = { 1800, 91, 0, 0 };
double maxNutrition[] = { 2200, GRB_INFINITY, 65, 1779 };

/* Set of foods */
const int nFoods = 9;
char* Foods[] =
{ "hamburger", "chicken", "hot dog", "fries",
"macaroni", "pizza", "salad", "milk", "ice cream" };
double cost[] =
{ 2.49, 2.89, 1.50, 1.89, 2.09, 1.99, 2.49, 0.89, 1.59 };

/* Nutrition values for the foods */
double nutritionValues[][4] = {
{ 410, 24, 26, 730 },
{ 420, 32, 10, 1190 },
{ 560, 20, 32, 1800 },
{ 380, 4, 19, 270 },
{ 320, 12, 10, 930 },
{ 320, 15, 12, 820 },
{ 320, 31, 12, 1230 },
{ 100, 8, 2.5, 125 },
{ 330, 8, 10, 180 }
};

/* Create environment */
if (error) goto QUIT;

/* Create initial model */
error = GRBnewmodel(env, &model, "diet", nFoods + nCategories,
NULL, NULL, NULL, NULL, NULL);
if (error) goto QUIT;

/* Initialize decision variables for the foods to buy */
for (j = 0; j < nFoods; ++j)
{
error = GRBsetdblattrelement(model, "Obj", j, cost[j]);
if (error) goto QUIT;
error = GRBsetstrattrelement(model, "VarName", j, Foods[j]);
if (error) goto QUIT;
}

/* Initialize decision variables for the nutrition information,
which we limit via bounds */
for (j = 0; j < nCategories; ++j)
{
error = GRBsetdblattrelement(model, "LB", j + nFoods, minNutrition[j]);
if (error) goto QUIT;
error = GRBsetdblattrelement(model, "UB", j + nFoods, maxNutrition[j]);
if (error) goto QUIT;
error = GRBsetstrattrelement(model, "VarName", j + nFoods, Categories[j]);
if (error) goto QUIT;
}

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

/* Nutrition constraints */
cbeg = malloc(sizeof(int) * nCategories);
if (!cbeg) goto QUIT;
cind = malloc(sizeof(int) * nCategories * (nFoods + 1));
if (!cind) goto QUIT;
cval = malloc(sizeof(double) * nCategories * (nFoods + 1));
if (!cval) goto QUIT;
rhs = malloc(sizeof(double) * nCategories);
if (!rhs) goto QUIT;
sense = malloc(sizeof(char) * nCategories);
if (!sense) goto QUIT;
idx = 0;
for (i = 0; i < nCategories; ++i)
{
cbeg[i] = idx;
rhs[i] = 0.0;
sense[i] = GRB_EQUAL;
for (j = 0; j < nFoods; ++j)
{
cind[idx] = j;
cval[idx++] = nutritionValues[j][i];
}
cind[idx] = nFoods + i;
cval[idx++] = -1.0;
}

error = GRBaddconstrs(model, nCategories, idx, cbeg, cind, cval, sense,
rhs, Categories);
if (error) goto QUIT;

/* Solve */
error = GRBoptimize(model);
if (error) goto QUIT;
error = printSolution(model, nCategories, nFoods);
if (error) goto QUIT;

printf("\nAdding constraint: at most 6 servings of dairy\n");
cind[0] = 7;
cval[0] = 1.0;
cind[1] = 8;
cval[1] = 1.0;
error = GRBaddconstr(model, 2, cind, cval, GRB_LESS_EQUAL, 6.0,
"limit_dairy");
if (error) goto QUIT;

/* Solve */
error = GRBoptimize(model);
if (error) goto QUIT;
error = printSolution(model, nCategories, nFoods);
if (error) goto QUIT;

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);

/* Free model */

GRBfreemodel(model);

/* Free environment */

GRBfreeenv(env);

return 0;
}

int printSolution(GRBmodel* model, int nCategories, int nFoods)
{
int error, status, i, j;
double obj, x;
char* vname;

error = GRBgetintattr(model, "Status", &status);
if (error) return error;
if (status == GRB_OPTIMAL)
{
error = GRBgetdblattr(model, "ObjVal", &obj);
if (error) return error;
for (j = 0; j < nFoods; ++j)
{
error = GRBgetdblattrelement(model, "X", j, &x);
if (error) return error;
if (x > 0.0001)
{
error = GRBgetstrattrelement(model, "VarName", j, &vname);
if (error) return error;
printf("%s %f\n", vname, x);
}
}
printf("\nNutrition:\n");
for (i = 0; i < nCategories; ++i)
{
error = GRBgetdblattrelement(model, "X", i + nFoods, &x);
if (error) return error;
error = GRBgetstrattrelement(model, "VarName", i + nFoods, &vname);
if (error) return error;
printf("%s %f\n", vname, x);
}
}
else
{
printf("No solution\n");
}

return 0;
}


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