Hi Luca,
This problem can be solved by inspection. You were given
> minimize { sum[from i=1 to 96] of {c1*x1(i)+c2*x2(i)+c3*x3(i)} }
> with this constraints:
> x1(i)+x2(i)+x3(i)=c4(i)
> x1(i)+x3(i)=c5
> x1>=5
> 0<=x2<=1 binary
> 0<=x3<=1 binary
>
> where x1, x2, x3 and c4 are vectors of 96 elements. c1,c2,c3,c5 are
> contants.
Subtracting the second equality from the first equality gives
x2(i) = c4(i)-c5
which tells us a couple of things. First, because x2(i) is binary, not
every
choice of parameters will lead to a feasible MIP solution. c4(i) must be
either c5 or c5 + 1. The second equality gives
x1(i) = c5 - x3(i) >= 5
which tells us c5 >= 5 for feasible solutions for x1(i), and c5 >= 6 for
nontrivial
solutions for x3(i). Assuming feasibility for x1(i) and x2(i), we can
substitute their solutions into the objective function
obj = C + { sum[from i=1 to 96] of {(c3-c1)*x3(i)} }
where C is a constant that I'm too lazy to write out. So it comes down to
the
values of (c3-c1). Provided c5 >= 6 then x3(i) = - sgn(c3-c1).
If you still want to write a solver for the problem you should be careful
about
handling coefficients.
Jeff
On Fri, Jan 4, 2013 at 6:35 AM, lucacoopers <[email protected]> wrote:
>
> Hi Raniere Silva.
> Thank you so much for your help.
> I need to build the model with the c language without using the mathprog
> and
> standalone solver.
>
> an example of code to resolve a minimization problem that I have is as
> follows:
>
> /* provaglpk.c */
>
> #include <stdio.h>
> #include <stdlib.h>
> #include <glpk.h>
>
> int main(void)
> { glp_prob *lp;
> int ia[1+1000], ja[1+1000];
> double x3, x6;
> double ar[1+1000], z, x1, x2, x4, x5;
> lp = glp_create_prob();
> glp_set_prob_name(lp, "provaglpk");
> glp_set_obj_dir(lp, GLP_MIN);
> glp_add_rows(lp, 1);
> glp_set_row_name(lp, 1, "p");
> glp_set_row_bnds(lp, 1, GLP_FX, 600, 0.0);
> glp_add_cols(lp, 6);
> glp_set_col_name(lp, 1, "x1");
> glp_set_col_bnds(lp, 1, GLP_DB, 0, 240);
> glp_set_obj_coef(lp, 1, 0.18);
> glp_set_col_name(lp, 2, "x2");
> glp_set_col_bnds(lp, 2, GLP_DB, 0, 480);
> glp_set_obj_coef(lp, 2, 0.17);
>
> glp_set_col_name(lp, 3, "x3");
> glp_set_col_bnds(lp, 3, GLP_DB, 0.0, 1.0);
> glp_set_col_kind(lp, 3, GLP_IV);
> glp_set_obj_coef(lp, 3, 0.2);
>
> glp_set_col_name(lp, 4, "x4");
> glp_set_col_bnds(lp, 4, GLP_DB, 0, 240);
> glp_set_obj_coef(lp, 4, 0.18);
> glp_set_col_name(lp, 5, "x5");
> glp_set_col_bnds(lp, 5, GLP_DB, 0, 480);
> glp_set_obj_coef(lp, 5, 0.17);
> glp_set_col_name(lp, 6, "x6");
> glp_set_col_bnds(lp, 6, GLP_DB, 0, 1);
> glp_set_col_kind(lp, 6, GLP_BV);
> glp_set_obj_coef(lp, 6, 0.2);
> ia[1] = 1, ja[1] = 1, ar[1] = 1.0;
> ia[2] = 1, ja[2] = 2, ar[2] = 1.0;
> ia[3] = 1, ja[3] = 3, ar[3] = 48;
> ia[4] = 1, ja[4] = 4, ar[4] = 1;
> ia[5] = 1, ja[5] = 5, ar[5] = 1;
> ia[6] = 1, ja[6] = 6, ar[6] = 48;
> glp_load_matrix(lp, 6, ia, ja, ar);
> int status;
> status = glp_simplex(lp, NULL);
> status = glp_intopt(lp, NULL);
> z = glp_get_obj_val(lp);
> x1 = glp_mip_col_val(lp, 1);
> x2 = glp_mip_col_val(lp, 2);
> x3 = glp_mip_col_val(lp, 3);
> x4 = glp_mip_col_val(lp, 4);
> x5 = glp_mip_col_val(lp, 5);
> x6 = glp_mip_col_val(lp, 6);
> printf("\nz = %f; x1 = %f; x2 = %f; x3 = %f; x4 = %f; x5 = %f; x6 =
> %f\n",z, x1, x2, x3, x4, x5 ,x6);
> glp_delete_prob(lp);
> system("pause");
> return 0;
> }
> /* eof */
>
> Tihs is a more complex problem.
>
> The solution that i need is like this.
>
> Do you help me?
>
> Thanks again! =)
> --
> View this message in context:
> http://old.nabble.com/Help%3A-How-to-build-MIP-model-tp34858053p34858521.html
> Sent from the Gnu - GLPK - Help mailing list archive at Nabble.com.
>
>
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