Re: [Help-glpk] Column kind violation in optimal solution

[Andrew Makhorin]

> I print out the solution of my problem and it is like the following

>  No. Column name  St   Activity     Lower bound   Upper bound    Marginal
> ------ ------------ -- ------------- ------------- -------------
> -------------
>      1 z[0][0]      B              0             0             1 
>      2 z[0][1]      NL             0             0             1      
> eps
>      3 z[0][2]      B           0.25             0             1 
>      4 z[0][3]      B           0.75             0             1 
>      5 z[1][0]      NU             1             0             1      
> eps
>      6 z[1][1]      B              0             0             1 
>      7 z[1][2]      NL             0             0             1      
> eps
>     .............
> I have a couple of questions regarding the result.
> 1. What does columns St and Marginal mean?

"St" is the status of auxiliary/structural variable in the basic solution
found: B means "basic", NL means "non-basic, lower bound is active",
NU means "non-basic, upper bound is active". "Marginal" is the reduced
cost of auxiliary/structural variable.

> 2. Activity is the value of the column variable in the optimal solution,
> right?

Yes.

>  But I have set the column kind to be binary variable by
> glp_set_col_kind(lp,Col_Num,GLP_BV);  How can the variables take 0.25 and
> 0.75 in the optimal solution?

The solution you obtained is a basic optimal solution to LP relaxation
of your instance. To obtain an integer optimal solution you should call
glp_intopt immediately after glp_simplex, and then use glp_print_mip
rather than glp_print_sol.