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## Re: [Help-glpk] MIP Problem

 From: Andrew Makhorin Subject: Re: [Help-glpk] MIP Problem Date: Tue, 13 Oct 2009 04:32:21 +0400

```> I'm trying to solve this simple problem:

> \* Problem: Unknown *\

> Maximize
>   obj: + 0.8 Z.1 + 0.2 Z.2

> Subject To
>   r.1: - Z.1 + U.1 <= 0.1
>   r.2: - Z.1 + U.1 >= -0.1
>   r.3: + Z.1 + U.1 <= 1
>   r.4: + Z.1 + U.1 >= 0.7
>   r.5: - Z.2 + U.1 <= 0.5
>   r.6: - Z.2 + U.1 >= 0.125
>   r.7: + Z.2 + U.1 <= 0.75
>   r.8: + Z.2 + U.1 >= 0.34

> Bounds
>   0 <= Z.1 <= 1
>   0 <= Z.2 <= 1
>   0 <= U.1 <= 1

> Generals
>   Z.1
>   Z.2
>   U.1

> End

> If I try to solve it from a C program using the simplex method it
> finds this solution:

> Z.1 = 0.55
> Z.2 = 0.3
> U.1 = 0.388977

> But if I try to solve it using the command:

> glpsol --simplex --cpxlp program_name.txt

> it says:

> glp_read_lp: 8 rows, 3 columns, 16 non-zeros
> glp_read_lp: 3 integer columns, all of which are binary
> ipp_basic_tech:  0 row(s) and 0 column(s) removed
> PROBLEM HAS NO PRIMAL FEASIBLE SOLUTION
> Time used:   0.0 secs
> Memory used: 0.0 Mb (35140 bytes)

> It says that the variable are integer but they should not be integer.

> Anyone could help me? What's wrong with it?

Nothing is wrong. Your instance is mip, because it has integer
variables defined in the section 'Generals'. The simplex solver,
glp_simplex, ignores integrality conditions and, thus, finds
optimal solution to lp relaxation. However, glpsol solves your
instance as mip and reports that it has no integer feasible points.

```