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## Re: [Help-glpk] Upper bound problem

 From: Andrew Makhorin Subject: Re: [Help-glpk] Upper bound problem Date: Mon, 16 Apr 2012 08:09:14 +0400

```> First of all, excuse my bad english. Im new at mathprog and trying to
> model some problem i get as output some strange thing:
>
>    No.   Row name        Activity     Lower bound   Upper bound
> ------ ------------    ------------- ------------- -------------
>     .....
>     .....
>
>      7 constraint
>                                    0                          -0
>      8 constraint
>                                    0                          -0
>      9 constraint
>                                   -3                          -0
>     10 constraint
>                                   -2                          -0
>
> I dont get why those values happen at this constraint, because neither
> of the variables or values are negative in the first place. The
> constraint is defined as follow:
>
> s.t. constraint{j in 1..n}: sum{i in 1..m} d[i,j] <= m * y[j];
>
> Where m is a param defined in the data, positive integer, y is a
> binary variable and d[i,j] are real variables between 0 and 1
> (0<=d<=1)
>
> Any help would be greatly appreciated!! thanks in advance

By definition (in MathProg) the auxiliary variable for a row
(constraint) is always the difference between left-hand and right-hand
linear forms of the constraint. Thus, in your case

constraint[j] = sum{i in 1..m} d[i,j] - m * y[j] <= 0.

Since the solution found is primal feasible, in the row section you see
non-positive values (activities) of auxiliary variables 'constraint[j]'.
For more details please see the MathProg language reference, Subsection
4.4 "Constraint statement".

```