Re: [Help-glpk] Combine linear program

[Andrew Makhorin]

> I would like to know if the following
> problem could be done with GLPK or any software (free) ?

> Let x(i,j) in {0,1} for i in I, and
> j in J, unknown variable
> Let y(i,j) in R, for i in I, j in J,
> unknown variable
> Let a(i,j), l(i,j) and u(i,j) known
> data
> Let K an subset of IxJ, K={(ik,jk)}
>  known

> Problem:

> Min sum( x( i , j ) )
>         subject
> to
>         $
> x( ik , jk )=1                
>               /* some x(i,j)=1, the
> others could be found */
>         $
> max    y( ik , jk ) >= a( ik , jk ) + U*x(ik,jk)
>          
>        subject to
>          
>       linear constraint on y(i,j)
>          
>       a(i,j)-l(i,j)*x(i,j) <= y(i,j) <= a(i,j)+u(i,j)*x(i,j)

You may write your model in GNU MathProg, a modeling language supported
by glpk, and then solve it with glpsol, the glpk stand-alone solver.
For more details please see the glpk documentation included in the
distribution tarball.