Re: [Help-glpk] [Fwd: variables with disjoint bounds]

[Kevin Hunter Kesling]

At 12:38am -0500 Fri, 15 Nov 2013, Kevin Hunter Kesling wrote:
> At 4:18pm -0500 Thu, 14 Nov 2013, Joseph Mundy wrote:
> > It is possible in glpk to represent variables with multiple bounds
> > that are disjoint? For example,
> >
> > 1<= x <=2 or 5<=x<=7. It seems that two different linear programs
> > must be formulated.
>
> Yes, it is generally possible.  Consider:
>
>      1 * b       <= x <= 2*b
>      5 * (1 - b) <= x <= 7 * (1 - b)
>
> where 'b' is a binary variable.  I don't know if GLPK supports
> multiple bounds directly on variables, but you can certainly
> incorporate the disjointness as standard constraints.

Ah crap.  That's embarrassing.  It's late, and I'm clearly beyond my 
useful hours.  That's not going to work, as x would have to be 0 to 
simultaneously satisfy both of those.  Consider instead:

    5*b + 1*(1-b) <= x <= 7*b + 2*(1-b)

You can still incorporate as constraints, however.

Kevin