[Help-glpk] Re: Simplex method infeasible, IP method feasible

[Andrew Makhorin]

Which version of glpk are you using? The matter is that in 4.0 there
was some defect due to which the simplex solver sometimes erroneously
reported that the problem had no feasible solution while it had. The
error appeared when some non-basic variables have large bounds that is
just as in your example. For this reason a routine that implements the
phase I was replaced in 4.1 by new one which is much more robust and
numerically stable. I tried your example with 4.1. So, if you are using
glpk 4.0, you need to upgrade it; please see:
http://mail.gnu.org/archive/html/help-glpk/2003-08/msg00028.html