[Help-glpk] need help to understand why glpk cant solve my problem

[olf]

First of all I would just like to say hello too you all and I hope I wont
make a complete fool out of myself for writing this :)

I am trying to solve a train dispatching problem.
I have a graph with 54 nodes and I want two trains to travel from
different starting nodes and switch places. So basically I want train a to
go from node i to node j and I want train b to go from node j to node i.
I have set up a simple mathematical model to avoid collisions between the
trains.

The error message I get from running this is the following:

spx_invert: the basis matrix is singular
spx_simplex: numerical problems with basis matrix
spx_simplex: sorry, basis recovery not implemented yet
mip_driver: cannot solve current LP relaxation
lpx_integer: cannot solve current LP relaxation

Now this is a fairly big problem and I am not sure glpk can solve it at all.
So I am mostly trying to understand _why_ it cant solve it.
My guess is that it just is to big, but I wanted to make sure that that is
the case and I hope maybe one of you could confirm it or explain it to me.

If you want the acctual data and model files just say so and I will supply
them.

Best regards

/Olle Claeson