However, it doesn't seem like the pre-processing removes the additional
variables, which I sort of expected/hoped for. My question is really if
the solver does something smart when such equality constaints are present
or if it would be worthwhile to merge the variables, either using a better
model or by pre-processing. I assume that there in general can be
round-off issues when performing this type of variable merging, but maybe
that is tractable.
Currently the glpk mip preprocessor performs only simple
transformations, in particular, it does not eliminate identical variables
defined by equality constraints like x = y.
I am implementing a new, more flexible version of the preprocessor common
for all three solvers (simplex, interior point, and branch-and-cut),
which will include processing such constraints. But I cannot say when
it will appear in glpk.