Re[3]: [Help-glpk] LPP & MIP

[Andrew Makhorin]

>Unfortunately, I don't understand why integer row singleton cannot be
>eliminated.  It might (in part) explain why the attached file doesn't work 
>(yet).  (I began to wrote a longer email then I wanted to verify my 
>assumptions then I wrote this piece of code then time goes so fast...)

Not all transformations performed by lpp can be applied to mip. Let, for
example, there be a column singleton, i.e. structural variable x has
non-zero constraint coefficient in the only constraint:

   (...) + a * x = b.        (1)

In this case the term (a * x) can be thought as a slack variable, and
if, say, a > 0 and x >= 0, we may eliminate this term:

   (...) <= b.               (2)

However, if x is of integer kind, such transformation cannot be applied,
because the left-hand side in (2) would be restricted to take on only
the values b (when x is 0), b - a (when x is 1), b - 2*a (when x is 2),
etc., while in lp it can take on any value not greater than b.


Andrew Makhorin