The Problem is a min-cost 2 layer network dimensioning with
* finite sets of node types, link interface cards, and link capacities
* some existing (zero-cost) hardware components
* unsplittable flow routing in second layer
* origianal network data from X-WiN planning (DFN Verein)
The LP contains
* binary variables for node types, link interface cards, and link capacities
* hardware compatibility constraints
* capacity constraints
* rank inequalities for unsplittable shortest path routings
* cost for new hardware
* binary variables for few end-to-end routing paths for few demands
Comment from Tobias Achterberg:
The two files "bley_xs1.lp.gz" and "bley_xs2.lp.gz" contain unrestricted integer
variables and big-M coefficients with M = 1e+20. However, these issues can
be "easily" resolved by one of the following approaches:
1. There is a feasible solution (for "bley_xs1.lp.gz") with the integer variables
all being smaller or equal to 32. Because they massively influence the objective
function, it should be safe to install upper bounds with a value of 100.
Afterwards, the preprocessor of the MIP solver should be able to reduce all the
big-M's to 100. I posted a new model called "bley_xs1noM.lp.gz" where I introduced
upper bounds of 100 to the integer variables. However, the 1e+20's are still
present in the model.
2. All the rows with the big-M's of 1e+20 are redundant (at least in the
"bley_xs1.lp.gz" I looked at). For each row, e.g.,
c527: 1e+20 x1034 + 1e+20 x1035 - x1050 + 1e+20 x3118 + 1e+20 x3119 >= 0
there is a global lower bound of the binaries, e.g.,
c548: x1034 + x1035 + x3118 + x3119 >= 1
that makes the big-M row redundant (at least if we treat 1e+20 as infinity).
However, neither CPLEX10.0 nor SCIP preprocessing found that redundancy.
Nevertheless, these rows don't seem to be a problem for the two solvers.
You may want to remove the big-M rows manually from the model.