Performance Difference between LP and MIP with fixed integer variables

GAMS
1

Hello GAMS experts!

I have a general and probably stupid question. I’m using GAMS/CPLEX. I’m wondering if there is any performance difference between “modeling the problem as an LP with all integer variables fixed as known parameter inputs” and “modeling the problem as an MIP with integers fixed using the following syntax”

binvar1.fx = 1

I guess they should have very similar performance even in large-scale problems? I’d appreciate if anyone with such an experience could enlighten me. Thanks!

Best,
Gabriel

2

Usually, there shouldn’t be a big difference in performance. But I guess in some corner cases solver behavior might be different. Fixing a variable means setting upper and lower bound to the same value. But it is still a variable and feasibility and integrality may be violated within the tolerances. If you set holdfixed=1, fixed variables will be truly treated as constants and are not passed to the solver.

I hope this helps!

Fred