Hello everyone!
Is it possible to obtain all extreme directions of a Linear Program in GAMS by using any of its solvers?
Best wishes.
This is possible only for toy problems. GAMS and its solver farm is for large scale optimization, so no luck. For a MIP though you can produce all feasible solutions, see e.g. https://www.gams.com/latest/docs/S_CPLEX.html#CPLEX_ENUMERATING_ALL_SOLUTIONS (still might take a very very long time). There is great academic software to analyze the underlying polyhedron of an LP, see e.g. https://polymake.org/doku.php.
Good luck,
-Michael