Kitamura and Stoye (2014) develop a nonparametric test for linear inequality constraints, when these are are represented as vertices of a polyhedron instead of its faces. They implement this test for an application to nonparametric tests of Random Utility Models. As they note in their paper, testing such models is computationally challenging. In this paper, we develop and implement more efficient algorithms, based on column generation, to carry out the test. These improved algorithms allow us to tackle larger datasets.