Right, ILP is a great tool for solving NP-complete problems relatively fast (depending on the solver, but there are some very good ones out there). However, as

Right, ILP is a great tool for solving NP-complete problems relatively fast (depending on the solver, but there are some very good ones out there). However, as a theoretical tool it probably is not that exciting unless you're ready to tackle P vs. NP this way. (Unless you move to semidefinite programming and the SDP hierarchies, where the progress is very exciting but not yet that applicable to scheduling, to the best of my knowledge.) > With a large, fairly homogenous environment it didn't outperform random assignment that well, though. It worked best with small, inhomogeneous loads. Yes, that's probably a piece of the puzzle that I don't have yet -- to know a theoretical model that is both useful in practice and at the same time greedy/randomized assignment is not "good enough" for practical uses.