Yes, that's right. NP-hard doesn't mean intractable in general, though it has acquired that reputation among computer types. Large mixed-integer programming pro

Yes, that's right. NP-hard doesn't mean intractable in general, though it has acquired that reputation among computer types. Large mixed-integer programming programs (millions of variables) are routinely solved in reasonable times (seconds to less than an hour). Sure, full or brute-force enumeration algorithms makes you hit the worst case complexity every time. However, most commercial mixed integer solvers don't use brute-force enumeration. Instead they pre-analyze the problem, and then employ a boatload of mathematical techniques--including heuristics--which exploit problem structure and prune off non-solutions and helps the solver reach a solution fairly quickly on average. (luck is involved, of course)