> But it's tricky to understand and implement and it struggles with real life constraints. i.e. This whole specialty just for integers.
Integers are actually harder to deal with than rational numbers in linear programming. Many solvers can also deal with a mixed problem that has both rational and integer variables.
Monte Carlo simulations are an entirely different beast. (Though you probably mean simulated annealing? But that's close enough, I guess. Linear programming is an optimization technique. Monte Carlo by itself doesn't have anything to do with optimization.)
One problem with these other approaches is that you get some answer, but you don't know how good it is. Linear programming solvers either give you the exact answer, or otherwise they can give you a provable upper bound estimate of how far away from the optimal answer you are.
Integers are actually harder to deal with than rational numbers in linear programming. Many solvers can also deal with a mixed problem that has both rational and integer variables.
Monte Carlo simulations are an entirely different beast. (Though you probably mean simulated annealing? But that's close enough, I guess. Linear programming is an optimization technique. Monte Carlo by itself doesn't have anything to do with optimization.)
One problem with these other approaches is that you get some answer, but you don't know how good it is. Linear programming solvers either give you the exact answer, or otherwise they can give you a provable upper bound estimate of how far away from the optimal answer you are.