A good manager doesn't try to eliminate conflict; he tries to keep it from wasting the energies of his people. If you're the boss and your people fight you openly when they think that you are wrong -- that's healthy.
If you don't do it with excellence, don't do it at all! Because if it's not excellent, it won't be profitable or fun, and if you're not in business for fun or profit, what the hell are you doing there?
Compromise is usually bad. It should be a last resort. If two departments or divisions have a problem they can't solve and it comes up to you, listen to both sides and then pick one or the other. This places solid accountability on the winner to make it work. Condition your people to avoid compromise.