[7thaccount]

The vast majority of the United States power grid (many thousands of power plants) are optimized in auctions every hour for the next day and every 5 minutes on the operating day. Finding the globally optimal solution is pretty important for both fairness and not wasting billions of dollars each year. I'd agree with you for a lot of problems though, but keep in mind there are plenty where they need full optimality or within a tiny percentage from it.

[raverbashing]

Yes and your very complex linear branch and bound solution won't run in 5 min.

That's what I'm getting at