Last time I flew, with SAS from Copenhagen, there was an announcement shortly before boarding that the plane was overbooked, and that they would make a payment to anyone willing to take a later flight. Can't remember off-hand what the payment was, but I think it was something a like a couple of hundred Euros; enough to make the delay worthwhile to anyone not in a rush. Nothing more was mentioned, so presumably this was enough to solve the problem. Sometimes taking a hit like that is the most sensible commercial solution in the longer term.