I once worked for a hospital that utilized mandatory OT.... It was a VERY common thing to use, and the newest employee always was the one picked. There were several times that I was mandated to work a total of 17 hours and had to return for my next shift 7 hours later. There were no deals, no days off in return, NOTHING. It really took a toll on me and my loved ones. They even tried to mandate me on my last evening shift! Fortunately I had enough common sense to relize that as of midnight I was no longer an employee! The nursing supervisor checked and found out that I was correct.
In my experience, if people are given a choice, they are more apt to pick up extra time....instead of being TOLD that they have to.