The main arc in Monsters, Inc. is that there is a scream shortage/energy crisis. However, there doesn't appear to be any night shift. All the scenes that happen later on at night seem to be "after everyone has gone home", the hallways are dark and there's no one around, really.
At the start of the Scare Floor scene we see Jerry say "Okay, people, Eastern Seaboard coming online." and a map of the world indicating what part they are working in. This means they're aware of the world as a whole and the time zones to know when kids go to sleep across them.
On top of that there are multiple Scare Floors as indicated by Mr Waternoose after the 23-19!
Mr Waternoose: An entire scare floor out of commission. What else could go wrong?
With all of this together (multiple Scare Floors, energy crisis, knowing the world) why is there no night shift? Surely the extra hours worked collecting scream would help solve the energy crisis?
For what it's worth, I don't think there's a shortage of scarers or monsters that want to be scarers. The problem appears to be a shortage of good scarers so even there more monsters working the night shift would probably help with the energy crisis a lot.