A situation that often happens to me is that I hire a bunch of staff at once in Theme Hospital either at the start of the hospital or during a major expansion, and from that point on, they all go for their staff breaks en masse as their tiredness values are in sync. This devastates the hospital as they leave many rooms vacant, and further staff rush out of their rooms to replace the missing staff, before rushing back to another room after treating just one or two patients, grinding my hospital to a halt.

In some levels I have the spare cash to just keep loads of spare staff hanging around (which causes the game to nag for having staff doing nothing), but in others that is not an option.

How do I prevent or deal with this kind of situation?