Many theater companies ask set (and other) designers on board just as soon as they decide their seasons and choose their directors. A few even choose designers before directors(though I think most directors would prefer the chance to at least cast a veto!). Other theaters wait till late. The worst-case, of course, is waiting till the last minute or past, as when they have to find a late replacement.
Accordingly - since this is April 2012 - I have just picked up two almost-last-minute shows for June... and one for February 2013. Two months away and ten months away.
I'm going to have to buy a new calendar.
Photo courtesy of Photos Public Domain.com