If  you check the box in the shipyard screen to idle, the shipyard will not build anything. This changes if there is a starbase nearby that needs a constructor. 

When I shipyard is idle that production is supposed to go back into the sponsoring planet as social manufacturing. That is what is 'supposed' to happen. I am not sure if this is the case as there have been reports of production not being funneled back to the sponsoring planet when the shipyard is idle. 

the idle button was replaced with Do Not Notify,  production always (as set by the global slider) is going to the yard even it it not building anything so it is  not being funneled back to the sponsoring planet when the shipyard is "idle".  Just confirmed in latest build.  WE NEED the idle button back

I want BOTH the ability to shutdown a shipyard (which allows me to keep the ship queue intact), and the ability to Idle is (after empty queue).

Both are really necessary and used for different reasons, and it's not an "either/or" choice.

And of course, we need to fix the transfer of production to/from military/social, because there's too many places that excess is simply lost and not transferred properly (or, at least, saved)