Is it possible to create a Wither Boss Farm in Vanilla Minecraft

Is it possible to create a Wither Boss Farm? I am in need of many Nether Stars. I have stockpiled a stack of Wither Skulls so I can create them, I just don't want to have to do all the work. I would rather sit back AFK while it goes through the lot.

Is there a way to automate the placing and killing of Withers of this scale? hopefully with a hopper collection solution to collect the Stars so they don't de-spawn. I know how to kill one, but it takes manual input to reset and start the killing process, and I want this to be automated.

Wither skulls can be automatically placed using a dispenser:

Unfortunately, there is no way to automatically place or generate soulsand. The best you can do is have a stockpile pushed in with pistons.

You'll then need another dispenser to drop water onto the wither so that the explosions do not damage anything, and finally some sort of killing device. The best way to do this is have pistons push the wither up into the roof of the nether, suffocating it.

Also remember to have some hoppers or hopper minecarts below to pick up the star.

Hook it all up with a timer so that:

1. Soulsand is pushed in
2. Dispensers place wither skulls
3. Dispenser places water
4. Wither explodes
5. Wither is killed
6. Water is picked back up
7. Repeat