The first batch shipment depends on how many PS3 slim have been manufactured since begining of July which is allegedly when Sony started the mass production :
http://news.cnet.com/8301-17938_105-10276122-1.html
For PS3 fat the launch consignment was of 4 million units, at a production rate of 200K a month : http://www.gamepro.com/article/news/75068/first-ps3-units-manufactured-this-month/
This time expect the production rate to be at least the double if not more due to several reasons :
- Sony dramatically increased the production of PS3 components in the begining of August
- Back in 2006 there was only one Taiwanese manufacturer, this time there are two
- The slim assembly is probably faster due to the reduction of components compared to 2006 PS3.
- Then they were producing two different models with different features, now there's only one.
- The assembly lines are probably running more smoothly than they were back in 2006
So my guess is that at least 2 to 2.5 million units have already been produced and partly shipped.
