Foxconn Technology Group, a Chinese conglomerate of manufacturers, has been Apple’s choice for building its popular Macs and iDevices for a while. But recently, Foxconn’s flagship unit, Hon Hai, has started to face a number of problems – many of which are a direct result of the high demand and low yield that always comes from a new Apple product announcement.

Foxconn chairman Terry Gou told reporters at a business forum today that demand for the iPhone 5 is exceeding demand, just like previous models. “”It’s not easy to make the iPhones,” said Gou. “We are falling short of meeting the huge demand.”

Eventually, like older iPhone models, production will meet demand – but it’ll likely be a while before that happens.

Reporters asked the chairman if Foxconn International Holdings, another unit held by parent company Foxconn, had taken on some production to help alleviate the now 3-4 week shipping times, but he didn’t comment on the matter.

If you preordered an iPhone 5, have you gotten it yet? If yours hasn’t arrived, how much longer will you be waiting?