According to the Financial Times, demand for Samsung's new Note 7 smartphone (launched just last week) is very strong - to the point that Samsung cannot supply enough phones and it had to delay the launch in some markets.
The Note 7, Samsung's flagship large smartphone (phablet), uses a 5.7" 2560x1440 (518ppi) flexible Super AMOLED dual-edge display. The FT quotes an analyst from Macquarie saying that the major production obstacle is at SDC, specifically "applying a new touch technology to plastic OLED screens".
It may simply be that SDC cannot produce enough flexible OLEDs. SDC currently produces most of its flexible OLEDs at its A3 line, which has a monthly capacity of 15,000 substrates (Gen-6) - this is enough for abound 9 million flexible OLEDs each month. Of course larger display size means less panels per month. SDC also operates the smaller (Gen-5.5) A2 pilot flexible OLED line with a monthly capacity of 8,000 substrates.
According to a report from March, SDC decided to double the capacity of its A3 flexible OLED line to 30,000 monthly substrates in a $325 million investment. Samsung hopes the new capacity will be ready by early 2017.
According to a new article at the Korea Herald, Samsung currently makes 40,000 flexible OLED substrates each month - and it is set to triple to 120,000 monthly substrates. This seems overly optimistic - perhaps the Korea Herald is looking several years into the future and already count the current expansion plan into account with the 40,000 monthly substrates (A3 stage 1 + A3 stage 2 + A2).
Of course Samsung needs to quickly increase its capacity as demand for its own flexible OLED phones is rising, Chinese phone makers are also buying flexible OLEDs, and of course there are many reports that Apple wants to use a flexible OLED in future iPhones.