Short answer: Board of Governors of the Federal Reserve System conducts annual estimates on net demand for U.S. banknotes (per denomination) from domestic and international institutions for the next fiscal year (while factoring in destruction rates and historical payments to and receipts from circulation).  The resulting order would then be sent to the U.S. Bureau of Engraving and Printing for production.

The full story: I forwarded this question to a Bureau of Engraving and Printing official.  The BEP official suggested us to first look at the bureau’s annual production data:

2010-2015 production data by denomination (I ported BEP data into a chart for better readability and added Federal Reserve’s 2015 data)

The annual production volume is a floating target.  The official clarified that its banknote production (at the denomination level) are based on requests from the Board of Governors of the Federal Reserve System

The BEP prints currency based on requests from the Board of Governors of the Federal Reserve System (Federal Reserve).  The Federal Reserve is responsible for placing currency into circulation and for removing it from circulation.

The Federal Reserve’s 2016 Banknote Print Order

The Federal Reserve further clarified its method in estimating the number of banknotes to order from the BEP for the next fiscal year (2016):

Currency Print Orders (2015 data: Currency Print Orders)

The Board of Governors (the Board), as the issuing authority for Federal Reserve notes, approved and submitted its fiscal year (FY) 2016 order for nearly 7.6 billion Federal Reserve notes, valued at $213.3 billion, to the U.S. Treasury Department’s Bureau of Engraving and Printing (BEP) on July 24, 2015

The nearly 7.6 billion notes included in the FY 2016 order reflect the Board’s estimate of net demand for currency from domestic and international customers. The print order is determined by denomination and is based on destruction rates and historical payments to and receipts from circulation. Historically, the majority of the notes that the Board orders each year replace unfit currency that Reserve Banks receive from circulation.  The estimated number of notes that Reserve Banks will destroy accounts for about 70 percent of the proposed FY 2016 print order and includes both unfit currency, as well as all old-designs of some denominations received from circulation.  The expected growth of Reserve Bank net payments (payments less receipts) to circulation and inventory management adjustments account for the remainder of the notes in the FY 2016 print order. The table below reflects the denominational breakdown of the Board’s FY 2016 order.

2016 Federal Reserve Note Print Order: