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Probably most public libraries operate at least from of EDI. It may just be one (eg electronic orders) type of EDI transaction. It's probably true to say that the real economies come from operating all or most EDI transcations--including EDI invoicing.

An overview of the standards employed in libraries is
"BIC EDI Standards and Implementation Guidelines Library Supply OVERVIEW
EDI standard in UK Library supply" BIC January 2008
http://www.bic.org.uk/files/pdfs/080115%20library%20supply%20overview%20draft%203.pdf