What a Director of Production at a small press does? According to Yanni Kuznia who holds that position at Subterranean Press they do a lot:
My work starts after the publishing arrangements with the author, agent, and/or original publisher (if applicable) have been made. The computer file for the book is sent to me and from there I must: prepare the file for the designer; approve the initial book design, proof the book (either myself or send it to somebody else), find artwork, choose the materials the book will be printed on, and bound in, and send everything off to be printed.
Sometimes I think writing is the easiest gig in publishing. (Except for when it isn’t . . . )