The Duty Officer System (Doff system), much like the admiralty system, offers you some unique rewards in game.
Below you will find a number of resources to offer insight for the starting player as well as for the more skilled player. Build your Duty Officer reserves, get the purple officers needed for your Bridge positions, and rake in the Dilithium rewards and energy credits.
To start, I would suggest you take a look at Doffaholic. It's a great guide for beginners and advanced Doff collectors. Almost every basic system of Duty Officers from collection & development to duty officer missions are reviewed in easy to understand terms. https://www.reddit.com/r/sto/wiki/advanced_doffing
For the more experienced Doff Slingers, hopefully some of the following references are of aid.
Should you identify a very specific Duty Officer you need to acquire, the following tool may be of help. http://thephoenixdivision.com/doffs.html
For those who wish to take DOFF's to the next level, there is doffTreckker 3.0. This is a downloadable spreadsheet / program (fuzzy on this) on googledocs. This program claims to be integrated and automatic. It's used to track multiple characters and track timers so you know when to restart a mission. It alleges that it will track all your doffs automatically. Should you try this out, I would love to hear your experiences as I have yet to try it myself. https://docs.google.com/spreadsheets/d/1IdSGB9vsHOzeAzTx4LGX1hKfd3WAW1tPOKDSznsSrbI/edit?pref=2&pli=1#gid=61
Some generalizations I encountered:
It is said that it is best to farm for Doffs+Dil on the FED side, Contraband+Dil on the KDF side. I agree contraband is easier on KDF side, but the Alpha Quadrant offers many opportunities for both parties to upgrade duty officers without using refugees (once mission chains “Diplomatic” are done).
On the KDF side, No crits are needed to get Contraband. Almost any Marauder mission with "Raid", "Pillage" or "Plunder" will do. (The Vulcan ships never have Contraband !).
Also for KDF the hard part is getting Refugees as they don't drop from the colonization chains it seems.
Try flying near the FED blocks and the "Offer sanctuary from federation" mission tends to pop up at an ok rate.
Addendum: exchanging duty officer some times results in Romulan Doffs that do not show up on Exchange officer mission. Mail those doffs to a Romulin toon to be broken down of via Romulan fleet duty officer missions on Romulis fleet! have yet to determine if fed/KDG Romulan doffs behave differently.
Have fun out there!