I'm teaching an applicationoriented graduate topics course this spring, where I would like to have students formulate and solve realistic instances of mathematical optimization problems. So I am interested in finding instances other than benchmark collections such as MIPLIB, etc., that have stories and data available. I have a couple of textbooks with some decent problems, including Williams's Model Building in Mathematical Programming, and some of the handbooks available from modeling language vendors. Any other recommendations for sources? asked 05 Jan '14, 18:44 Matthew Salt... ♦ 
You may want to look at the OPTMODEL companion to Paul William's book. While the data there are the same as they are in the book, you could generate new SAS datasets very easily and have them "just work". answered 05 Jan '14, 22:31 Leo 
For realworld sized problems with realworld constraints, the optimization competitions provide good cases (although they are not specifically aimed at LP/IP/NLP):
answered 06 Jan '14, 03:23 Geoffrey De ... ♦ 
Minelib might be interesting to you. answered 06 Jan '14, 04:06 Erling_MOSEK 
I have found the INFORMS journal Interfaces to be a great source of realistic optimization models. Most of the articles on optimization applications provide a detailed story, with plenty of messy details as one finds in the "real" world, plus a complete mathematical formulation in an appendix. The catch is that there's no data provided. Nevertheless I successfully turned several articles into class modeling projects by inventing nontrivial data; in my experience it was a lot easier to invent data than to invent stories to go with "textbook" models. answered 06 Jan '14, 11:25 4er 
Depending on how open you are towards "hipster" (ML/data science, SNA, etc.) problems,
and
could be worth a look. Two more "classical" OR challenges from Kaggle are: [Just for the sake of completeness: even more ML data sets  probably missing your "have a story"requirement, though  can be found via http://www.quora.com/Data/WherecanIfindlargedatasetsopentothepublic]. And since VRPPD/BBSS problems are "en vogue" these days, too ...
[or http://arxiv.org/abs/1312.3971 to gather your own set of instance data from web APIs] answered 07 Jan '14, 14:47 fbahr ♦ packing santa's sleigh is fun and still open (until the rest of the month IIRC). As far as I 've read the forums on it, no one is using LP/IP on it though. Most seem to go with construction heuristics only.
(08 Jan '14, 02:08)
Geoffrey De ... ♦

By "realisticsized" do you mean too big for a spreadsheet/needs to be handled by the OR department v. can be handled by (free) Frontline Solver/would be done by a lone analyst? Some of my MBAs wound up doing "realworld" models that fit comfortably in Excel.