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I am primarily a discrete mathematician (designs/finite geometries), and I've been using Gurobi to solve some integer programming problems related to my research. While I'm comfortable using the software, I feel like I would like to better understand the mathematics involved.

I'm interested in learning about the polytope defined by an integer programming problem. I'd also like to know about formulating problems; what makes a formulation of a problem "good" or "bad"?

I'm less interested in getting too in-depth about the mechanics of the different algorithms (I'm happy to just know which are better than others in certain situations).

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Nemhauser-Wolsey is the encyclopedia. It's a very tough read though, if you don't already know what you're doing. http://www.amazon.com/Integer-Combinatorial-Optimization-Laurence-Wolsey/dp/0471359432

I really like these notes by Krumke. They're a really good supplement (and even standalone) for your IP studies. http://staff.guilan.ac.ir/staff/users/salahi/fckeditor_repo/file/ip-lecture-new.pdf

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