The reference books should cover the wide range of problem-solving techniques and methods.

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    $\begingroup$ This post came up in the "low quality" review queue. It is both a very broad question and very opinion based. I suggest limiting the scope of the question, e.g. by limiting the question to OR introduction books. $\endgroup$ – Michael Feldmeier Jul 3 '19 at 7:59
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    $\begingroup$ I think this question should specify either the topic or the level of complexity instead of asking others of sorting them. Lists of books can be ok in principle, but I really think a list that can reasonable contain any book on OR ever is far too broad. I strongly recommend specifying this before reopening it. $\endgroup$ – Discrete lizard Jul 3 '19 at 10:06
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    $\begingroup$ Furthermore, letting people 'just' lists OR-books is all well and good, but I'd rather that they do so in a more organised manner that fits within the Q&A model of SE. I think that having those books split over multiple threads, clustered by relevance to a specific problem or type of reader, is a much better end-result than putting everything in a single thread. $\endgroup$ – Discrete lizard Jul 3 '19 at 10:13
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    $\begingroup$ If this is supposed to be a FAQ or 'reference source' it should be on our Meta (and possibly a Wiki). $\endgroup$ – Rob Jul 3 '19 at 13:27
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    $\begingroup$ I disagree with @Discrete lizard 's comment. I like one-stop shopping, at least when it's done well (enough). $\endgroup$ – Mark L. Stone Jul 3 '19 at 13:42

For books with a focus on industrial applications, see this other question of this forum

As textbooks, I would recommend to have a look at:

For Modeling:

H.P. Williams. Model building in mathematical programming. John Wiley & Sons, 2013.

D. Chen, R.G. Batson, Y. Dang. Applied Integer Programming: Modeling and Solution. John Wiley & Sons, 2009.

MOSEK Modeling Cookbook How to formulate and reformulate conic optimization problems (convex QP, SOCP, SDP, Exponential Cone, Power Cone, and mixed integer). Requires some "mathematical maturity" to understand. This is very helpful for users of CVX, CVXPY, CVXR, YALMIP. Note, this is complementary to H.P. Williams "Model building in mathematical programming", because Williams doesn't cover any conic optimization material.

Graph Theory and Algorithms:

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin. Network flows, 1988.

Linear Programming:

V. Chvátal. Linear Programming. New York: W.H. Freeman, 1983.

D. Bertsimas and J. N. Tsitsiklis. Introduction to Linear Optimization, Athena Scientific, 1997.

G.B. Dantzig. Linear Programming and Extensions.Reprinted in 1998 by Princeton Press.

G.B. Dantzig and M.N. Thapa Linear Programming 1: Introduction, Springer, 1997 and Linear Programming 2: Theory and Extension, Spinger, 2003. Linear Programming 2, especially, is hard-core. I think these books supersede and render G.B. Dantzig "Linear Programming and Extensions" to be of historical interest only.

Integer Programming:

D. Bertsimas and R. Weismantel. Optimization over Integers. Belmont, MA: Dynamic Ideas, 2005.

G. Desaulniers, J. Desrosiers, and M. M. Solomon. Column Generation. New York: Springer, 2005.

G. Nemhauser, and L. Wolsey. Integer and Combinatorial Optimization. Wiley, 1988.

L. Wolsey. Integer programming, John Wiley & Sons Canada, 1998

M. Conforti, G. Cornuéjols, G. Zambelli. Integer Programming, GTM 271, Springer, 2014.

Convex Optimization:

S. Boyd and L. Vandenberghe Convex Optimization. Cambridge University Press, 2004 (freely downloadable at provided link). Also serves as good background for non-convex optimization.

A. Ben-Tal, A. Nemirovski Lectures on Modern Convex Optimization, 2013 (most recent version). Very advanced mathematically.

N. Parikh and S. Boyd, Proximal Algorithms, now Foundations and Trends in Optimization, 2013. Errata. Mostly algorithms, a few examples.

J. Tropp, An Introduction to Matrix Concentration Inequalities, now Foundations and Trends in Optimization, 2014. Goes beyond Ben-Tal and Nemirovski in such areas as operator convexity and matrix (quantum) relative entropy.

L. Vandenberghe and M. Andersen. Chordal Graphs and Semidefinite Optimization, now Foundations and Trends in Optimization, 2015. Advanced material in Semidefinite Optimization (Programming), i.e., SDP.

Nonlinear Optimization:

J. Nocedal, S. Wright. Numerical Optimization. Springer, 2006.

A. Beck. Introduction to nonlinear optimization: Theory, algorithms, and applications with MATLAB. SIAM, 2014.

Geometric Programming

S. Boyd, Seung-Jean Kim, L. Vandenberghe, and A. Hassibi. A tutorial on geometric programming, Optimization and Engineering, 2007. A tutorial journal article covering geometric programming and generalizations and extensions, starting from basics and proceeding to more advanced material.

Combinatorial Optimization:

A. Schrijver. Combinatorial Optimization - Polyhedra and Efficiency. Springer, 2003

Stochastic Optimization:

A.J. King, and S.W. Wallace. Modeling with Stochastic Programming. Springer, 2012.

J.R. Birch, and F. Louveaux. Introduction to stochastic programming. Springer Science & Business Media, 2011.

A. Shapiro, D.Dentcheva, and A. Ruszczyński. Lectures on Stochastic Programming: Modeling and Theory. SIAM, 2009.

Robust Optimization:

A. Ben-Tal, L. El Ghaoui, and A. Nemirovski. Robust optimization. Princeton University Press, 2009.

P. Kouvelis, and G. Yu. Robust Discrete Optimization and Its Applications. Springer, 1997.

Transportation Problems

G. Peyré, M. Cuturi, Computational Optimal Transport, now Foundations and Trends in Machine Learning, 2019. Very advanced and theoretical. Shows how to formulate and calculate such things as Wasserstein distance as computational optimal transport problems. This is not an Intro to OR Transportation Problem book.

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    $\begingroup$ Thanks Stefano Gualandi for your suggestions! $\endgroup$ – Rajasekhar Kadambur Jul 3 '19 at 6:41
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    $\begingroup$ I'd like to add A. Ben-Tal, A. Nemirovski - Lectures on Modern Convex Optimization (www2.isye.gatech.edu/~nemirovs/lmco_run.pdf) and Ben-Tal, A., El Ghaoui, L., Nemirovski, A. - Robust Optimization (sites.google.com/site/robustoptimization) $\endgroup$ – JakobS Jul 3 '19 at 7:21
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    $\begingroup$ Jakob, I have made my answer a community wiki, this way it should be easy to add other books to this list. Please, go ahead and add the two books you are suggesting. $\endgroup$ – Stefano Gualandi Jul 3 '19 at 7:30
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    $\begingroup$ per meta (not just OR Meta, SE meta in general) basic questions should not be made community wikis. The fact that some people remove other peoples additions just demonstrates once more that this question is too opinion based, and thus just remain closed until further specified. $\endgroup$ – Michael Feldmeier Jul 3 '19 at 10:11
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    $\begingroup$ @Mark L. Stone i didnt delete it. I just added amir beck, ben-tal and birge. While I was editing I got a message saying the post is edited now. So maybe when I finished my part the other change is included in my part. No idea who deleted it for what reason. $\endgroup$ – independentvariable Jul 3 '19 at 13:25

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