Operations research may be loosely described as the study of
optimal resource allocation. Mathematically, this is the study of
optimization. Depending on the options and constraints in the setting,
this may involve linear programming, or quadratic-, convex-, integer-,
Some links to the history of Operations Research can be found at
the Military Operations Research Society and on J. E. Beasley's home page.
For numerical optimization techniques (conjugate gradient, simulated
annealing, etc.) see 65, Numerical Analysis.
Discrete optimization problems (traveling salesman, etc.) are principally
treated in Combinatorics.
The word "programming" in this context is essentially unrelated to
computer programming; for that topic see Computer Science
- 90B: Operations research and management science (for discrete assignment problems see also 05-XX.)
- 90C: Mathematical programming, see also 49MXX, 65KXX
This was among the larger of the areas of the Math Reviews database.
90C (Mathematical programming) is one of the largest 3-digit areas (and
90C30 (nonlinear programming) is one of the largest 5-digit areas!), but
the other subfields were also fairly large.
Starting in the year 2000 sections A and D were removed from this
heading; a new primary classification Game theory, economics, social and behavioral sciences will be added which will include
most of what has been in those sections.
Browse all (old) classifications for this area at the AMS.
Some references for management and operations research:
Bodin, Lawrence; Golden, Bruce; Assad, Arjang; Ball, Michael:
"Routing and scheduling of vehicles and crews. The state of the art",
Comput. Oper. Res. 10 (1983), no. 2, 63--211. MR85g:90062
Grosh, Doris Lloyd: "A primer of reliability theory",
John Wiley & Sons, Inc., New York, 1989. 373 pp. ISBN 0-471-63820-X MR91d:90048
Alj, A.; Faure, R.: "Guide de la recherche opérationnelle"
(French: Guide to operations research) in two volumes.
Vol. I.: "Les fondements (Foundations)";
Masson, Paris, 1986. 265 pp. ISBN 2-903607-55-9 MR91g:90060.
Vol. 2: "Les applications (Applications)";
Masson, Paris, 1990. 434 pp. ISBN 2-903607-61-3 MR91g:90061.
Some references for mathematical programming and optimization:
"State of the art in global optimization",
Computational methods and applications (Conf. Princeton University, Princeton, New Jersey, April 1995)
Edited by C. A. Floudas and P. M. Pardalos.
Nonconvex Optimization and its Applications, 7.
Kluwer Academic Publishers, Dordrecht, 1996. 651 pp. ISBN 0-7923-3838-3 MR97a:90004
(For previous years' conference see MR96f:90013, MR96f:90005)
"Mathematical programming: the state of the art",
(Proc. 11th Intern. Symp. Mathematical Programming, University of Bonn, Bonn, August, 1982),
Edited by Achim Bachem, Martin Grötschel and Bernhard Korte.
Springer-Verlag, Berlin-New York, 1983. 655 pp. ISBN 3-540-12082-3 MR84j:90004
V. Chvátal: "Linear Programming", W.H. Freeman 1983, ISBN 0-7167-1195-8.
Gomory, R. E.: "Mathematical programming",
Amer. Math. Monthly 72 1965 no. 2, part II 99--110. MR30#4595
Geoffrion, Arthur M.:
"A guided tour of recent practical advances in integer linear programming",
ACM SIGMAP Newslett. No. 17 (1974), 22--32. MR54#14776
Paris, Quirino: "A primer on Karmarkar's algorithm for linear programming",
Stud. Develop. 12 (1985), no. 1-2, 131--155. MR87i:90148
Linear programming FAQ:
World Wide Web version or
Nonlinear programming FAQ:
World Wide Web version or
Operations Research test data sets
Numerical optimization software is discussed as part of 65K: Mathematical programming, optimization and variational techniques.
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Last modified 2000/01/28 by Dave Rusin. Mail: