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Optimization Methods

Type of study Follow-up Master
Language of instruction Czech
Code 157-0372/01
Abbreviation OM
Course title Optimization Methods
Credits 6
Coordinating department Department of Systems Engineering and Informatics
Course coordinator doc. Mgr. Ing. František Zapletal, Ph.D.

Subject syllabus

1) Linear programming problems and their solving
2) Conditions for existence of an optimal solution
3) Stochastic programming - principles, presumptions, applications
4) Stochastic programming models without involving the risk measure
5) Stochastic programming - single stage model with probability constraints
6) Stochastic programming - penalization in the objective function
7) Stochastic programming - models with risk measures
8) Uncertainty and fuzzy sets, basics of fuzzy algebra.
9) Fuzzy optimization - possibilistic mean values, types of uncertainty, alpha-cut approach, possibility, and necessity measures.
10) Flexible programming
11) Introduction to Data Envelopment Analysis (DEA).
12) Basic DEA models and their assumptions.

E-learning

Studijní opory TpB:
https://lms.vsb.cz/course/view.php?id=72589


Studenti čerpají z povinné a doporučené literatury. Navíc mají k dispozici rozšířené podklady k přednáškám a sbírku řešených příkladů s komentáři.

Literature

SHAPIRO, Alexander, RUSZCZYNSKI, Andrzej a Darinka DENTCHEVA. Lectures on Stochastic Programming: Modeling and Theory, 2009. ISBN 978-0-89871-687-0 .
FIEDLER, Miroslav a kol. Linear optimization problems with inexact data. New York: Springer, 2006. ISBN 0-387-32697-9.
PRÉKOPA, András. Stochastic programming. Dordrecht: Kluwer Academic Publishers, c1995. Mathematics and its applications, v. 324. ISBN 0-7923-3482-5.

Advised literature

TAHA, Hamdy A. Operations research: an introduction. 9. vyd. International ed. Upper Saddle River: Pearson, 2011. ISBN 978-0-13-139199-4.
SHAPIRO, Alexander a Andrzej RUSZCZYŃSKI, ed. Stochastic programming. Amsterdam: Elsevier, 2003. Handbooks in operations research and management science, v. 10. ISBN 0-444-50854-6 .
VLACH, Milan a Jaroslav RAMÍK. Generalized concavity in fuzzy optimization and decision analysis. Boston: Kluwer Academic Publishers, c2002. International series in operations research & management science, 41. ISBN 0-7923-7495-9.


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