157-0472/01 – Optimization methods (OMk)

Gurantor department	Department of Systems Engineering	Credits	5
Subject guarantor	doc. Mgr. Ing. František Zapletal, Ph.D.	Subject version guarantor	doc. Mgr. Ing. František Zapletal, Ph.D.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	1	Semester	summer
		Study language	Czech
Year of introduction	2019/2020	Year of cancellation
Intended for the faculties	EKF	Intended for study types	Follow-up Master

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
CHY0034	Mgr. Ing. Lucie Chytilová, Ph.D.
TOL0013	prof. Mehdi Toloo, Ph.D.
ZAP149	doc. Mgr. Ing. František Zapletal, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Part-time	Credit	6+6

Subject aims expressed by acquired skills and competences

The aim of the course is to present advanced optimization methods to students. In particular, an emphasis is put on optimization under risk and uncertainty and efficiency evaluation.

Teaching methods

Lectures
Tutorials

Summary

Students learn both the theoretical background and possibilities of applications in practice. They will get know how to define a mathematical optimization model when risk (stochastic programming) and uncertainty (fuzzy programming) are involved and how to solve these models using software (Solver, GAMS).

Compulsory 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.

Recommended literature:

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.

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Test (DEA + stochastic programming + fuzzy programming).

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Linear programming (model, solution, duality). 2. Necessary and sufficient conditions of optima (KKT conditions), Trap of local optima). 3. Risk - random variables and its description. 4. Stochastic programming - introduction, classification. 5. Stochastic programming - single-stage models, chance constraints. 6. Stochastic programming - two-stage models (models with recourse), multi-stage models. 7. Stochastic programming - mean-risk portfolio models. 8. Introduction to fuzzy sets, logic and algebra. 9. Fuzzy programming - selected defuzzification measures, alpha-cuts, possibilistic programming. 10. Fuzzy programming - flexible programming models. 11. Data Envelopment Analysis (DEA) - introduction. 12. Data Envelopment Analysis (DEA) - CCR and BCC model.

Conditions for subject completion

Part-time form (validity from: 2020/2021 Summer semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Credit	Credit	100 (100)	51	2
Credit	Written test	75	36	2
Written project - application of DEA methods	Semestral project	25	15	2

Mandatory attendence participation: There is no limit for lecture attendance.

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Conditions for subject completion and attendance at the exercises within ISP: There is no limit for lecture attendance.

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Form	Study language	Tut. centre	Year	Type of duty
2023/2024	(N0413A050014) Economics and Management	(S02) Management	K	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(N0413A050014) Economics and Management	(S02) Management	K	Czech	Ostrava	1	Compulsory	study plan
2021/2022	(N0413A050014) Economics and Management	(S02) Management	K	Czech	Ostrava	1	Compulsory	study plan
2020/2021	(N0413A050014) Economics and Management	(S02) Management	K	Czech	Ostrava	1	Compulsory	study plan
2019/2020	(N0413A050014) Economics and Management	(S02) Management	K	Czech	Ostrava	1	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction