157-0372/02 – Optimization Methods (OM)

Gurantor departmentDepartment of Systems EngineeringCredits5
Subject guarantordoc. Mgr. Ing. František Zapletal, Ph.D.Subject version guarantordoc. Mgr. Ing. František Zapletal, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesEKFIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
CHY0034 Mgr. Ing. Lucie Chytilová, Ph.D.
SIN0085 Ing. Markéta Šindlerová
SVA0158 Ing. Miloš Švaňa
TOL0013 prof. Mehdi Toloo, Ph.D.
VOL0133 Ing. Jan Volný
ZAP149 doc. Mgr. Ing. František Zapletal, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 2+2

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



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:

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.

Way of continuous check of knowledge in the course of semester


Other requirements

Test on fuzzy programming Test on stochastic programming Test on DEA Oral exam


Subject has no prerequisities.


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

Full-time form (validity from: 2020/2021 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit Credit 45 (45) 23 2
        Stochastické a fuzzy programování Written test 30  15 2
        Written project - application of DEA methods Semestral project 15  7 2
Mandatory attendence participation: 60 % of seminars

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Conditions for subject completion and attendance at the exercises within ISP: 60 % of seminars

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (N0413A050014) Economics and Management (S02) Management P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0413A050014) Economics and Management (S02) Management P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0413A050014) Economics and Management (S02) Management P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0413A050014) Economics and Management (S02) Management P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0413A050014) Economics and Management (S02) Management P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

2022/2023 Summer
2021/2022 Summer
2020/2021 Summer
2019/2020 Summer