157-0372/01 – Optimization Methods (OM)

Gurantor departmentDepartment of Systems EngineeringCredits6
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 introduction2015/2016Year of cancellation
Intended for the facultiesEKFIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher 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 studyWay of compl.Extent
Full-time Credit and Examination 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

Zápočet: - aktivní účast na cvičení - účast na cvičení alespoň 70 % - získání minimálně 23 bodů ze 45 Zkouška: - ústní


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

Other requirements

Active attendance at seminars, study at home, study of mandatory literature, individual consultations.


Subject has no prerequisities.


Subject has no co-requisities.

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.

Conditions for subject completion

Full-time form (validity from: 2018/2019 Winter semester, validity until: 2020/2021 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 45 (45) 23
                Stochastic programming Written test 20  8
                Fuzzy programming Written test 13  5
                Data envelopment analysis (DEA) Written test 12  5
        Examination Examination 55  28
Mandatory attendence parzicipation: 60% of seminars

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (N0688A050001) Information and Knowledge Management KM P Czech Ostrava 1 Compulsory study plan
2019/2020 (N6209) Systems Engineering and Informatics (6209T017) Informatics in Economics P Czech Ostrava 1 Compulsory study plan
2018/2019 (N6209) Systems Engineering and Informatics (6209T017) Informatics in Economics P Czech Ostrava 1 Compulsory study plan
2017/2018 (N6209) Systems Engineering and Informatics (6209T017) Informatics in Economics P Czech Ostrava 1 Compulsory study plan
2016/2017 (N6209) Systems Engineering and Informatics (6209T017) Informatics in Economics P Czech Ostrava 1 Compulsory study plan
2015/2016 (N6209) Systems Engineering and Informatics (6209T025) System Engineering and Informatics P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner