157-9986/01 – Optimisation (O)

Gurantor departmentDepartment of Systems EngineeringCredits10
Subject guarantordoc. Mgr. Ing. František Zapletal, Ph.D.Subject version guarantordoc. Mgr. Ing. František Zapletal, Ph.D.
Study levelpostgraduateRequirementCompulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2020/2021Year of cancellation
Intended for the facultiesEKFIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
ZAP149 doc. Mgr. Ing. František Zapletal, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Part-time Examination 28+0

Subject aims expressed by acquired skills and competences

The aim of this subject is to extend knowledge on and experience with mathematical modelling, with a special focus on optimization. Students will be able to solve complex optimization problems of convex, stochastic and fuzzy programming.

Teaching methods

Individual consultations


The subject is divided into 4 parts, in which various subfields of optimization are explored: A) Non-linear models and existence of their optimal solution (convex programming), Bender's decomposition. B) Logical relationships between decision variables and constraints (OR, XOR, implication). C) Stochastic programming - optimization with random parameters (static models, dynamic models - multi-stage models, non-anticipativity constraints, static and dynamic risk measures, coherent, convex and time-consistent risk measures, D) fuzzy programming - optimization under uncertainty (with fuzzy parameters and relations - a way how to involve qualitative and subjective data.

Compulsory literature:

SHAPIRO, Alexander a Andrzej RUSZCZYNSKI, ed. Stochastic programming. Amsterdam: Elsevier, 2003. Handbooks in operations research and management science, v. 10. ISBN 0-444-50854-6. FIEDLER, Miroslav. Linear optimization problems with inexact data. New York: Springer, c2006. 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:

BIRGE, John R. a François LOUVEAUX. Introduction to stochastic programming. 2nd ed. New York: Springer, c2011. Springer series in operations research. ISBN 978-1-4614-0236-7. KALL, Peter a János MAYER. Stochastic linear programming: models, theory, and computation. 2nd ed. New York: Springer, c2011. International series in operations research & management science, 156. ISBN 978-1-4419-7728-1. SAKAWA, Masatoshi, Hitoshi YANO a Ichiro NISHIZAKI. Linear and multiobjective programming with fuzzy stochastic extensions. New York: Springer, c2013. International series in operations research & management science, 203. ISBN 978-1-4614-9398-3.

Way of continuous check of knowledge in the course of semester

The final evaluation of a student is based on his/her activity during the semester and results of the oral exam.


Information are provided to students at the lectures, through the LMS system. In LMS, there is an extended descriptions of the lectures and recommended literature.

Other requirements

Students must have a proactive approach and pass the oral exam.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1) Systemic approach, mathematical modelling. 2) Convex programming 3) Logical constraints 4) Risk measures 5) Single-stage and multi-stage stochastic programming. 6) Multi-stage stochastic programming. 7) Chance-constrained programming 8) Benders decomposition method. 9) Basics of fuzzy logic, algebra and set theory. 10) Possibilistic programming. 11) Flexible programming. 12) Intuitionistic fuzzy sets and their use in optimization.

Conditions for subject completion

Part-time form (validity from: 2020/2021 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (P0311D050019) Systems Engineering and Informatics P Czech Ostrava Compulsory study plan
2021/2022 (P0311D050019) Systems Engineering and Informatics K Czech Ostrava Compulsory study plan
2020/2021 (P0311D050019) Systems Engineering and Informatics P Czech Ostrava Compulsory study plan
2020/2021 (P0311D050019) Systems Engineering and Informatics K Czech Ostrava Compulsory study plan

Occurrence in special blocks

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