Course detail

Mathematical models of Decision Making

ÚSI-RSMODAcad. year: 2025/2026

General approaches to decision-making; fundamental decision-making models; decision situations are introduced. Special attention will be paid to the branch of mathematical modelling: Stochastic and optimization models. The presented material will deepen students understanding of topics discussed in the previous RSMAT course. The related methods will be presented using examples of their application and involve the maximum use of suitable software: Statistica, GAMS and Matlab.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Karpíšek, CSc.

Department

Institute of Forensic Engineering (ÚSI)

Entry knowledge

Basic knowledge of calculus at the Bachelor’s level; elementary knowledge of computer technology at the level needed to be able to use application software. The course content is linked to the RSMAT course taught in the previous semester.

Rules for evaluation and completion of the course

Course unit credit requirements: active participation in seminars, mastery of the course content, and the submission of a semestral assignment. Examination (written): practical part (4 tasks), theoretical part (4 tasks); the ECTS evaluation scale will be used.
Attendance at seminars is monitored, and the teacher chooses the manner in which absences are compensated for.

Aims

Students will obtain useful knowledge of decision-making models involving uncertainty and risk. They will also learn how to apply the studied models and methods in the related areas of application.
Students will become familiar with fundamental terms, methods and analytical techniques related to decision-making models, including risk elements. Specific ways of reasoning that are typical for decision-making under uncertainty and risk will be developed and enhanced.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

KLAPKA A KOL.: Metody operačního výzkumu, VUTIUM 2001, ISBN 80-214-1839-7
POPELA, P.: Nonlinear Programming, University of Malta, učební texty ÚM VUT v Brně, 2001.
POPELA, P.: Stochastic Programming, University of Malta, učební texty ÚM VUT v Brně, 2003.
POPELA, P.: Stochastic Programming, University of Malta, učební texty ÚM VUT v Brně, 2003.

Recommended reading

KALL, P., WALLACE, S.W.: Stochastic Programming, Wiley 1993, ISBN 0471951080
MINOUX, M.: Mathematical Programming, Wiley, 1988, ISBN 0471901709
WILLIAMS, H. P.: Model Building in Mathematical Programming, Wiley 1993, ISBN 0471941115.

Classification of course in study plans

  • Programme RRTES_P Master's

    specialization RRTS , 1 year of study, summer semester, compulsory
    specialization RRES , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Zdeněk Karpíšek, CSc.

Syllabus

1. Selected deterministic models: linear and nonlinear optimization.
2. Selected models of multicriteria optimization and decision-making.
3. Selected engineering optimization models: inverse problems.
4. Selected deterministic, stochastic, and heuristic methods of finding and improving solutions.
5. Selected decision-making models - optimization software.
6. Models of decision-making under risk and uncertainty - deterministic reformulations and their properties.
7. Mathematical models of decision-making under risk and uncertainty - engineering applications.
8. Mathematical models of decision-making under risk and uncertainty - discrete mathematics applications.
9. Selected stochastic decision-making models for network flows.
10. Multistage models and dynamic programming.
11. Dynamic models - scenario-based techniques, applications in GAMS.
12. Mathematical modelling of advanced decision-making structures.
13. Decision making models for conflicts; model transformations and approximations.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Karpíšek, CSc.