Course detail

Mathematical models of Decision Making

ÚSI-RSMODAcad. year: 2020/2021

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.

Learning outcomes of the course unit

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.


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.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

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

Planned learning activities and teaching methods

Tuition takes place via lectures and seminars. The lectures focus on the explanation of basic principles, the methods of the given discipline, problems and example solutions. The seminars mainly support practical mastery of the subject matter presented in lectures or assigned for individual study with the active participation of students.

Assesment methods and criteria linked to learning outcomes

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.

Language of instruction


Work placements

Not applicable.

Course curriculum

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.


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.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is monitored, and the teacher chooses the manner in which absences are compensated for.

Classification of course in study plans

  • Programme RRTES_P Master's

    specialization RRES , 1. year of study, summer semester, 5 credits, compulsory
    specialization RRTS , 1. year of study, summer semester, 5 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


26 hours, compulsory

Teacher / Lecturer