Course detail

Mathematical models of Decision Making

ÚSI-2SBMMAcad. year: 2011/2012

General approaches to decision making; fundamental decision making models; decision situations are introduced. Stochastic and optimization models as special branches of mathematical modelling are under focus. The presentation of principle ideas will be linked to themes discussed in the previous 2SAMZ course. The solution methods will be presented by using application areas-related examples and suitable software: Statistica, GAMS, Matlab.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Learning outcomes of the course unit

Fundamental concepts, methods and analytical techniques related to decision making models including risk elements will be studied. Specific ways of reasoning, typical for decision making under uncertainty and risk will be developed and enhanced.

Prerequisites

Basic knowledge of Calculus techniques; elementary knowledge of windows based applied software. The course content is linked to 2SAMZ course taught in the previous semester.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Course-unit credit requirements: active participation in seminars, mastering the subject matter, and delivery of semester assignment. Examination (written form): a practical part (4 tasks), a theoretical part (4 tasks); ECTS evaluation used.

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 solution improving methods.
5. Selected decision making models - software for optimization
6. Decision making models under risk and uncertainty - deterministic reformulations and their properties.
7. Decision making models under risk and uncertainty - engineering applications.
8. Decision making models 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 transforamtions and approximations.

Work placements

Not applicable.

Aims

Students will learn useful knowledge of decision making models involving uncertainty and risk. They will also learn how apply studied models and methods in the related application areas.

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

Attendance at seminars is controlled and the teacher decides on the compensation for absences.

Recommended optional programme components

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.
GAMS User's Guide, www.gams.com

Recommended reading

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.

Classification of course in study plans

  • Programme MRzI Master's

    branch RFI , 1 year of study, summer semester, compulsory
    branch RCH , 1 year of study, summer semester, compulsory
    branch RSK , 1 year of study, summer semester, compulsory
    branch RSZ , 1 year of study, summer semester, compulsory
    branch RIS , 1 year of study, summer semester, compulsory
    branch REZ , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Exercise

26 hod., compulsory

Teacher / Lecturer