Course detail

Optimization Methods I

FSI-FOA-KAcad. year: 2021/2022

The introductory part of this course deals with systems theory and systems analysis. It explains the essence of a system and relationships between the system and its environment. The next part of this course, operations research, presents tools for solving various types of decision problems. This part shows possibilities of optimizing structure and behaviour of systems, and gives foundations for applying the system approach to solving decision problems. On one hand, the course is focused on typical problems of socio-technical systems, and on the other hand on theoretical and application aspects of solution methods. The course gives foundations for applying the system approach to solving decision problems.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. RNDr. Ing. Miloš Šeda, Ph.D.

Department

Institute of Automation and Computer Science (ÚAI)

Learning outcomes of the course unit

Students will be able to distinguish different kinds and types of systems, and will acquire knowledge of ways of their modelling. They will be able to use a system approach to solving problems, and will acquire knowledge of basic techniques and tools for analysis, synthesis and optimization of systems. Students will have a clear overview of operations research models and methods. They will be able to choose a proper approach to decision problem solving, and construct mathematical models for solving practical problems. They will acquire knowledge of fundamental principles of operations research methods, and will be able to solve operations research problems by means of computer.

Prerequisites

Linear algebra, differential calculus, probability theory, mathematical statistics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course-unit credit: Active participation in the seminars, elaboration of a given project. Examination: Written.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

To explain basic approaches to modelling socio-technical systems and their effective management. To provide students with an overview of models, methods and applications of operations and systems analysis. To teach constructing mathematical models for solving practical problems. To explain theoretical foundations of operations and systems analysis and principles of working basic methods. To teach using acquired knowledge to design, implementation and management of systems.

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

Attendance at seminars is controlled. An absence can be compensated for via solving additional problems.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BOMZE, L.M.; GROSSMANN, W.: Optimierung Theorie und Algorithmen. BI-Wiss.-Verl., Mannheim, pp. 610, 1993. ISBN 3-411-15091-2.
LITTLECHILD, S.; SHUTLER, M. (eds.): Operations Research in Management. Prentice Hall, New York, pp. 298, 1991. ISBN 0-13638-8183
SKYTTNER, L.: General Systems Theory. An Introduction. Macmillan Press, London, pp. 290, 1996. ISBN 0-333-61833-5.

Recommended reading

KLAPKA, J.; DVOŘÁK, J.; POPELA, P.: Metody operačního výzkumu. VUTIUM, Brno, 2001. ISBN 80-214-1839-7

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme N-AIŘ-K Master's 1 year of study, summer semester, compulsory

Type of course unit

 

Guided consultation in combined form of studies

22 hod., compulsory

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

1. Basic notions of systems theory, classification of systems.
2. Modelling systems. Systems analysis and operations research.
3. Linear programming problems and their properties.
4. Methods of solving linear programming problems.
5. Sensitivity analysis and duality.
6. Transportation and distribution problems.
7. Formulation and properties of nonlinear programming problems. Optimality conditions.
8. Methods of solving nonlinear programming problems.
9. Integer programming problems, branch-and-bound method.
10. Stochastic optimization problems.
11. Multicriteria decision problems.
12. Problems and methods of game theory.
13. Models of queueing systems.

Guided consultation

43 hod., optionally

Teacher / Lecturer

prof. RNDr. Ing. Miloš Šeda, Ph.D.

Syllabus

1. Models of systems, systems analysis.
2. Formulating optimization models.
3. Linear problems, graphical solution.
4. Solving linear problems by means of simplex method.
5. Solving transportation problems.
6. Solving nonlinear problems by means of Kuhn-Tucker conditions.

Elearning

eLearning: currently opened course