Course detail

Systems Theory and Operations Research

FSI-XAZAcad. year: 2010/2011

The introductory part of this course, systems theory, explains the essence of a system and relationships between the system and its environment with a view to a selected kind of socio-technical systems. 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

RNDr. Jiří Dvořák, CSc.

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 in socio-technical systems, 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

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 attendance at the seminars, elaboration of semester project.
Examination: written test (problems and questions), oral exam.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Goals of the course: 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 research. To teach constructing mathematical models for solving practical problems. To explain theoretical foundations of operations research and principles of working basic methods. To teach using acquired knowledge to design, implementation and management of socio-technical systems.

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

The attendance at the seminars is controlled. An absence can be compensated for via solving given problems.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Skyttner, L. General Systems Theory. An Introduction. Macmillan Press Ltd., London, 1996.
Turban E., Meredith J. Fundamentals of Management Science. Irwin, Boston, 1991.
Winston, W.L. Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmont, 2004.

Recommended reading

Jablonský, J. Operační výzkum. Kvantitativní modely pro ekonomické rozhodování. Professional Publishing, Praha, 2002.
Klapka, J., Dvořák, J., Popela, P. Metody operačního výzkumu. VUTIUM, Brno, 2001.
Pitra, Z. Teorie systémů. MŠMT, Praha, 1989.

Classification of course in study plans

  • Programme N3901-2 Master's

    branch M-MŘJ , 1 year of study, summer semester, compulsory
    branch M-MŘJ , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Jiří Dvořák, CSc.

Syllabus

1. Basic notions of systems theory, classification of systems.
2. Modelling systems. Systems analysis and operations research.
3. Formulation and properties of linear programming problems.
4. One-phase simplex method.
5. Two-phase simplex method.
6. Duality theory and sensitivity analysis.
7. Formulation and properties of nonlinear programming problems. Optimality conditions.
8. Methods of solving nonlinear programming problems.
9. Integer programming, branch-and-bound method.
10. Basic concepts of graph theory.
11. Network analysis, CPM and PERT.
12. Models of queuing systems.
13. Complex decision problems.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

RNDr. Jiří Dvořák, CSc.

Syllabus

1. Formulating optimization models and their solving in MS Excel.
2. Formulating optimization models and their solving in GAMS.
3. Formulating and solving linear programming models.
4. One-phase simplex method.
5. Two-phase simplex method.
6. Possible terminations of simplex method.
7. Duality and sensitivity analysis.
8. Solving nonlinear programming problems.
9. Solving integer programming problems.
10. Solving problems of graph theory.
11. Solving problems of project network analysis.
12. Solving queuing problems.
13. Solving complex decision problems.