Course detail

Optimization Methods I

FSI-FOA-AAcad. year: 2024/2025

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

English

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)

Entry knowledge

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

Rules for evaluation and completion of the course

Course-unit credit: Active participation in the seminars, elaboration of a given project. Examination: Written.
Attendance at seminars is controlled. An absence can be compensated for via solving additional problems.

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.
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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N-ENG-Z Master's 1 year of study, summer semester, recommended course

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. RNDr. Ing. Miloš Šeda, 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.

Exercise

12 hod., compulsory

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.

Computer-assisted exercise

14 hod., compulsory

Teacher / Lecturer

prof. RNDr. Ing. Miloš Šeda, Ph.D.

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. Solving nonlinear and integer programming problems.
5. Solving stochastic optimization problems.
6. Solving multicriteria problems and problems of game theory.
7. Solving queueing problems.