Course detail

# Operational and Systems Analysis

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.

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.

Recommended optional programme components

Not applicable.

Skyttner, L.: General Systems Theory: Problems, Perspectives, Practice. World Scientific Publishing, Singapore, 2006. (EN)
KLAPKA, J.; DVOŘÁK, J.; POPELA, P.: Metody operačního výzkumu. VUTIUM, Brno, 2001. ISBN 80-214-1839-7 (CS)
PITRA, Z.: Teorie systémů. MŠMT, Praha, 1989. (CS)
Taha, H. A.: Operations Research: An Introduction. Prentice Hall, New Jersey, 2010. (EN)
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Martin, R. K.: An Introduction to Management Science: Quantitative Approaches to Decision Making. South-Western College Publishing, Boston, 2011. (EN)
JABLONSKÝ, J.: Operační výzkum. Kvantitativní modely pro ekonomické rozhodování. Professional Publishing, Praha, 2002. (CS)
Zelinka, I., Snášel, V., Abraham, A. (eds.): Handbook of Optimization. From Classical to Modern Approach. Berlin, Springer-Verlag, 2012. (EN)
TURBAN, E., MEREDITH, J.: Fundamentals of Management Science. Irwin, Boston, 1991. (EN)
Zelinka, I., Oplatková, Z., Šeda, M., Ošmera, P., Včelař, F.: Evoluční výpočetní techniky. Principy a aplikace. BEN – technická literatura, Praha, 2009. (CS)

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.

Language of instruction

Czech

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.

Classification of course in study plans

• Programme M2I-P Master's

branch M-AIŘ , 1. year of study, winter semester, 6 credits, compulsory

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

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 queuing systems.

Exercise

13 hours, compulsory

Teacher / Lecturer

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

13 hours, compulsory

Teacher / Lecturer

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 queuing problems.