Course detail

Operations Research

FAST-NAB025Acad. year: 2022/2023

Models in operations research.
Theory of graphs and networks
Optimization graph algorithms.
Project scheduling.
Linear programming, general, integer problems.
Transportation and assignment.
Queueing analysis.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

Ing. Jan Holešovský, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Knowledge of basic notions and properties of graphs and networks, linear programming problems and queueing analysis.

Prerequisites

The basics of linear algebra, the basics of probability theory, the basics of statistics, Spreadsheets

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. Models in operations research
2. Definition of a graph and its description
3. Eulerian a Hamiltonian graphs
4. Minimum spanning tree, maximal flow in a network, optimal paths in graphs
5. Critical Path Method, Program Evaluation and Review Technique
6. Source analysis
7. Types of linear programming problems
8. Simplex method
9. Integer problems
10. Transportation problems
11. Assignment problems
12. Introduction into the queueing theory
13. Optimization of queueing systems

Work placements

Not applicable.

Aims

After the course, students should understand the basic notions and properties of graphs and networks, linear programming problems and queueing analysis. They should master the basics of calculus and be able to apply their knowledge in the follow-up courses.

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

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BAZARAA, M.S., JARVIS, J.J., SHERALI, H.D. Linear Programming and Network Flows. 4th ed. Hoboken: Wiley, 2010. 768 p. ISBN 978-0-470-46272-0.
NOVOTNÝ, J. Základy operačního výzkumu. Brno: FAST, 2006.

Recommended reading

GROSS, J.,YELLEN, J., ANDERSON, M. Graph Theory and Its Applications. New York: CRC Press, 1998, 592 p. ISBN 978-1-4822-4948-4.
ŠUBRT, T. Ekonomicko-matematické metody. Plzeň: VN Aleš Čeněk, 2011. ISBN: 978-80-7380-345-2.

Classification of course in study plans

  • Programme NPC-MI Master's 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Ing. Jan Holešovský, Ph.D.

Syllabus

1. Models in operations research 2. Definition of a graph and its description 3. Eulerian a Hamiltonian graphs 4. Minimum spanning tree, maximal flow in a network, optimal paths in graphs 5. Critical Path Method, Program Evaluation and Review Technique 6. Source analysis 7. Types of linear programming problems 8. Simplex method 9. Integer problems 10. Transportation problems 11. Assignment problems 12. Introduction into the queueing theory 13. Optimization of queueing systems

Exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Jan Holešovský, Ph.D.

Syllabus

1. EXCEL in operations research. 2. Graphs description. 3. Optimization graph algorithms. 4. Branch and bound method. 5. Tavelling salesman problem. 6. Network analysis methods. 7. Project scheduling. 8. Methods for solving linear programming problems. 9. Production planning. 10. Methods for solving distribution problems. 11. Transportation problem. 12. Integer problems methods. 13. Assignment problem. Seminar evaluation.