Course detail

Operations Research

FAST-BA009Acad. year: 2024/2025

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)

Entry knowledge

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

Rules for evaluation and completion of the course

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

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

Study aids

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. (EN)
DEMEL, J. Grafy a jejich aplikace. Academia, 2002, 258 s. ISBN 80-200-0990-6.  (CS)
NOVOTNÝ, J. Základy operačního výzkumu. Brno: FAST, 2006. (CS)

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.  (EN)
ŠUBRT, T. Ekonomicko-matematické metody. Plzeň: VN Aleš Čeněk, 2011. ISBN: 978-80-7380-345-2.  (CS)

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.