Course Details

Operations Research

Academic Year 2024/25

NAB025 course is part of 1 study plan

​ NPC-MI Summer Semester 1st year

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

Credits

4 credits

Language of instruction

Czech

Semester

summer

Course Guarantor

Ing. Jan Holešovský, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit and examination

Entry Knowledge

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

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.

Basic Literature

NOVOTNÝ, J. Základy operačního výzkumu. Brno: FAST, 2006.
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.

Recommended Reading

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

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/282702

Lecture

13 weeks, 2 hours/week, elective

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

13 weeks, 2 hours/week, compulsory

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.