Course detail

Operations Research

FAST-BA05Acad. year: 2013/2014

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

5

Mode of study

Not applicable.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Knowledge of basic notions and properties of graphs and networks, optimization graph algorithms and project scheduling. Knowledge of linear programming problems, general, integer problems, transportation and assignment. Orientation in 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

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lecture, seminar.

Assesment methods and criteria linked to learning outcomes

Successful completion of the scheduled tests and submission of solutions to problems assigned by the teacher for home work. Unless properly excused, students must attend all the workshops. The result of the semester examination is given by the sum of maximum of 80 points obtained for a written test and a maximum of 20 points from the seminar.

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

GROSS, Jonathan a YELLEN, Jay: Graph Theory and its applications. New York: CRC Press, 1998. (EN)
ŠUBRT, Tomáš: Ekonomicko-matematické metody. Plzeň: VN Aleš Čeněk, 2011. ISBN: 978-80-7380-345-2. (CS)

Recommended reading

TAHA, Hamdy, A.: Operations research. An introduction.. New York: Macmillan Publishing Company, 1992. (EN)
DEMEL, Jiří: Grafy a jejich aplikace. Academia, 2002. (CS)
NOVOTNÝ, Jiří: Základy operačního výzkumu. FAST, 2006. (CS)

Classification of course in study plans

  • Programme B-K-C-SI Bachelor's

    branch E , 3. year of study, summer semester, compulsory

  • Programme B-P-E-SI Bachelor's

    branch E , 3. year of study, summer semester, compulsory

  • Programme B-P-C-SI Bachelor's

    branch E , 3. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

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 hours, compulsory

Teacher / Lecturer

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.