Course detail

Stochastic Models in Logistics

FSI-SEP-AAcad. year: 2025/2026

The course provides an introduction to the theory of stochastic processes, covering key topics such as types and fundamental characteristics of stochastic processes, time series decomposition, Markov chains, Poisson processes, and queueing theory. Students will gain practical skills in application of this methods in describing and predicting stochastic processes using appropriate software tools.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Mgr. Zuzana Hübnerová, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Rudiments of probability theory and mathematical statistics, linear regression models.

Rules for evaluation and completion of the course

Course-unit credit requirements: active participation in seminars, demonstration of basic skills in practical data analysis on PC in a project, and succesfull solution of possible written tests.

Examination: oral exam, questions are selected from a list of 3 set areas (30+30+40 points). At least a basic knowledge of the terms and their properties is required in each of the areas. Evaluation by points: excellent (90 - 100 points), very good (80 - 89 points), good (70 - 79 points), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points).


Attendance at seminars is compulsory whereas the teacher decides on the compensation for absences.

Aims

The course objective is to make students familiar with the principles of the theory of stochastic processes and models used for their analysis. At seminars, students apply theoretical procedures on simulated or real data using suitable software. The semester is concluded with a project of analysis and prediction of a real stochastic process.

The course provides students with basic knowledge of modeling stochastic processes (time series decomposition, Markov chains, Poisson processes, Queueing theory) and ways to estimate their assorted characteristics in order to describe the mechanism of the process behavior on the basis of its observations. Students learn basic methods used for real data evaluation which might be encountered in logistics.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Brockwell, P.J., Davis, R.A. Introduction to time series and forecasting. 3rd ed. New York: Springer, 2016. 425 s. ISBN 978-3-319-29852-8. (EN)
Grimmett, G., Stirzaker, D.: Probability and random processes. Oxford; New York: Oxford University Press. 2001. (EN)
Tijms, H.C. A First Course in Stochastic Models, John Wiley & Sons, 2003. 478 p. ISBN:9780471498803 (EN)
Shortle, J.F., Thompson, J.M., Gross, D., Harris, C.M. Fundamentals of Queueing Theory, 5th ed. John Wiley & Sons, 2018. 576 p. ISBN: 978-1-118-94352-6  (EN)
Shumway, R., Stoffer, D. Time Series Analysis and Its Applications With R Examples. Springer, 2017. 978-3-319-52452-8. (EN)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N-LAN-A Master's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Mgr. Zuzana Hübnerová, Ph.D.

Syllabus

  1. Stochastic process: types, fundamental properties, stationarity.
  2. Decomposition model and estimation of individual components (smoothing, polynomial regression).
  3. Trend estimation with seasonality. Randomness tests.
  4. Autocorrelation function, partial autocorrelation function, and cross-correlation.
  5. Markov chains I.
  6. Markov chains II.
  7. Random walk, generating functions.
  8. Continuous-time Markov processes.
  9. Poisson processes.
  10. Birth-and-death processes.
  11. Queueing systems.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Zuzana Hübnerová, Ph.D.

Syllabus

  1. Input, storage, and visualization of data, simulation of stochastic processes, queueing systems especially.
  2. Decomposition model and estimation of individual components (smoothing, polynomial regression, Box-Cox transformation).
  3. Trend estimation with seasonality. Randomness tests.
  4. Autocorrelation function, partial autocorrelation function, and cross-correlation.
  5. Markov chains I.
  6. Markov chains II.
  7. Random walk, generating functions.
  8. Continuous-time Markov processes.
  9. Poisson processes.
  10. Birth-and-death processes.
  11. Queueing systems
  12. Tutorials on student projects