Stochastic Models in Logistics (FSI-SEP-A)

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.

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

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.

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.

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

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.

Grimmett, G., Stirzaker, D.: Probability and random processes. Oxford; New York: Oxford University Press. 2001.

Tijms, H.C. A First Course in Stochastic Models, John Wiley & Sons, 2003. 478 p. ISBN:9780471498803