Course detail
Stochastic Models in Logistics
FSI-SEP-A Acad. year: 2025/2026 Summer semester
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.
Supervisor
Department
Learning outcomes of the course unit
Prerequisites
Rudiments of probability theory and mathematical statistics, linear regression models.
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
English
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.
Specification of controlled education, way of implementation and compensation for absences
The study programmes with the given course
Programme N-LAN-A: Logistics Analytics, Master's
branch ---: no specialisation, 5 credits, compulsory
Type of course unit
Lecture
26 hours, optionally
Syllabus
- Stochastic process: types, fundamental properties, stationarity.
- Decomposition model and estimation of individual components (smoothing, polynomial regression).
- Trend estimation with seasonality. Randomness tests.
- Autocorrelation function, partial autocorrelation function, and cross-correlation.
- Markov chains I.
- Markov chains II.
- Random walk, generating functions.
- Continuous-time Markov processes.
- Poisson processes.
- Birth-and-death processes.
- Queueing systems.
Computer-assisted exercise
26 hours, compulsory
Syllabus
- Input, storage, and visualization of data, simulation of stochastic processes, queueing systems especially.
- Decomposition model and estimation of individual components (smoothing, polynomial regression, Box-Cox transformation).
- Trend estimation with seasonality. Randomness tests.
- Autocorrelation function, partial autocorrelation function, and cross-correlation.
- Markov chains I.
- Markov chains II.
- Random walk, generating functions.
- Continuous-time Markov processes.
- Poisson processes.
- Birth-and-death processes.
- Queueing systems
- Tutorials on student projects