Course: Probabilistic Models

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Course title Probabilistic Models
Course code KEM/PMO
Organizational form of instruction Lecture + Tutorial
Level of course Master
Year of study not specified
Semester Winter and summer
Number of ECTS credits 5
Language of instruction Czech
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Lukáš Ladislav, Doc. RNDr. Ing. CSc.
  • Svoboda Milan, Ing. Mgr. Ph.D.
Course content
Course content : - Introduction to mathematical models in economics. Deterministic and stochastic models. Static and dynamic models. Theory of systems - basics. - Stochastic processes - basics. Markov chains - introduction. - Decision making processes using Markov chains. - Applications of Markov chains in marketing, corporate economics and finance. - Theory of queues, poisson process, waiting line models - basic characteristics. - Simple exponential models - M/M/1, M/M/m. - Other models - closed, with preferences ones, M/G/1. - Optimalization of simple waiting line models M/M/1, M/M/m with cost-oriented objective function. - Inventory theory - overview, basic characteristics. Inventory control optimization models. - Deterministic models - EOQ, POQ, and others. Multi-product inventory models. - Deterministic models - cont. Stochastic models, news-boy problem. - Stochastic models - determination of safety stock under aggregated demand with normal distribution, (Q,r) model, (s,S) model. 13. Stochastic models using theory of queues approach and their optimization.

Learning activities and teaching methods
Individual study, Self-study of literature, Lecture
  • Contact hours - 52 hours per semester
  • Preparation for an examination (30-60) - 60 hours per semester
  • Graduate study programme term essay (40-50) - 40 hours per semester
professional knowledge
Pre-requisities - to pass subjects: Operations research (KEM/OV), and Statistics (KEM/STA).
learning outcomes
Student is able to: - Construct and apply Markov chains with various applications in marketing, business, and finance, - Construct and apply waiting line models with economic applications (e.g. M/M/1, M/M/m, M/M/m/./r, etc.), - Apply various classic inventory models both deterministic and stochastic ones (e.g. news-boy problem, EOQ, POQ, multi-product models, dynamic models with stochastic demand, (Q,r), (s,S) models, etc.), - get basics of sw Mathematica acquainted.
teaching methods
Self-study of literature
Individual study
assessment methods
Combined exam
Seminar work
Recommended literature
  • ANDERSON, D. R. - SWEENEY, D. J. - WILLIAMS, T. A. An Introduction to Manaagement Science - Quantitative Approaches to Decision Making.
  • HUŠEK, R., LAUBER, J. Aplikace stochastických procesů I, učební text. Praha : VŠE, 1986.
  • HUŠEK, R., LAUBER, J. Simulační modely. 1. vyd. Praha : SNTL, 1987.
  • HUŠEK, R., MAŇAS, M. Matematické modely v ekonomii. Vyd. 1. Praha : SNTL, 1989. ISBN 80-03-00098-X.
  • JABLONSKÝ, J. Operační výzkum : kvantitativní modely pro ekonomické rozhodování. 2. vyd. Praha : Professional Publishing, 2002. ISBN 80-86419-42-8.
  • LUKÁŠ, L. Pravděpodobnostní modely v managementu - Markovovy řetězce a systémy hromadné obsluhy. Academia, Praha, 2009. ISBN 978-80-200-1704=8.
  • LUKÁŠ, L. Pravděpodobnostní modely v managementu - Teorie zásob a statistický popis poptávky. Praha, 2012. ISBN 978-80-200-2005-5.
  • MACEK, J., MAINZOVÁ, E. Základní metody operační analýzy. Plzeň : ZČU, 1995. ISBN 80-7082-200-7.
  • RENDER, B., HANNA, M. E., STAIR, R. M. Jr. Quantitative analysis for management. 1eight ed. Upper Saddle River : Prentice Hall, 2003. ISBN 0-13-049543-3.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester