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Lecturer(s)
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Trnka David, Prof. Dr. Ing.
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Course content
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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. Stochastic models using theory of queues approach and their optimization.
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Learning activities and teaching methods
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Individual study, Self-study of literature, Lecture
- Contact hours
- 52 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
- Graduate study programme term essay (40-50)
- 40 hours per semester
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| prerequisite |
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| Knowledge |
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| to pass subjects Operations research and Statistics. |
| Skills |
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| N/A |
| Competences |
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| N/A |
| learning outcomes |
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| Knowledge |
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| get basics of sw Mathematica acquainted. |
| 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.) |
| Skills |
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| N/A |
| Competences |
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| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Self-study of literature |
| Individual study |
| Skills |
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| Lecture |
| Competences |
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| Lecture |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Seminar work |
| Skills |
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| Combined exam |
| Competences |
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| Combined exam |
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Recommended literature
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ANDERSON, D. R. - SWEENEY, D. J. - WILLIAMS, T. A. An Introduction to Manaagement Science - Quantitative Approaches to Decision Making.
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LUKÁŠ, L. Pravděpodobnostní modely některých manažerských úloh. Plzeň : Západočeská univerzita, 2005. ISBN 80-7043-402-3.
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LUKÁŠ, L. Pravděpodobnostní modely v managementu - Markovovy řetězce a systémy hromadné obsluhy. Academia, Praha, 2009. ISBN 978-80-200-1704=8.
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LUKÁŠ, L. Pravděpodobnostní modely. Plzeň : Západočeská univerzita, 2005. ISBN 80-7043-388-4.
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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.
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