| Course Unit Code | 342-3344/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| DOR028 | doc. Ing. Michal Dorda, Ph.D. |
| Summary |
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| Graduates of the course will get acquainted with the importance of optimization methods from operational analysis for solving problems of technical and transport practice, with basic optimization tasks and algorithms related to the transport network, with basic types of tasks and algorithms related to traffic planning on transport networks. service systems, the possibilities of their mathematical modeling and determination of their basic operating characteristics. |
| Learning Outcomes of the Course Unit |
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| In transport, there are a number of decision-making tasks that can be effectively addressed using operational analysis tools. The course aims to acquaint students with selected tools that can be used to solve these decision-making tasks. These are tools based on graph theory, linear programming and queing theory. |
| Course Contents |
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1) Introduction to graph theory, basic concepts.
2) Eulerian trail, minimal spanning trees, Hamiltonian paths.
3) Distances in graphs - Floyd's algorithm.
4) Project management - Critical path method.
5) Planning the service of traffic network from one center - Little's algorithm.
6) Localization of emergency centers - Hakimi algorithm.
7) Introduction to linear programming - transport problem.
8) Mathematical model of a transport problem.
9) Algorithm for solving a transport problem.
10) Basic knowledge of probability theory.
11) Introduction to queueing theory, M/M/n/n queueing system.
12) M/M/n/∞ queueing system.
13) M/M/n/m queueing system.
14) Reserve. |
| Recommended or Required Reading |
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| Required Reading: |
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BONDY, John Adrian a MURTY, U. S. R. Graph theory. New York: Springer, c2008. ISBN 978-1-84628-969-9.
CHVÁTAL, Vašek. Linear programming. New York: W.H. Freeman, c1983. ISBN 0-7167-1587-2.
BOLCH, Gunter. Queueing networks and Markov chains: modeling and performance evaluation with computer science applications. 2nd ed. Hoboken: Wiley, c2006. ISBN 0-471-56525-3. |
Studijní opory k předmětu – http://homel.vsb.cz/~dor028/Opory/.
DANĚK, Jan a TEICHMANN, Dušan. Optimalizace dopravních procesů. Ostrava: VŠB - Technická univerzita Ostrava, 2005. ISBN 80-248-0996-6.
FRONC, Martin B. Operačná analýza I. 2. preprac. vyd. Bratislava: Alfa, 1989. ISBN 80-05-00219-X.
JABLONSKÝ, Josef. Operační výzkum: kvantitativní modely pro ekonomické rozhodování. Praha: Professional Publishing, 2002. ISBN 80-86419-23-1.
KLUVÁNEK, Pavol a BRANDALÍK, František. Operační analýza I: teorie hromadné obsluhy. Bratislava: Alfa, 1982.
BONDY, John Adrian a MURTY, U. S. R. Graph theory. New York: Springer, c2008. ISBN 978-1-84628-969-9.
CHVÁTAL, Vašek. Linear programming. New York: W.H. Freeman, c1983. ISBN 0-7167-1587-2.
BOLCH, Gunter. Queueing networks and Markov chains: modeling and performance evaluation with computer science applications. 2nd ed. Hoboken: Wiley, c2006. ISBN 0-471-56525-3.
|
| Recommended Reading: |
|---|
BONDY, John Adrian a MURTY, U. S. R. Graph theory. New York: Springer, c2008. ISBN 978-1-84628-969-9.
CHVÁTAL, Vašek. Linear programming. New York: W.H. Freeman, c1983. ISBN 0-7167-1587-2.
BOLCH, Gunter. Queueing networks and Markov chains: modeling and performance evaluation with computer science applications. 2nd ed. Hoboken: Wiley, c2006. ISBN 0-471-56525-3. |
ČERNÝ, Ján a KLUVÁNEK, Pavol. Základy matematickej teórie dopravy. Bratislava: Veda, 1991. ISBN 80-224-0099-8.
JANÁČEK, Jaroslav. Optimalizace na dopravních sítích. Žilina: Žilinská univerzita, 2002. ISBN 80-8070-031-1.
JANÁČEK, Jaroslav. Matematické programování. 2. opr. vyd. Žilina: Žilinská univerzita, 2003. ISBN 80-8070-054-0.
PASTOR, Otto a TUZAR, Antonín. Teorie dopravních systémů. Praha: ASPI, 2007. ISBN 978-80-7357-285-3.
TUZAR, Antonín, MAXA, Petr a SVOBODA, Vladimír. Teorie dopravy. Praha: Vydavatelství ČVUT, 1997. ISBN 80-01-01637-4. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 35 | 18 |
| Examination | Examination | 65 | 16 |