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Lecturer(s)
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Prokop Roman, prof. Ing. CSc.
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Hrabec Dušan, Ing. Ph.D.
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Cerman Zbyněk, Mgr. Ph.D.
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Course content
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1. Operational research: Introduction and models. 2. Linear programming: problem types, one-phase simplex method. 3. Two-phase simplex method. 4. Dual problem. 5. Transportation problem: balanced. 6. Transportation problem: unbalanced. 7. Graph theory introduction: Basic definitions. 8. Graphs classification. 9. Optimal path in graphs, network flow. 10. Project management: network graph construction, CPM methods. 11. Project management: resource analysis. 12. Introduction to queueing theory. 13. Optimization of mass service systems. 14. Illustration of applications and existing software (GAMS, AMPL, Wolfram Mathematica, Matlab, Arena).
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Learning activities and teaching methods
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Lecturing, Practice exercises
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| prerequisite |
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| Knowledge |
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| Standard knowledge and abilities gained in high school mathematical courses and university mathematics in the first year of the study (e.g., elementary functions, linear algebra and differential calculus). |
| Standard knowledge and abilities gained in high school mathematical courses and university mathematics in the first year of the study (e.g., elementary functions, linear algebra and differential calculus). |
| learning outcomes |
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| For the course completion, students should gain and prove the following abilities: - mathematically assess and formulate a given problem, - to choose a suitable solution approach, - to solve the problem. |
| For the course completion, students should gain and prove the following abilities: - mathematically assess and formulate a given problem, - to choose a suitable solution approach, - to solve the problem. |
| assess and formulate a given problem and its mathematical model |
| assess and formulate a given problem and its mathematical model |
| Characterize and analyze assigned tasks and suggest, know solution approaches |
| Characterize and analyze assigned tasks and suggest, know solution approaches |
| Know the principles and categories of mathematical optimization (e.g., linear and integer programming and their properties) and know to assign the problem to a particular class of mathematical optimization |
| Know the principles and categories of mathematical optimization (e.g., linear and integer programming and their properties) and know to assign the problem to a particular class of mathematical optimization |
| Know solution approaches and, based on properties of the mathematical model, suggest a solution approach, and alternatively solve the problem |
| Know solution approaches and, based on properties of the mathematical model, suggest a solution approach, and alternatively solve the problem |
| to know basic principles of graph theory |
| to know basic principles of graph theory |
| know to assess and solve the transportation problem |
| know to assess and solve the transportation problem |
| know principles and methods for project management |
| know principles and methods for project management |
| Skills |
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| Classify areas and problems of operations research |
| Classify areas and problems of operations research |
| Characterize and analyze assigned tasks and suggest a solution approach |
| Characterize and analyze assigned tasks and suggest a solution approach |
| Create a mathematical model of the assigned problem from mathematical optimization (especially in linear and integer programming) and assign the problem to a particular class of mathematical optimization |
| Create a mathematical model of the assigned problem from mathematical optimization (especially in linear and integer programming) and assign the problem to a particular class of mathematical optimization |
| Know, based on properties of the mathematical model, to suggest a solution approach and to solve the problem |
| Know, based on properties of the mathematical model, to suggest a solution approach and to solve the problem |
| To know some selected at least basic solvers and software used to solve optimization problems |
| To know some selected at least basic solvers and software used to solve optimization problems |
| use graph theory for the description of given problems |
| use graph theory for the description of given problems |
| create and solve selected problems spanning to "project management" category |
| create and solve selected problems spanning to "project management" category |
| teaching methods |
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| Knowledge |
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| Lecturing |
| Lecturing |
| Practice exercises |
| Practice exercises |
| assessment methods |
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| Composite examination (Written part + oral part) |
| Composite examination (Written part + oral part) |
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Recommended literature
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ČERNÝ, J. a ČERNÁ, A. Manažerské rozhodování o dopravních systémech. Univerzita Pardubice, 2014. ISBN 978-80-7395-849-7.
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DUPAČOVÁ, J. a LACHOUT, P. Úvod do optimalizace. MFF UK v Praze, 2011. ISBN 978-80-7378-176-7.
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GHIANI, G., LAPORTE, G. a MUSMANO, R. Introduction to Logistics Systems Planning and Control. John Wiley & Sons, 2005. ISBN 978-04-7001-404-2.
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HRABEC, D. Optimalizace, studijní materiály, přednáškové slidy. Zlín, 2018.
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KUBIŠOVÁ, A. Operační výzkum. Vysoká škola polytechnická Jihlava, 2014. ISBN 978-80-87035-83-2.
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NOVOTNÝ, J. Základy operačního výzkumu. FAST VUT v Brně, 2006.
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VOLEK, J. LINDA,B. Teorie grafů - Aplikace v dopavě a veřejné správě. Univerrzita Pardubice, 2012. ISBN 978-80-7395-225-9.
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