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Lecturer(s)
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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. Graph theory introduction: Basic definitions. 3. Graphs classification. 4. Optimal path in graphs, network flow. 5. Project management and stockpile management. 6. Linear programming, problem types. 7. Simplex method. 8. Integer problems. 10. Transportation and logistic problems. 11. Assignment problems. 12. Introduction to queueing theory. 13. 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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