| Course Unit Code | 157-0574/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Choice-compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | English |
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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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| ZAP149 | doc. Mgr. Ing. František Zapletal, Ph.D. |
| Summary |
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| The student will get acquainted with the methodological knowledge of application system disciplines, especially in the areas of linear programming, structural analysis and network analysis. The application of selected quantitative methods strengthens students' logical and systemic thinking skills in solving decision-making problems in economic systems. |
| Learning Outcomes of the Course Unit |
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| The aim of the course is methodological knowledge as systemic application of discipline, especially in the areas of linear programming and network analysis. The application of selected quantitative methods reinforces students' logical and systemic skills in solving decision-making problems in economic systems. |
| Course Contents |
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1. Operation research as a systemic basis for quantitative decision making. Development and systemic features of operation research. Process of economic-mathematical modeling. Classification of operation research methods, usability in solving economic problems.
2. Introduction to linear programming (LP) + general solution of optimization problem + parts of mathematical model + set of possible solutions + possible number of solution of LP + different types of LP.
3. Graphical solution of LP problem - general procedure, limitations for using graphical solution, possible sets of acceptable solutions, consequences of limitation of the equation in models, sensitivity analysis of optimum in graphical solution, possible solutions of LP problems.
4. Canonical form of LP problem, simplex table, algorithm of solution for single-phase and two-phase simplex method, individual steps of simplex method, interpretation of simplex tables.
5. Duality of LP problem - the importance of duality, basic theorems on duality, symmetric and asymmetric dual models, shadow prices and their use for sensitivity analysis, solution stability intervals.
6. Transport problems - specification of traffic problems, classification of traffic problems, searching for acceptable solution (VAM, MSR, IM), search for optimal solution - MODI.
7. Multicriterial linear programming - motivation and application, solution dominance, aggregation of purpose functions according to defined weights, tasks with compromise solution.
8. Introduction to network analysis (SA) and graph theory - embedding in the framework of project management, target and possibility of application, classification and definition of network analysis methods, project specification and network graph creation, fictional edges.
9. CPM - time analysis in network graph, types of reserves and their importance, critical path and its analysis, percentage of criticality and possibilities of use from the perspective of risk management, project criticism, linear diagram, analysis of project resources.
10. PERT method - stochastic time analysis, density of activity duration distribution and mean and variability characteristics, density distribution of the earliest possible end date of the whole project and corresponding characteristics, typical problem of using PERT method.
11. Input-output analysis - visualization of the system (elements and flows), basic logic and assumptions.
12. Input-output analysis - chess board tables, equilibria in Leontief's models (sales and inputs), applications. |
| Recommended or Required Reading |
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| Required Reading: |
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HILLIER, Frank and Mark HILLIER. Introduction to Management Science, McGraw-Hill Interamericana de Espaňa S.L., 6th Edition, 2021. 642 p. ISBN: 9781260091854.
WINSTON, Wayne L. and S. Christian ALBRIGHT. Practical Management Science, Cengage Learning, 6th Edition, 2018. 888 p. ISBN: 9781337406659.
ANDERSON, David R., SWEENEY, Dennis J., WILLIAMS, Thomas A., CAMM, Jeffrey D. and James J. COCHRAN. An Introduction to Management Science: Quantitative Approach, Cengage Learning, 15th Edition, 2018. 912 p. ISBN: 9781337406529. |
ŠUBRT, Tomáš a kol. Ekonomicko-matematické metody. 3. upravené a rozšířené vydání. Plzeň: Vydavatelství a nakladatelství Aleš Čeněk, s.r.o., 2019. 354 stran. ISBN 978-80-7380-762-7.
JANOVÁ, Jitka a KOLMAN, Pavel. Vybrané kapitoly z operačního výzkumu. Třetí vydání. Brno: Mendelova univerzita v Brně, 2018. 113 s. ISBN 978-80-7509-546-6.217. ISBN 978-80-248-0190-2.
JABLONSKÝ, Josef. Operační výzkum: kvantitativní modely pro ekonomické rozhodování. Praha: Professional Publishing, 2007. 323 s. ISBN 978-80-86946-44-3. |
| Recommended Reading: |
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TAYLOR, Bernard. Introduction to Management Science, 13th Edition, Pearsons, 2018. 864 p. ISBN 978-978-0134730660.
ISICHENKO, Michael. Quantitative Portfolio Management: The Art and Science of Statistical Arbitrage, 1st Edition, Wiley, 2021. 304 p. ISBN 978-1119821328.
HANEVELD KLEIN, K. Willem, VLERK van der, H. Maarten and Ward ROMEIJNDERS. Stochastic Programming: Modeling Decision Problems Under Uncertainty, 1st Edition, Springer, 2020. 261 p. ISBN 978-3030292218. |
KOLMAN, Pavel, JANOVÁ, Jitka a ŠÁCHA, Jakub. Vybrané kapitoly z operačního výzkumu: cvičebnice. Třetí vydání. Brno: Mendelova univerzita v Brně, 2018. 126 stran. ISBN 978-80-7509-545-9.
KUBIŠOVÁ, Andrea. Operační výzkum. 1. vyd. Jihlava: Vysoká škola polytechnická Jihlava, 2014. 178 s. ISBN 978-80-87035-83-2. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Other activities |
| Assesment methods and criteria |
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| Tasks are not Defined |