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Lecturer(s)
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Stoklasa Jan, Mgr. et Mgr. Ph.D.
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Ženčák Pavel, RNDr. Ph.D.
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Pavlačka Ondřej, RNDr. Ph.D.
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Course content
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1. Historical development of mathematical modeling in Economics; classification of mathematical modelling tools in Economics, basic principles of designing mathematical models in Operations Research. 2. Historical overview of linear programming, general formulation of linear programming problems, applications of linear programming. 3. Formulation of the mathematical model, graphical solution of simple problems. 4. Algorithm of simplex method in standard form and spreadsheet computation. 5. The duality theory in linear programming and its economic interpretation. 6. The transportation problem: Formulation of the problem, special methods for computing the initial and optimal solutions. 7. Integer linear programming: Introduction to principles of basic methods (branch and bound method, cutting plane methods). 8. Graph theory - basic concepts, oriented, evaluated, Euler and Hamilton graphs. 9. Graph theory - finding the shortest path in a graph, vertex and edge colouring of graphs, graph algorithms, flows in networks. 10. Network analysis - activity on arrow models - basic concepts, CPM method. 11. Network analysis - PERT method, time-cost analysis. 12. Network analysis - activity on node models - basic concepts, MPM method.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Demonstration, Projection (static, dynamic)
- Attendace
- 52 hours per semester
- Homework for Teaching
- 30 hours per semester
- Preparation for the Exam
- 40 hours per semester
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Learning outcomes
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The course introduces the theory and methods for solving linear programming problems, the basics of graph theory and network analysis.
Comprehension Understand the basic terms in linear programming and the methods for solution of linear programming problems, graph theory and network analysis. After completing this course, the student will be able to apply the presented methods on real-life problems.
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Prerequisites
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Basic knowledge of mathematical analysis and linear algebra.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: student has to be able to aply the presented mathematical methods to solve given excercies. Exam: student has to understand the presented methods and their theoretical basis.
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Recommended literature
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F. S. Hillier, G. J. Lieberman. (2001). Introduction to operations research, 7th edition. New York.
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G.B. Dantzig. (1963). Linear programming and extensions. North Holland.
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G.B. Dantzig. (1966). Lineárne programovanie a jeho rozvoj. SVTL Bratislava.
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J. Jablonský. (2002). Operační výzkum: kvantitativní metody pro ekonomické rozhodování. Praha.
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J. Volek. (2001). Operační výzkum I. Pardubice.
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J.Plesník, J Dupačová, M. Vlach. (1990). Lineárne programovanie. ALFA, Bratislava.
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J.Švrček. (1995). Lineární programování v úlohách. Vydavatelství UP Olomouc.
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R. Hušek, M. Maňas. (1989). Matematické modely v ekonomii. Praha.
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Ženčák, P. (2013). Lineární programování. Olomouc: Univerzita Palackého v Olomouci.
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