Lecturer(s)


Stoklasa Jan, Mgr. et Mgr. Ph.D.

Ženčák Pavel, RNDr. Ph.D.

Talašová Jana, doc. RNDr. CSc.

Course content

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, timecost analysis. 12. Network analysis  activity on node models  basic concepts, MPM method.

Learning activities and teaching methods

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

Learning outcomes

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 reallife problems.

Prerequisites

Basic knowledge of mathematical analysis and linear algebra.

Assessment methods and criteria

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.

Recommended literature


F. S. Hillier, G. J. Lieberman. (2001). Introduction to operations research, 7th edition. New York.

G.B. Dantzig. (1963). Linear programming and extensions. North Holland.

G.B. Dantzig. (1966). Lineárne programovanie a jeho rozvoj. SVTL Bratislava.

J. Jablonský. (2002). Operační výzkum: kvantitativní metody pro ekonomické rozhodování. Praha.

J. Volek. (2001). Operační výzkum I. Pardubice.

J.Plesník, J Dupačová, M. Vlach. (1990). Lineárne programovanie. ALFA, Bratislava.

J.Švrček. (1995). Lineární programování v úlohách. Vydavatelství UP Olomouc.

R. Hušek, M. Maňas. (1989). Matematické modely v ekonomii. Praha.

Ženčák, P. (2013). Lineární programování. Olomouc: Univerzita Palackého v Olomouci.
