Operations Research

The aim of the course is to acquaint students with mathematical modelling in management and with the most useful mathematical methods of management science. The first part of the course is devoted to linear optimization (the simplex method, duality in linear programming, multiple criteria optimization). The contents of the second part of the course are project management (network diagrams, critical paths, time analysis of deterministic and stochastic projects, time-cost and time-resource analysis of deterministic projects).

Credit Requirements:
Duly submission of seminar works and at least 40 percent of points from each of two credit tests relating to the seminar works.

Examination Requirements:
The exam has two parts - written and oral ones. In the written part, students have to show that they can recognise types of optimization problems, to choose suitable methods to solve them and suggest a suitable solution. To pass this part it is necessary to obtain at least 50 percent of points from the test. The written part could be forgiven if the student has at least 65 percent of points from the credit tests. The oral examination is focused on work with PC and discussions about the solution of the written part of the examination. The final mark is based on the results of the credit tests, the written and oral parts of the examination. To pass the oral part it is necessary to answer at least one of three questions.

1. Introduction to Operations Research and Linear Optimization (LO). Formulation of different types of LO problems.
2. Graphical solution of LO problems, incl. conditions passing through the origin. Different types of feasible sets.
3. The Simplex Method. Interpretation of a result, SW for LO models.
4. The interpretation of LO models results - in a Simplex method table, in SW. Post-optimization analysis.
5. Introduction to Multiple-criteria Decision Making (MCDM). Basic terms and data preparation.
6. Weights construction methods.
7. The basic methods of MCDM and the software for MCDM.
8. Data Envelopment Analysis (DEA) - introduction and graphical solution of basic models.
9. LP models for DEA problems.
10. A solution of DEA problems with software and post-optimization analyses.
11. Project Analysis, Network Analysis - displaying of the project.
12. Deterministic projects. Critical Path Method (CPM). Critical activities, time reserves.
13. Stochastic projects - PERT, assumptions for PERT. Post-optimization analysis in PERT.
14. Cost and source optimization of the projects. Time-cost trade-offs-crashing, incl. SW.

Equivalence: Operační výzkum OA, KOA

Students will be able to create models of particular optimization problems from every-day life, to choose appropriate mathematical models and to use software to suggest the optimal solutions and explain and implement it.

• Garanti: doc. RNDr. Jana Klicnarová, Ph.D.
• Přednášející: Mgr. Michal Houda, Ph.D., doc. RNDr. Jana Klicnarová, Ph.D.
• Cvičící: Mgr. Tomáš Roskovec, Ph.D.

• https://moodle.ef.jcu.cz/course/view.php?id=1676
• TZENG, Gwo-Hshiung; HUANG, Jih-Jeng. Multiple attribute decision making: methods and applications. CRC press, 2011.
• Chinneck, John W. Practical Optimization: A Gentle Introduction. Online text.
• VANĚČKOVÁ, E. Ekonomicko-matematické metody. České Budějovice: ZF JU, 1996.
• kol. http://moodle.ef.jcu.cz/course/view.php?id=195 pro prezenční studium.
• HILLIER F. S., LIEBERMAN G. J. Introduction to Operations Research. New York: McGraw-Hill, 2000, 2005, 2010 (kapitoly 1-6 a 9-10).
• JABLONSKÝ, J. Operační výzkum. Praha: VŠE, 1998.
• Leitmanová Faltová, I., Klufová, R., Freibelová, J., Klicnarová, J. Regionální rozvoj - přístupy a nástroje. Praha, 2012. ISBN 978-80-87197-58-5.

Monologická (výklad, přednáška, instruktáž), Dialogická (diskuze, rozhovor, brainstorming), Práce s multimediálními zdroji (texty, internet, IT technologie), Blended learning

Ústní zkouška, Test