# OPF:INMBAOPA Operational Analysis - Course Information

## INMBAOPA Operational Analysis

**School of Business Administration in Karvina**

Summer 2023

**Extent and Intensity**- 2/1/0. 6 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- Ing. Radomír Perzina, Ph.D. (lecturer)
**Guaranteed by**- Ing. Radomír Perzina, Ph.D.

Department of Informatics and Mathematics - School of Business Administration in Karvina

Contact Person: Mgr. Radmila Krkošková, Ph.D. **Timetable**- Thu 10:35–12:10 A412
- Timetable of Seminar Groups:

*R. Perzina* **Prerequisites**(in Czech)- FAKULTA ( OPF ) && TYP_STUDIA ( B ) && ( FORMA ( P ) || FORMA ( Z ))
**Course Enrolment Limitations**- The course is only offered to the students of the study fields the course is directly associated with.

**fields of study / plans the course is directly associated with**- Economics and Management (programme OPF, B_EME)

**Course objectives**- The aim of this course is to teach the students basic principles of mathematical methods for modeling economical situations. The students should manage theoretical background of selected methods and models and be able to use Microsoft Excel Solver for solving operational analysis problems on PC.
**Syllabus**- 1. Principles and methods of Operational Analysis

History and principles of Operational Analysis, stages in application of Operational Analysis, classification of Operational Analysis branches.

2. Linear programming

Economical and mathematical model, economical meaning of particular parts of mathematical model, basic elements of linear programming (LP), graphic representation of a feasible solutions set of a two-variables LP problem and solving the problem. General economical and mathematical model, base solutions of a linear programming model. The principle of Simplex method, the number of LP problem optimal solutions determination, solving the LP problem by Excel Solver.

3. Duality in linear programming

Duality as a relation between two LP problems, construction of dual problem, relations between primal and dual problem, economical interpretation of optimal solutions of both problems, sensitivity analysis.

4. Application of linear programming

Construction of the mathematical model for the following problems: Cutting stock problem, Nutrition problem, Financial project analysis, Portfolio optimization problem, Production problem, Transportation Problem. Solving the problems by Excel. Interpretation of results.

5. Optimization problems on graphs

Basic elements, basic definitions. Planar graph, complete graph, loop, cycle. Minimal spanning tree algorithm, Eulerian path, the shortest path and maximal flow algorithms.

6. Project Management

Project graph, project analysis by critical path method – CPM. Project analysis by method PERT, basic characteristics of project analysis, i.e. mean value of activity time, standard deviation of activity time, mean value of project completion time and standard deviation of project completion time, probability of finishing the project in planned time.

- 1. Principles and methods of Operational Analysis
**Literature**- HILLIER, F.S., LIEBERMAN, G.J., NAG, B., BASU, P., 2017. Introduction to Operations Research. New York: Mc Graw Hill. ISBN 978-9339221850
- RARDIN, R.L., 2016. Optimization in Operations Research. Cambridge: Pearson. ISBN 978-0134384559

*required literature*- TAHA, H.A., 2016. Operations Research: An Introduction. Cambridge: Pearson. ISBN 978-0134444017
- CARTER, M., Price, C.C., RABADI, G., 2018. Operations Research: A Practical Introduction. Boca Raton: CRC Press. ISBN 978-1498780100
- KOCAY, W., KREHER, D.L., 2016. Graphs, Algorithms, and Optimization. Boca Raton: CRC Press. ISBN 978-1482251166

*recommended literature***Teaching methods**- lectures, seminar classes, class discussion
**Assessment methods**- Compulsory participation in seminars at least 50%, seminar paper (30% evaluation) final examination test (70% evaluation). The minimum required number of points for passing the course is 60% of the total number of points.
**Language of instruction**- English
**Further Comments**- Study Materials

- Enrolment Statistics (recent)

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