# OPF:INMNPEMM Economic and Mathematical Meth - Course Information

## INMNPEMM Economic and Mathematical Methods

**School of Business Administration in Karvina**

Winter 2017

**Extent and Intensity**- 2/1/0. 5 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Jaroslav Ramík, CSc. (lecturer)

Ing. Radomír Perzina, Ph.D. (seminar tutor)

prof. RNDr. Jaroslav Ramík, CSc. (seminar tutor)

Ing. Filip Tošenovský, Ph.D. (seminar tutor) **Guaranteed by**- prof. RNDr. Jaroslav Ramík, CSc.

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

Contact Person: Mgr. Radmila Krkošková, Ph.D. **Prerequisites**(in Czech)- K absolvování předmětu nejsou vyžadovány žádné podmínky a předmět může být zapsán nezávisle na jiných předmětech.
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Business Economics in Trade and Services (programme OPF, N_EKOMAN)
- Managerial Informatics (programme OPF, N_SYSINF)
- Marketing and Management (programme OPF, N_EKOMAN)

**Course objectives**- The objective is to provide a deeper insight in exact methods of economic modelling, theoretical tools of selected methods and models, related especially to optimization techniques of mathematical modelling and its applications in economic disciplines, and to teach known software including Excel for solving such problems.
**Syllabus**- 1. What are economic mathematical methods (EMM)

2. Mathematical tools of EMM

3. Optimization problems, function extremes

4. Mathematical programming

5. Linear programming

6. Transportation problem, assignment problem

7. Multicriteria and goal programming

8. Data Envelopment Analysis (DEA)

9. Assessment of production unit efficiency, using DEA

10. Mathematical methods for portfolio optimization

11. Sharpe's, Markowitz's and index portfolio models

12. Optimization problems in graphs

13. Time and Resource analysis of projects

1. Economic mathematical models (EMM)

Mathematics and economics, model classification, mathematical tools as a language for modelling economic phenomena.

2. Mathematical tools of EMM

Functions of one and several real variables, matrix and its inverse, vectors, sets of linear equations with n unknown variables, mathematical functions in MS Excel.

3. Optimization problems, function extremes

Optimization problems, mathematical programming, equivalent forms of problems, local and global extremes, existence of the solution to an optimization problem

4. Mathematical programming

Convex and concave functions, sets, saddle points, Kuhn-Tucker conditions, duality in mathematical programming

5. Linear programming

Linear programming, optimal resource allocation, basic solution, (non)degenerated solution, one-phase and two-phase Simplex method.

6. Transportation problem, assignment problem

Primary and dual LP problems, duality, transportation problem, assignment problem, examples of real applications.

7. Multicriteria and goal programming

Multicriteria programming, goal programming, non-dominated solution, Pareto solution, scalarization.

8. Data Envelopment Analysis (DEA)

Homogeneous production units, efficiency, DEA, constant and varying returns to scale, CRS model, VRS model, orientation on inputs, orientation on outputs, superefficiency.

9. Assessment of production unit efficiency, using DEA

Application of the DEA Frontier plug-in for Excel to assess production unit efficiency

10. Mathematical methods for portfolio optimization

Portfolio optimization, yield, risk, efficient frontier, efficient portfolio, stochastic portfolio model.

11. Sharpe's, Markowitz's and index portfolio models

Sharpe's model, Markowitz's model, single-index model, beta coefficient, application of Excel Solver for portfolio optimization.

12. Optimization problems in graphs

Graph, network, minimum spanning tree, the shortest path in a graph, maximum flow problem. Example applications of the methods.

13. Time and Resource analysis of projects

Network diagram, CPM method, PERT method, MPM method. Example applications of the methods.

- 1. What are economic mathematical methods (EMM)
**Literature**- RAMÍK, J.
*Ekonomicko-matematické metody*. Karviná, OPF SU, 2008. info

*required literature*- KLEIN, M. W.
*Mathematical methods for economics*. McGraw-Hill, 2009. ISBN 9780071635325. info - RAMÍK, J., PERZINA, R.
*Moderní metody hodnocení a rozhodování*. Karviná : SU v Opavě, OPF v Karviné, 2008. ISBN 978-80-7248-497-3. info - RAMÍK, J., ČEMERKOVÁ, Š., MIELCOVÁ, E.
*Operační analýza pro ekonomy*. Karviná, OPF SU, 2004. ISBN 80-7248-199-3. info - JABLONSKÝ, J.
*Operační výzkum: kvantitativní modely pro ekonomické rozhodování*. Praha : Professional Publishing, 2002. ISBN 80-86419-23-1. info

*recommended literature*- RAMÍK, J.
**Teaching methods**- Skills demonstration

Seminar classes **Assessment methods**- Written exam

Written test **Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- https://elearning.opf.slu.cz/course/view.php?id=608

Written examination, 70% attendance in seminars.Activity Difficulty [h] Ostatní studijní zátěž 66 Přednáška 26 Seminář 13 Zkouška 40 **Summary**145

- Enrolment Statistics (Winter 2017, recent)
- Permalink: https://is.slu.cz/course/opf/winter2017/INMNPEMM