## INMNPEMM Economic and Mathematical Methods

Winter 2015
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
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.
Literature
recommended literature
• KLEIN, M. W. Mathematical methods for economics. McGraw-Hill. ISBN 9780071635325. 2009. info
• RAMÍK, J., PERZINA, R. Moderní metody hodnocení a rozhodování. Karviná : SU v Opavě, OPF v Karviné. ISBN 978-80-7248-497-3. 2008. info
• RAMÍK, J., ČEMERKOVÁ, Š., MIELCOVÁ, E. Operační analýza pro ekonomy. Karviná, OPF SU. ISBN 80-7248-199-3. 2004. info
• JABLONSKÝ, J. Operační výzkum: kvantitativní modely pro ekonomické rozhodování. Praha : Professional Publishing. ISBN 80-86419-23-1. 2002. info
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
Written examination, 70% attendance in seminars.
ActivityDifficulty [h]
Ostatní studijní zátěž66
Přednáška26
Seminář13
Zkouška40
Summary145
The course is also listed under the following terms Winter 2014, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023, Winter 2024.
• Enrolment Statistics (Winter 2015, recent)