OPF:MMENKEMM Economic and Mathematical Meth - Course Information

MMENKEMM Economic and Mathematical Methods

Extent and Intensity

0/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Jaroslav Ramík, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jaroslav Ramík, CSc.
Department of Informatics and Mathematics – School of Business Administration in Karvina

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)
• 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.
  

Literature

required literature
• RAMÍK, Jaroslav. Ekonomicko-matematické metody (EMM): Pro prezenční a kombinovanou formu studia. Karviná: Slezská univerzita v Opavě, Obchodně podnikatelská fakulta v Karviné, 2008. Výsledek v databázi "Databáze výstupů projektů Operačního programu Vzdělávání pro konkurenceschopnost" info

recommended 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

Teaching methods

One-to-One tutorial
Skills demonstration

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.
Information on the extent and intensity of the course: Přednáška 12 HOD/SEM.

Teacher's information

Written examination, 70% attendance in seminars;

Activity	Difficulty [h]
Konzultace	6
Ostatní studijní zátěž	93
Přednáška	6
Zkouška	40
Summary	145

• Enrolment Statistics (Winter 2013, recent)
  
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