OPF:MMENAEMM Economic and Mathematical Meth - Course Information

MMENAEMM Economic and Mathematical Methods

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

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

• Economy of Enterprise in Trade and Services (programme OPF, N_EKOMAN)
• Managerial Informatics (programme OPF, N_SYSINF)

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, 2009. ISBN 9780071635325. info
• WISNIIEWSKI, M. Quantitative Methods for Decision Makers. London: Pitman Publishing, 1997. ISBN 0-273-62404-0. info

Teaching methods

Skills demonstration
Seminar classes

Assessment methods

Written exam
Written test

Language of instruction

English

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.

Activity	Difficulty [h]
Ostatní studijní zátěž	66
Přednáška	26
Seminář	13
Zkouška	40
Summary	145

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