XINM2735 Economic and Mathematical Methods

School of Business Administration in Karvina
Winter 2015
Extent and Intensity
0/0. 5 credit(s).
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 offered to students of any study field.
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.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
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