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  • Úvod

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    Reg. No. CZ.1.07/2.2.00/28.0326
    Subject: Operations Research
    Form of study: full-time
    Subjetc´s goals: Get the knowledge of the basic principles and methods of mathematical modeling decision situations. Learning to deal with standard linear programming, multi-criteria decision making, game theory and network analysis.
    Learning outcomes:
    • skills:
    • To describe the basic principles of modeling decision problems and their applications in military environments.
    • abilities:
    • To use basic methods for modeling and solving decision problems.
    • competences:
    • Student is able to use and interpret the outcomes of the methods described above.
    Subject continuity: The course builds on knowledge gained in the first semester in Mathematics.
    Conditions for successful completion of the course:
    • Written and oral examination of the substances specified subject content.
    Basic literature:
    • ŠMEREK, M., MOUČKA, J. Ekonomicko–matematické metody. Brno: UO, 2008, 122 s. ISBN 978-80-7231-526-0.
    • MOŠOVÁ, V. Lineární programování. Vyškov: VVŠ PV, 1996.
    • HOLOUBEK, J. Ekonomicko-matematické metody. Brno: MZLU, 2006, 153 s. ISBN 80-7157-970-X.
    • MOUČKA, J. Úvod do teorie her. VVŠ PV: Vyškov, 1998, 104 s. ISBN 80-7231-024-0.
    • KOŘENÁŘ, V., FIALA, P. Optimální programování. VŠE: Praha, 1998.
    Recommended readings:
    • JABLONSKÝ, J. Operační výzkum. Praha: VŠE, 2001.
    • FIALA, P., JABLONSKÝ, J., MAŇAS, M. Vícekriteriální rozhodování. VŠE: Praha, 1994, 316 s. ISBN 80-7079-748-7.

  • Téma 1

    Mathematical modeling.

    Linear programming problems.

    • Mathematical modeling Soubor PDF
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      Introduction to linear programming problems

      Mathematical Principles of linear programming

      • The system of linear equations

      Graphical method for solving linear programming problems

      412.0 KB
    • Mathematical modeling – exercise. Soubor PDF
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      Mathematical Principles of linear programming

      • The system of linear inequalities

      Formulation of linear programming problems

      • The production planning problem
      • Mixing problem
      • Partition problem

      Graphical method - examples

      513.1 KB

  • Téma 2

    The simplex method

    • The simplex method. Soubor PDF
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      The simplex method

      Method of articifial variables

      402.3 KB
    • The simplex method – exercise. Soubor PDF
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      Simplex method – examples

      Method of artificial variables – examples

      262.2 KB

  • Téma 3

    Duality in Linear Programming.

    • Duality in Linear Programming. Soubor PDF
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      The concept of duality and the construction of a dual problem

      The dual simplex method

      340.9 KB
    • Duality in linear programming – exercise. Soubor PDF
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      Duality in linear programming - Exercise

      Problems on using of the dual simplex method

      260.7 KB

  • Téma 4

    Balanced Transportation Problem.

  • Téma 5

    Unbalanced Transportation Problem.

    • Unbalanced transportation problem. Soubor PDF
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      Unbalanced transportation problem and properties of solutions:

      • Degenerate solution of transportation problem
      • Alternativ solution of transportation problem
      • Nonbasic optimal solution
      • Unbalanced transportation problem
      321.4 KB
    • Unbalanced transportation problem – exercise. Soubor PDF
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      Degenerate and alternative solution of transportation problems – examples

      Unbalanced transportation problem – examples

      239.3 KB

  • Téma 6

    Assignment problem.

    • The assignment problem. Soubor PDF
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      The assignment problem of minimization type

      The assignment problem of maximization type

      277.7 KB
    • The assignment problem – exercise. Soubor PDF
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      The assignment problems of minimization type – examples

      The assignment problems of maximization type – examples

      268.4 KB

  • Téma 7

    Multi-criteria evaluation of alternatives.

  • Téma 8

    Multicriterial programming.

    • Multicriterial programming. Soubor PDF
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      Multicriterial programming

      • The method of aggregation of objective functions
      • Lexicographical method
      • Method of goal programming
      379.0 KB
    • Multicriteria programming – exercise. Soubor PDF
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      • The lexicographical method – examples
      • The method of aggregation of objective functions – examples
      • The method of goal programming – examples
      254.7 KB

  • Téma 9

    Game Theory.

    • Game Theory. Soubor PDF
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      Game Theory – introduction

      The matrix games

      Matrix games solved in the field of pure of strategies

      291.3 KB
    • Matrix games − mixed strategies. Soubor PDF
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      The Matrix games solved in the field of mixed strategies:

      • The matrix games of type 2 × 2
      • The principle of dominating
      • The matrix games of type 2 × n and m × 2. Graphical method.
      429.3 KB

  • Téma 10

    Game Theory.

    • Linear programming in matrix games. Soubor PDF
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      Matrix games in general case

      Matrix games solved by converting to linear programming problem

      230.3 KB
    • Matrix games generally solved – exercise. Soubor PDF
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      Matrix games solved by converting to LP problem – examples

      Matrix games generally solved – examples

      303.1 KB

  • Téma 11

    Graph theory.

    • Graph theory. CPM method. Soubor PDF
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      Basic terms of graph theory

      Critical Path Method

      255.2 KB
    • CPM method – exercise. Soubor PDF
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      CPM method – examples

      201.6 KB

  • Téma 12

    Method PERT.

    • Method PERT Soubor PDF
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      Method PERT (Program Evaluation Review Technique).

      195.3 KB
    • PERT method – exercise. Soubor PDF
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      PERT method – example

      165.8 KB