INMPOAN Operational Analysis

School of Business Administration in Karvina
Winter 2018
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
Ing. Elena Mielcová, Ph.D. (lecturer)
prof. RNDr. Jaroslav Ramík, CSc. (lecturer)
Ing. Elena Mielcová, Ph.D. (seminar tutor)
Ing. Radomír Perzina, Ph.D. (seminar tutor)
prof. RNDr. Jaroslav Ramík, CSc. (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 offered to students of any study field.
Course objectives (in Czech)
Poskytnout základní matematické metody k modelování ekonomických situací. Zvládnout teoretický základ vybraných metod a modelů a naučit se používat Excel Solver k řešení úloh operačního výzkumu na personálním počítači.
Syllabus
  • 1. Principles and methods of Operational Analysis
    2. Linear programming: Introduction
    3. Economical and mathematical model of a linear programming problem, base solutions
    4. Linear programming: Solution
    5. Duality in linear programming models
    6. Integer linear programming
    7. Transportation problem
    8. Application of linear programming
    9. Graph Theory: basic principles and definitions
    10. Optimization problems on graphs: the shortest path and maximal flow algorithms
    11. Project management 1: Time analysis
    12. Project management 2: PERT
    13. Project management 3: Costs and sources
    1. Principles and methods of Operational Analysis
    History and principles of Operational Analysis, stages in application of Operational Analysis, classification of Operational Analysis branches.
    2. Linear programming: Introduction
    Economical and mathematical model, economical meaning of particular parts of mathematical model, basic elements of linear programming (LP), graphic representation of a feasible solutions set of a two-variables LP problem and solving the problem.
    3. Economical and mathematical model of a linear programming problem, base solutions
    General economical and mathematical model, economical meaning of particular parts of mathematical model, base solutions of a linear programming model
    4. Linear programming: Solution
    The principle of Simplex method, the number of LP problem optimal solutions determination, solving the LP problem by Excel Solver and QSB
    5. Duality in linear programming
    Duality as a relation between two LP problems, construction of dual problem, relations between primary and dual problem, economical interpretation of optimal solutions of both problems, sensitivity analysis.
    6. Integer linear programming
    Importance of integer and binary conditions, existence of integer optimal solution, assignment problem, basic principles of solving integer programming problems, solving the integer linear programming problem by Excel Solver and QSB.
    7. Transportation problem.
    Economical model of the transportation problem, mathematical model of the transportation problem, initial solution of the transportation problem, application of the transportation problem for production scheduling, solving the problem by Excel and QSB.
    8. Application of linear programming
    Construction of the mathematical model for the following problems: Cutting stock problem, Nutrition problem, Financial project analysis, Portfolio optimization problem, Production problem. Solving the problems by Excel and QSB. Interpretation of results.
    9.Graph Theory: basic principles and definitions
    Graph theory: basic elements, basic definitions, minimal spanning tree algorithm, Eulerian path .
    10. Optimization problems on graphs: the shortest path and maximal flow algorithms
    Shortest route and maximal flow problem, solving graph optimization problems by QSB.

    11. Project management 1: Time analysis
    Project graph, project analysis by critical path method - CPM
    12. Project management 2: PERT
    Project analysis by method PERT, basic characteristics of project analysis, i.e. mean value of activity time, standard deviation of activity time mean value of project completion time and standard deviation of project completion time, probability of finishing the project in planned time.
    13. Project management 3: Costs and sources, node
    Costs of activity realization, basic costs models, costs optimization of simple network project manually and by computer program QSB, problems of aggregation and desegregation of network graphs, possibilities of node evaluated network graphs.
Literature
    required literature
  • RAMÍK, J., ČEMERKOVÁ, Š., MIELCOVÁ, E. Operační analýza pro ekonomy. Karviná, OPF SU, 2004. ISBN 80-7248-199-3. info
    recommended literature
  • JABLONSKÝ, J. Operační výzkum. Praha: VŠE, 1996. info
  • UNČOVSKÝ, L. a kol. Modely sieťovej analýzy. ALFA, Bratislava, 1991. info
  • KOLÁŘ, J., ŠTĚPÁNKOVÁ, O., CHYTIL, M. Logika, algebry a grafy. SNTL, Praha, 1989. info
  • HUŠEK, R., MAŇAS, M. Matematické modely v ekonomii. Praha: SNTL, 1989. info
  • LAŠČIAK, A. a kol. Optimálne programovanie. Bratislava: SNTL/ALFA, 1983. info
  • BECK, J., LAGOVÁ, M., ZELINKA, J. Lineární modely v ekonomii. Praha: SNTL/ALFA, 1982. info
  • MAŇAS, M. Optimalizační metody. Praha: SNTL, 1979. info
  • WALTER, J. a kol. Operační výzkum. Praha: SNTL, 1973. info
Teaching methods
Skills demonstration
Seminar classes
Assessment methods
Written exam
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2014, Winter 2015, Winter 2016, Winter 2017.
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