MMEBAOAN Operational Analysis for Economists

School of Business Administration in Karvina
Winter 2013
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jaroslav Ramík, CSc. (lecturer)
Ing. Elena Mielcová, Ph.D. (seminar tutor)
Ing. Radomír Perzina, 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
Course objectives
The course objective is to teach the students basic principles of mathematical methods for modeling economical situations. The students should manage theoretical background of selected methods and models and be able to use Excel Solver and the program QSB for solving operational analysis problems on PC.
Syllabus
  • 1. Principles and methods of Operational Analysis
    2. Economical and mathematical model of a linear programming problem and its graphical interpretation
    3. Solving the linear programming problem
    4. Application of linear programming
    5. Duality in linear programming
    6. Transportation problem
    7. Integer linear programming
    8. Optimization problems on graphs
    9. Project management 1: Time analysis
    10. Project management 2: PERT, GERT
    11. Project management 3: Costs and sources, node evaluated network graphs
    12. Queuing models
    1. Principles and methods of Operational Analysis
    Principles of Operational Analysis, stages in application of Operational Analysis, classification of Operational Analysis branches.
    2. Economical and mathematical model of a linear programming problem and its graphical interpretation
    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. Solving the linear programming problem
    The principle of Simplex method, the number of LP problem optimal solutions determination, solving the LP problem by Excel Solver and QSB.
    4. 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.
    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. 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.
    7. 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.
    8. Optimization problems on graphs
    Graph theory basic elements, minimal spanning tree, shortest route and maximal flow problem, solving graph optimization problems by QSB.

    9. Project management 1: Time analysis
    Project graph, project analysis by critical path method - CPM manually and by the computer program QSB.
    10. Project management 2: PERT, GERT
    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.
    11. Project management 3: Costs and sources, node evaluated network graphs
    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.
    12. Queuing models
    Queuing systems, characteristics and structure of queuing systems, simple exponential queuing model - M/M/1, exponential model with parallel lines - M/M/c, optimization of queuing models, solving of queuing systems with QSB.
Literature
    recommended literature
  • ALEVRAS, D., PADBERG, M. W. Linear Optimization and Extensions Problems and Solutions. Berlin: Springer, 2001. ISBN 3-540-41744-3. info
  • SYDSAETER, K. STORM, A., BERCK, P. Economists' Mathematical Manual. Berlin: Springer, 2000. ISBN 3-540-65447-X. info
  • WILLIAMS, H. P. Model Building Mathematical Programming. Chichester: John Wiley & Sons, 1993. ISBN 0-471-94111-5. info
  • TAHA, H. A. Operations Research An Introduction. Englewood Cliffs: Prentice Hall, 1992. ISBN 0-13-187659-7. info
Teaching methods
Skills demonstration
Seminar classes
Assessment methods
Written exam
Language of instruction
English
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
test, 70% attendance at the seminars, exam test
ActivityDifficulty [h]
Ostatní studijní zátěž41
Přednáška26
Seminář13
Zkouška40
Summary120
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