Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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    Operations Research

    A tantárgy neve magyarul / Name of the subject in Hungarian: Operációkutatás gazdaságinformatikusoknak

    Last updated: 2010. május 7.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics     		Gazdaságinformatikus mesterképzési szak
    Course ID Semester Assessment Credit Tantárgyfélév
    TE90MX50 1 3/1/0/v 5  
    3. Course coordinator and department Dr. Illés Tibor,
    4. Instructors dr. Gazdag-Tóth Boglárka PhD assistant professor Department of Differential Equations
    5. Required knowledge Linear algebra, discrete mathematics, probability theory.
    6. Pre-requisites
    Ajánlott:
    none
    7. Objectives, learning outcomes and obtained knowledge The course is concerned with operations research models in the economy.  It also provides the necessary theoretical background for developing solutions of the problems arising in the field of operational research. It teaches the use of modeling languages, optimization packages in operations research.
    8. Synopsis

    1 . Week: Economic models resulting in linear programming problems (e.g. portfolio selection problem). Different forms of the linear programming problems. Graphical solution.

    2 . Week: Recollection of results from linear algebra. Elementary basis transformation, basic solution. The simplex method for the normal form of the linear programming problems. Possibility of alternative optimal solutions. Unbounded problems. Solution by Excel.
     
    3 . Week: The dual problem. Meaning of the dual problem. Duality theorems.
     
    4 . Week: Two phase simplex algorithm. The dual of a general linear programming problem.

    5 . Week: The theorem of complementarity. Economic interpretation shadow prices. Balanced transportation problem.

    6 . Week: Simplex tableau of the transportation problem. The dual problem. Optimality criterion. The non-balanced problem. Prohibitive tariffs. Complex transportation problem.

    7 . Week: The assignment problem. Network models: shortest path problem.

    8 . Week: Basic models of network programming: maximal flow, minimal spanning tree.

    9 . Week: Critical Path Method (CPM), network design.

    10 . Week: Integer linear programming models. The branch and bound method.

    11 . Week: The main techniques for random number generation.
     
    12 . Week: Inventory models.

    13 . Week: Applications of the scheduling theory. Firm allocation models.

    14 . Week: Multi objective programming. Birth and death processes and their application for the solution of a special queuing problem.


    Seminars:

    2. Week: The use of Excel solver
    4. Week: Modeling language: GAMS
    6. Week: Modeling language: AMPL
    8. Week: Solver: XpressMP
    10. Week: Solver: CPLEX
    12. Week: Mixed programming problems
    14. Week: Mixed programming problems

    9. Method of instruction 3 lectures and 1 seminar per week
    10. Assessment • The condition of getting a signature is submission of the homework. The due date of the homework submission is the last day of the teaching period.
    • The exam is oral.
    11. Recaps Replacement of the homework is possible on the replacement week.
    12. Consultations On dates fixed personally by the lecturer.
    13. References, textbooks and resources • Wayne L. Winston, Operations Research. Applications and Algorithms, 3rd edition, Wadsworth Inc., 1994.
    14. Required learning hours and assignment
    Kontakt óra56
    Félévközi készülés órákra20
    Felkészülés zárthelyire0
    Házi feladat elkészítése14
    Kijelölt írásos tananyag elsajátítása0
    Vizsgafelkészülés60
    Összesen

    150

    15. Syllabus prepared by dr. Szántai Tamás DSc professor Department of Differential Equations
    Comments none