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