Mathematical Economics 1

Lecturer:

Josef Jablonský (gar.)

Tutor:

Josef Jablonský (gar.)

Supervisor:

Department of Software Engineering in Economy

Synopsis:

The course introduces selected models and methods for economic decision making. The main attention is given to optimization models of linear programming, possibilities of their real applications and their solving by means of the current software products.

Requirements:

Syllabus of lectures:

1.Economic decision making - an introduction

2.Formulation of the mathematical programming problems, typocal linear programming problems

3.Introduction to the Theory of linear programming, graphical solving of Lp problems

4.Simplex method

5.Two-phase simplex metod.

6.Tudory of duality in linear programming.

7.Sensitivity analysis.

8.Post-optimality changes and parametric programming

9.Distribution LP problems

10.Transportation problem and its solving

11.Assignment problem, traveling salesman problem.

12.Integer programming - typical problems

13.Cutting planes methods, branch and bounds algoritms.

Syllabus of tutorials:

1.Formulation of typical linear programming problems

2.Formulation of typical linear programming problems

3.Graphical solving of LP problems

4.Simplex method

5.Simplex method

6.Duality in LP problems - formulation of dual problems, dual variables and their economic interpretation

7.Stability in LP problems

8.Post-optimality analysis

9.Integer programming - cutting planes

10.Integer programming - branch and bounds

11.Transportation problem - initial solution

12.Transportation problem - optimal solution

13.Special problems of LP - assignment, travelling salesman, covering, etc.

Study Objective:

Inform students about basic algorithms for solution of linear and integer programming problems and software products for modelling and optimization.

Upon successful completion of this course, students will be able to apply basic operational research methods and models for solving of real decision making problems. The will be familiar with software products for mathematical modelling and optimisation.

Study materials:

Key sources:

1.Jablonský, J.: Operační výzkum - kvantitativní modely pro ekonomické rozhodování. Professional Publishing, Praha 2002,2003, 2004.

Recommended sources:

1.Lagová, M., Jablonský, J.: Lineární modely. Oeconomica, Praha 2009.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: