# Optimal Programming I

- Credits: 6
- Ending: Examination
- Range: 2P + 2C
- Semester: winter
- Year: 1, 2
- Faculty of Economic Informatics

## Teachers

## Included in study programs

**Teaching results**

Upon successful completion of the course, students will acquire the following knowledge:

- knowledge and understanding of the possibilities of using optimal programming approaches as instruments to support decision-making,

-knowledge and understanding of selected methods for solving optimization problems of linear, integer and bivalent programming.

Upon successful completion of the course, students will acquire the following skills:

- ability to use selected methods for solving linear, integer and bivalent programming problems,

- ability to work with Python software system and with Solver for Excel software system for solving linear, integer and bivalent programming problems.

Upon successful completion of the course, students will acquire the following competencies:

-practical skills and competencies associated with the application of models and methods of linear, integer and bivalent programming in the analysis of specific decision-making tasks using adequate software (Python, Solver for Excel).

**Indicative content**

1. Optimal programming as an instrument to support decision making. Overview of mathematical methods (disciplines) in the field of optimal programming. Concepts of economic model and economic-mathematical model. Classification of economic-mathematical models.

2. General formulation of the mathematical programming problem. Scalar optimization problem and multicriteria decision making problem. Linear and nonlinear programming problems. Integer and bivalent programming problems. Specific examples of economic formulation of mathematical programming problems.

3. Linear programming concepts. Linear programming as part of mathematical programming. Basic concepts and properties of solving linear programming problems. Graphical and algebraic solution of the linear programming problem.

4. Methods for solving linear programming problems - classification: simplex method (primary and dual algorithm, revised algorithm), interior-point method. Algorithms and their complexity.

5. Simplex method - primary algorithm, primary algorithm using artificial variables.

6. Special cases in solving linear programming problems.

7. Theory of duality in linear programming problems. Economic interpretation of duality theory. Duality properties.

8. Dual simplex algorithm.

9. Sensitivity analysis and its economic interpretation.

10. Revised simplex algorithm.

11. Interior-point method.

12. Models with integer and bivalent variables and their economic interpretations. Cutting planes method for solving integer programming problems. Branch and bound method for solving integer programming problems.

13. Bivalent programming - explicit enumeration, Balas additive algorithm.

**Support literature**

1. CHOCHOLATÁ, M. 2013. Lineárne programovanie pre manažérov. Bratislava: Vydavateľstvo EKONÓM.

2. WILLIAMS, H.P. 2013. Model Building in Mathematical Programming. London: John Wiley and Sons.

3. LAŠČIAK, A. a kol. 1990. Optimálne programovanie. 2. upravené vydanie. Bratislava: Alfa.

**Requirements to complete the course**

30 % work at seminars and writing of projects

70 % combined final exam

**Student workload**

156 hours

26 hours lecture attendance

26 hours seminar attendance

26 hours preparation for lectures

26 hours preparation for seminars

26 hours writing a seminar paper

26 hours preparation for final exam

**Language whose command is required to complete the course**

Slovak

Date of approval: 11.03.2024

Date of the latest change: 16.05.2022