Course detail

Optimization Methods

FSI-VO1Acad. year: 2021/2022

The course deals with the following topics: The role of optimization methods in operations research, cybernetics and systems sciences. Systems modelling. Systems analysis tasks. Optimization problems. Formulation and properties of optimization problems. Simplex method. Artificial basis applications. Non-linear and convex problems. Quasi-convex programming. Dynamic programming of discrete deterministic processes. Critical Path Method. Examples of applications of operations research methods in technical and economic practice.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

prof. RNDr. Ing. Miloš Šeda, Ph.D.

Department

Institute of Automation and Computer Science (ÚAI)

Learning outcomes of the course unit

<b>Knowledge: </b>Students will know basic approaches to operational research and systems analysis as a tool for creation of methods for the solution of problems of automation and computer science, and technological and economical problems in mechanical engineering.
<b>Skills: </b>Students will be able to formulate simple problems of operational research from the practice of mechanical engineering and economics. They will be able to create mathematical models for the above problems, select methods of their solution and implement them using computer technology.

Prerequisites

Knowledge of the basics of mathematical analysis, algebra, theory of sets, statistics and probability.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course-unit credit: Active participation in the seminars, elaboration of a given project. Examination: Written and oral.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The aim of the course is to extend students' basic knowledge of the applied mathematics towards interdisciplinary and system direction, and make students familiar with basic approaches and methods for the solution of mathematized problems of economics in mechanical engineering and technology with aids of computer science.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is required. An absence can be compensated for via solving additional problems.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BAZARAA, M, S.; SHERALI, H. D.; SHETTY, C. M.: Nonlinear Programming. Wiley, 2013.
BOMZE, L.M.; GROSSMANN, W.: Optimierung Theorie und Algorithmen. BI-Wiss.-Verl., Mannheim, pp. 610, 1993. ISBN 3-411-15091-2.
KLAPKA, J., PIŇOS, P.: Decision support system for multicriterial R&D and information systems projects selection. European Journal of Operational Research. 2002, vol. 140, is. 2, s. 434-446. Dostupný z WWW: .
LITTLECHILD, S.; SHUTLER, M. (eds.): Operations Research in Management. Prentice Hall, New York, pp. 298, 1991. ISBN 0-13638-8183
SKYTTNER, L.: General Systems Theory. An Introduction. Macmillan Press, London, pp. 290, 1996. ISBN 0-333-61833-5.
WINSTON, W.L.: Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmont, 2004.

Recommended reading

JABLONSKÝ, J. Operační výzkum: kvantitativní modely pro ekonomické rozhodování. Professional Publishing, 2007.
KLAPKA, J.; DVOŘÁK, J.; POPELA, P.: Metody operačního výzkumu. VUTIUM, Brno, 2001.
WINSTON, W.L.: Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmont, 2004.

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme B3S-P Bachelor's

    branch B-AIŘ , 3 year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. RNDr. Ing. Miloš Šeda, Ph.D.

Syllabus

1. Operations research, its methodology and relations to systems theory and cybernetics. Modelling of the system.
2. Problems of the systems analysis. Optimization problems.
3. Formulations and properties of the linear programming problems.
4. Basic theorem of linear programming.
5. Simplex method and its deduction and derivation.
6. Artificial basis method (two-phase simplex method).
7. Dual problem and sensitivity analysis.
8. Convex non-linear problems. Kuhn-Tucker theorem. Wolfe's method for quadratic programming.
9. Quasi-convex nonlinear problems. Linear fractional programming.
10. Bellman Optimality Principle.
11. Dynamic programming of discrete deterministic processes and its applications.
12. Basics of network analysis. Critical Path Method.
13. Multi-criterial optimization and multi-criterial selection.

Exercise

14 hod., compulsory

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

1. Formulation of linear optimization models.
2. Formulation of linear problems, graphical solution.
3. Simplex algorithm.
4. Solution of linear problems applying artificial basis.
5. Solution of simple non-linear problems by means of Kuhn-Tucker conditions.
6. Solution of quadratic and linear fractional problems.
7. Network analysis. CPM method.

Computer-assisted exercise

12 hod., compulsory

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

1. Solution of linear optimization problems in MS Excel.
2. Solution of linear optimization problems by means of GAMS.
3. Solution of non-linear and integer problems in MS Excel.
4. Solution of non-linear and integer problems by means of GAMS.
5. Solution of dynamic programming problems in MS Excel.
6. Solution of multi-criteria problems in MS Excel.

Elearning

eLearning: currently opened course