Course detail

Optimization Methods

FSI-VO1CompulsoryBachelor's (1st cycle)Acad. year: 2017/2018Winter semester3. year of study6  credits

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.

Learning outcomes of the course unit

Knowledge: 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.
Skills: 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.

Recommended optional programme components

Not applicable.

Recommended or required reading

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.
BOMZE, L.M.; GROSSMANN, W.: Optimierung Theorie und Algorithmen. BI-Wiss.-Verl., Mannheim, pp. 610, 1993. ISBN 3-411-15091-2.
KLAPKA, J.; DVOŘÁK, J.; POPELA, P.: Metody operačního výzkumu. VUTIUM, Brno, 2001.
LITTLECHILD, S.; SHUTLER, M. (eds.): Operations Research in Management. Prentice Hall, New York, pp. 298, 1991. ISBN 0-13638-8183
JABLONSKÝ, J. Operační výzkum: kvantitativní modely pro ekonomické rozhodování. Professional Publishing, 2007.
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: .
WINSTON, W.L.: Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmont, 2004.
BAZARAA, M, S.; SHERALI, H. D.; SHETTY, C. M.: Nonlinear Programming. Wiley, 2013.

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.

Language of instruction

Czech

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.

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

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.

seminars

14 hours, compulsory

Teacher / Lecturer

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. Formulation and solution of simple non-linear problems.
6. Solution of multi-criteria problems.
7. Network analysis. CPM method.

seminars in computer labs

12 hours, compulsory

Teacher / Lecturer

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.

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