Pravděpodobně máte vypnutý JavaScript. Některé funkce portálu nebudou funkční.

Course detail

Optimization I

Subjet code :	FSI-VO1
Faculty:	Faculty of Mechanical Engineering
Academic year:	2011/2012
Open:	Yes
Supervisor:	prof. RNDr. Ing. Miloš Šeda, Ph.D.
Department:	Institute of Automation and Computer Science

Study level:	Master's
Study form:	full-time study
Language of instruction:	Czech
Number of credits:	6
Completion:	course-unit credit and examination
Year of study:	1
Semester:	winter
Duty:	compulsory

The study programmes with the given course

Objective of the course – aims of the course unit: 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.
Objective of the course – learning outcomes and competences: 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, to apply basic methods for their solution and to realise the methods by aids of contemporary tools of computer science.
Prerequisites: Knowledge of the basics of mathematical analysis, algebra, theory of sets, statistics and probability.
Course contents (annotation): The course deals with the following topics: Operations research, its methodology and relations to system theory and cybernetics. 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.
Teaching methods and criteria: Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Assesment methods and criteria linked to learning outcomes: Course-unit credit: Active participation in the seminars, elaboration of a given project. Examination: Written.
Specification of controlled education, way of implementation and compensation for absences: Attendance at seminars is controlled. An absence can be compensated for via solving additional problems.
Recommended reading: WINSTON, W.L.: Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmont, 2004. SKYTTNER, L.: General Systems Theory. An Introduction. Macmillan Press, London, pp. 290, 1996. ISBN 0-333-61833-5. 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. ISBN 80-214-1839-7 LITTLECHILD, S.; SHUTLER, M. (eds.): Operations Research in Management. Prentice Hall, New York, pp. 298, 1991. ISBN 0-13638-8183 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.

Type of course unit:

Lecture:	39 hours, optionally
Teacher:	doc. RNDr. Jindřich Klapka, CSc.
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. 9. Quasiconvex programming. 10. Bellman Optimality Principle. 11. Dynamic programming of discrete deterministic processes and its applications. 12. Basics of network analysis. Critical Path Method. 13. Multicriterial Optimization and Multicriterial Selection.
seminars:	14 hours, compulsory
Teacher:	prof. RNDr. Ing. Miloš Šeda, 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. 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:	prof. RNDr. Ing. Miloš Šeda, 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 multi-criteria problems in MS Excel. 6. Information about software products for network analysis.