Optimization Models (FSI-0OM)

Academic year 2020/2021
Supervisor: RNDr. Pavel Popela, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The course objective is to emphasize optimization modelling and solution methods related knowledge. Computer-aided optimization is focused.
Learning outcomes and competences:
Although the course is designed for mathematical engineers, it is useful also for engineering students dealing with optimization problems.
Prerequisites:
Basic concepts of calculus, linear algebra, and programming.
Course contents:
The course presents fundamental mathematical models and methods for solving of optimization engineering problems. It is based on the author's experience with similar courses at the EU and US universities (Computer-Aided Optimization). It is suitable for students interested in the solution of such problems coming from various specializations and years of study. Examples of typical problems involve cases studied and solved within the framework of BUT and FME projects. Particular instances are solved by using a suitable software (MS Excel, Matlab, GAMS aj.). Modelling rules are systematicaly applied: problem formulation and analysis, model building and classification, the use of theory, transforamtions and algorithms, solution analysis and interpretation. The examples of linear, network, nonlinear, integer, dynamic and uncertain models are introduced.
Teaching methods and criteria:
The course is taught through exercises which are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
The student is asked to participate on the solution of proposed problems.
Controlled participation in lessons:
The active participation at seminars is assumed.
Type of course unit:
    Computer-assisted exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Computer-assisted exercise Basic models (applied in logistics)
Linear models (production related applications)
Special (network flow and integer) models (transportation problems)
Nonlinear models (aplikace norem)
General models (parametric, multicriteria, nondeterministic,
dynamic, hierarchical)

Course participance is obligatory.
Literature - fundamental:
1. GAMS User's Guide, GAMS Corp. 2021
2. GAMS Solver's Guide GAMS Corp., 2021
3. Williams, H.P. Model Building in Mathematical Programming, 4th edition. J.Wiley and Sons, 2012.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B3A-P full-time study B-MAI Mathematical Engineering -- Cr 2 Elective 1 3 W