Course detail
Optimization Methods II
FSI-VPP-K Acad. year: 2021/2022 Winter semester
The course deals with the following topics: The basis of mathematical process theory. Optimal regulation. The principle of Bellman as a tool for optimization of multistage processes with a general non-linear criterion function. Optimum decision policy. Dynamic programming as a tool for creation of methods for a solution of the deterministic and stochastic decision optimization problems in discrete as well as continuous range and its computation aspects. Pontryagin maximum principle. Fuzzy regulation. Applications in practical problems solution in economical decisions and in technological process control. Optimization in project management in the stages of multicriteria projects selection into portfolio in case of a restricted resource, of resource scheduling in deterministic, stochastic and fuzzy case, of cost analysis of projects and monitoring the deviations between real and scheduled projects course.
Language of instruction
Czech
Number of ECTS credits
6
Supervisor
Department
Learning outcomes of the course unit
Knowledge: Students will know basic principles and algorithms of methods applicable to the optimization of the deterministic, stochastic and fuzzy processes, discrete and continuous. They will be made familiar with basic principles and algorithms of methods that are appropriate to creation of decision-support systems for project management, as the tool for the identification, selection and realization of projects. Skills: Students will be able to apply the above methods to the solution of the practical problems from economic decision, problems of increasing of the reliability of technological devices, problems of automation control of technological processes and problems of project management, by using of contemporary tools of the computer science. They will be able to work with modern decision-support systems.
Prerequisites
Knowledge of the basics of mathematical analysis, algebra, theory of sets, statistics and probability.
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.
Aims
The aim of the course is to inform the students about creations and applications of mathematical methods for optimal control of technological and economic processes e.g. in the automation of mechanical systems, in the management of production in mechanical engineering, in project management and in optimization of information systems, using contemporary tools 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.
The study programmes with the given course
Programme N-AIŘ-K: Applied Computer Science and Control, Master's, compulsory
Type of course unit
Guided consultation in combined form of studies
22 hours, compulsory
Teacher / Lecturer
Syllabus
1. Basics of mathematical processes theory. Bellman optimality principle and dynamic programming. Mitten generalization of dynamic programming.
2. Optimization of continuous decision process. Pontryagin's maximum principle.
3. Deterministic application of dynamic programming.
4. An example of the optimal fuzzy regulation and fuzzy control of technological processes.
5. Stochastic applications of dynamic programming. Controlled Markov chains.
6. Increasing reliability of technological devices.
7. Basic notions of network analysis methods, CPM method.
8. Calculation by stochastic evaluation of activities (method PERT). A comparison of the results obtained by the method PERT with the results of the simulation methods.
9. Cost analysis of a project including application of fuzzy linear programming to the solution of two-criterion time-cost problem. Heuristic methods for scheduling with resources constraints.
10. Multi-criterial projects selection. Synergistic effects and hierarchical dependencies of projects.
11. Monitoring deviations between scheduled state and real state of project. System SSD-graph.
12. Balancing production belt and assembly line.
13. Scheduling production processes.
Guided consultation
43 hours, optionally
Syllabus
1. Solution of dynamic programming problems in Excel and Matlab. Container loading problem.
2. Resources allocation problem. Reduction of state vector dimension.
3. Examples of process optimization by means of step-by-step approximations methods.
4. Examples of continuous processes optimization from the area of regulation and control.
5. Dynamic programming of stochastic processes. Optimization of mining plan.
6. Production control for uncertain demand. Controlled Markov chains.
7. Example of optimizing reliability of serially connected system.
8. Practical examples of graphs and networks. Implementation of the CPM method in Excel and Matlab.
9. Numerical applications of the PERT method.
10. Example of the project scheduling by fuzzy linear programming.
11. Examples of heuristic scheduling in case of constrained resources.
12. Reducing project duration.
13. Evaluation of semester projects.