Course details
Optimization Methods and Queuing Theory
DPC-TK1 FEKT DPC-TK1 Acad. year 2024/2025 Winter semester 4 credits
This study unit is made of two main parts. The first part deals with various currently used optimization methods. Students are first introduced to general Optimization theory. Then various forms of Mathematical Programming are dealt with. After the introduction into Linear and Integer Programming, the attention is given to Nonlinear Programming from its backgrounds like Convexity Theory and optimization conditions to overview and practical use of various optimization algorithms. A practically oriented introduction into Dynamic Programming with finite horizon follows. Students are also introduced into backgrounds of Stochastic Programming and Dynamic programming with infinite horizon, in particular to methods of solving Bellman's equations. The first part is closed by introduction to heuristic optimization algorithms.
The second part of the unit deals with the Queuing Theory. Various models of single queue systems and queuing networks are derived. The theory is then used by solving practical problems. Students are also introduced into simulation methods that are the only feasible solution method when a theoretical model is not available.
Guarantor
Language of instruction
Completion
Time span
- 39 hrs seminar
Department
Instructor
Learning objectives
Developing awareness of various optimization methods from their mathematical background to their application in solving practical problems.
Developing awareness of mathematical models of Queuing Theory and their use in solving technical problems including simulation methods.
Obtaining the skills of studying, understanding, and applying mathematical models as specified in the unit contents. Ability to build mathematical programs solving particular optimization problems. Ability to use software packages that solve mathematical programs. In case of Queuing Theory it is understanding of the mathematical models and ability to apply them in practice.
Prerequisite knowledge and skills
Proficiency in mathematical disciplines at M.Eng. level
Study literature
- Sklenář, J.: Dynamic Programming Theory and Applications. Teaching notes, University of Malta, 2017.
- Popela, P.: Nonlinear Programming. Teaching notes, University of Malta, 2003.
- Attard, N., Sklenář, J.: Linear Programming. Teaching notes, University of Malta, 2007.
- Sklenář, J.: Introduction to Integer Linear Programming. Teaching notes, University of Malta, 2017.
- Sklenář, J.: Infinite Horizon Dynamic Programming Models. Teaching notes, University of Malta, 2017.
- Popela, P.: Stochastic Programming. Teaching notes, University of Malta, 2008.
- Sklenář, J.: Queuing Theory - Worksheets. Teaching notes, University of Malta, 2016.
- Sklenář, J.: Network Flow Models. Teaching notes, University of Malta, 2017.
Fundamental literature
- Popela, P., Sklenář, J.: Optimization. Teaching notes, University of Malta, 2003.
- Sklenář, J.: Queuing Theory. Teaching notes, University of Malta, 2016.
Progress assessment
examination
Schedule
| Day | Type | Weeks | Room | Start | End | Capacity | Lect.grp | Groups | Info |
|---|---|---|---|---|---|---|---|---|---|
| Tue | exam | 2025-01-07 | T12/SC 7.66 | 11:00 | 16:00 | Závěrečná zkouška | |||
| Tue | seminar | lectures | T12/SE 5.127 | 18:00 | 20:50 | 8 | 1DVI | xx | Sklenář |
Course inclusion in study plans
- Programme DIT, any year of study, Compulsory-Elective group O
- Programme DIT, any year of study, Compulsory-Elective group O
- Programme DIT-EN (in English), any year of study, Compulsory-Elective group O
- Programme DIT-EN (in English), any year of study, Compulsory-Elective group O
- Programme VTI-DR-4, field DVI4, any year of study, Elective
- Programme VTI-DR-4, field DVI4, any year of study, Elective
- Programme VTI-DR-4 (in English), field DVI4, any year of study, Elective