Course detail

Optimization Methods and Queuing Theory

FEKT-DPA-TK1Acad. year: 2023/2024

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.

Language of instruction

English

Number of ECTS credits

4

Mode of study

Not applicable.

Offered to foreign students

The home faculty only

Entry knowledge

Proficiency in mathematical disciplines at M.Eng. level

Rules for evaluation and completion of the course

examination

Aims

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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Popela, P., Sklenář, J.: Optimization. Teaching notes, University of Malta, 2003. (EN)
Sklenář, J.: Queuing Theory. Teaching notes, University of Malta, 2016. (EN)

Recommended reading

Sklenář, J.: Dynamic Programming Theory and Applications. Teaching notes, University of Malta, 2017. (EN)
Popela, P.: Nonlinear Programming. Teaching notes, University of Malta, 2003. (EN)
Attard, N., Sklenář, J.: Linear Programming. Teaching notes, University of Malta, 2007. (EN)
Sklenář, J.: Introduction to Integer Linear Programming. Teaching notes, University of Malta, 2017. (EN)
Sklenář, J.: Infinite Horizon Dynamic Programming Models. Teaching notes, University of Malta, 2017. (EN)
Popela, P.: Stochastic Programming. Teaching notes, University of Malta, 2008. (EN)
Sklenář, J.: Queuing Theory - Worksheets. Teaching notes, University of Malta, 2016. (EN)
Sklenář, J.: Network Flow Models. Teaching notes, University of Malta, 2017. (EN)

Classification of course in study plans

  • Programme DPA-KAM Doctoral, any year of study, winter semester, compulsory-optional
  • Programme DPAD-EEC Doctoral, any year of study, winter semester, compulsory-optional
  • Programme DPA-EKT Doctoral, any year of study, winter semester, compulsory-optional
  • Programme DPA-EIT Doctoral, any year of study, winter semester, compulsory-optional
  • Programme DPAD-EIT Doctoral, any year of study, winter semester, compulsory-optional
  • Programme DPA-MET Doctoral, any year of study, winter semester, compulsory-optional
  • Programme DPA-SEE Doctoral, any year of study, winter semester, compulsory-optional
  • Programme DPA-TLI Doctoral, any year of study, winter semester, compulsory-optional
  • Programme DPA-TEE Doctoral, any year of study, winter semester, compulsory-optional

Type of course unit

 

Seminar

39 hours, optionally

Teacher / Lecturer