Czech

Not applicable.

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.

Proficiency in mathematical disciplines at M.Eng. Level

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

examination

1. Optimization Theory. Terminology, various types and existence of solutions (Weierstrass theorem). Methods based on Calculus.
2. Linear Programming. Theory and Simplex Method.
3. Integer Programming. Solution methods and use of indicator variables in building models that are out of scope of Linear Programming (models with logical conditions, disjunctive constraints, and similar.)
4. Theory of Nonlinear Programming. Convex sets and functions, optimality conditions.
5. Optimization algorithms of Nonlinear Programming and their application.
6. Dynamic Programming with finite horizon. Introduction to recursion, solution of various practical problems by the methods of Dynamic Programming.
7. Introduction to Stochastic Programming. Terminology, basic forms of Deterministic Equivalents and their solution.
8. Introduction to Dynamic Programming with infinite horizon. Terminology, Markov Decision Process, Bellman's equations and their solution.
9. Heuristic optimization algorithms as a method to solve problem of local optima (genetic and similar algorithms based on populations of solutions).
10. Basics of Queuing Theory, introduction to stochastic processes, Poisson process in detail.
11. Models of simple single queue systems (model M/M/1 and similar).
12. Advanced single queue models (M/G/1, G/M/1 and similar). Network models, Jackson theorem.
13. Simulation methods and their use in analysis of queuing systems.

Not applicable.

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.

Not applicable.

Not applicable.

Not applicable.

POPELA, P.; SKLENÁŘ, J. Optimization. Teaching notes, University of Malta, 2003. (EN)
SKLENÁŘ, J. Dynamic Programming Theory and Applications. Teaching notes, University of Malta, 2017. (EN)

ATTARD, N.; SKLENÁŘ, J. Linear Programming. Teaching notes, University of Malta, 2007. (EN)
POPELA, P. Nonlinear Programming. Teaching notes, University of Malta, 2003. (EN)
POPELA, P. Stochastic Programming. Teaching notes, University of Malta, 2008. (EN)
SKLENÁŘ, J. Infinite Horizon Dynamic Programming Models. Teaching notes, University of Malta, 2017. (EN)
SKLENÁŘ, J. Introduction to Integer Linear Programming. Teaching notes, University of Malta, 2017. (EN)
SKLENÁŘ, J. Network Flow Models. Teaching notes, University of Malta, 2017. (CS)
SKLENÁŘ, J. Queuing Theory - Worksheets. Teaching notes, University of Malta, 2016. (EN)
SKLENÁŘ, J. Queuing Theory. Teaching notes, University of Malta, 2016. (EN)