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Terminated in academic year 2022/2023

Operations Research I

Type of study Follow-up Master
Language of instruction Czech
Code 460-4121/01
Abbreviation OV I
Course title Operations Research I
Credits 4
Coordinating department Department of Computer Science
Course coordinator doc. Ing. Lenka Skanderová, Ph.D.

Subject syllabus

Operations Research (OR) is a discipline of applying advanced analytical methods to make better decisions. Also known as management science or decision science, it involves the application of information technology in designing systems to operate in the most effective way, or deciding how to allocate scarce human resources, money, equipment, or facilities. This course will address the different aspects of OR.

Lectures:
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1. Introduction to operations research.
2. Modeling.
3. Linear programming.
4. Simplex method - graphic form.
5. Simplex method - algebraic form. Relations between graphic and algebraic form.
6. Simplex method - tableau form. Relations between algebraic, and tableau form.
7. Transportation problem - Vogel's approximation.
8. Transportation problem - Russell's approximation.
9. Transportation problem - optimality test. Optimization of the sub-optimal solution provided by Vogel's or Russell's method.
10. Assignment problem - simplex method, Hungarian algorithm. Relations between transportation and assignment problem.
11. Constrained optimization - stochastic methods.
12. Dynamic constrained optimization - stochastic methods.
13. Large-scale optimization problems.
14. Network optimization models.

Seminars:
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1. Modeling.
2. Simplex method - graphic form.
3. Simplex method - algebraic form.
4. Simplex method - tableau form.
5. Transportation problem, Vogel's approximation.
6. Transportation problem, Russell's approximation.
7. Optimality test. Optimization of the sub-optimal solution.
8. Assignment problem. Application of the simplex method, assignment problem conversion (to transportation problem).
9. Constrained optimization using stochastic methods. Implementation of the state-of-the-art algorithms of differential evolution and particle swarm optimization. Application of the algorithm to the selected engineering problems.
10. Dynamic constrained optimization using stochastic methods. Implementation of the selected algorithms developed to solve the dynamic constrained optimization problems.
11. Techniques used in stochastic methods to improve the convergence and quality of the provided solutions. Sub-populations, clustering, diversity preservation techniques. The balance between exploration and exploitation.
12. Implementation of the stochastic methods developed for large-scale optimization.
13. Network optimization models - maximum flow problem.
14. Network optimization models - minimum cost flow problem.

Literature

[1] Taha Hamdy (2010) Operations Research: An Introduction (9th Edition). ISBN-13: 978-0132555937 
[2] Winston Wayne (2003) Operations Research: Applications and Algorithms. ISBN-13: 978-0534380588 
[3] Pinedo M. (2012) Scheduling: Theory, Algorithms, and Systems. Springer. ISBN-13: 978-1461419860
[4] Hillier, F. S. (2012): Introduction to operations research. Tata McGraw-Hill Education. ISBN: 0072321695 

Advised literature

[1] Marlow W. Mathematics for Operations Research. Dover Publications. ISBN-13: 978-0486677231