| Course Unit Code | 460-4121/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | |
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| Prerequisities | Course Unit Code | Course Unit Title |
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| 460-4086 | Biologically Inspired Algorithms |
| Name of Lecturer(s) | Personal ID | Name |
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| SKA206 | doc. Ing. Lenka Skanderová, Ph.D. |
| Summary |
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Operations research (OR) is a set of scientific disciplines focused on decision and optimization problems. Also known as management science or decision science, it involves the application of various mathematical methods and computer science in the design and optimization of systems and in the search for optimum decisions, especially regarding resource allocation.
The course introduces basic principles, problems, and methods of operations research. It discusses the historical context, properties of solved problems, and the impact of operations research. Mathematical modeling of real-world problems as well as the task of parameter optimization is presented. Linear programming techniques and their application will be discussed.
Besides the deterministic methods, stochastic techniques will be introduced with regard to the actual research publications in this area. At the end of the course, students will be capable to select and apply the most appropriate method (deterministic or stochastic). |
| Learning Outcomes of the Course Unit |
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The aim of this course is to introduce the basic deterministic and advanced stochastic methods for solving different combinatorial/discrete optimization problems. The different problems from the area of transportation, assignment, and scheduling will be discussed.
At the end of the course, the students will be able to solve various tasks from the area of production control and planning, logistics, routing, etc. |
| Course Contents |
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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.
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| Recommended or Required Reading |
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| Required Reading: |
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[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 |
[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 |
| Recommended Reading: |
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| [1] Marlow W. Mathematics for Operations Research. Dover Publications. ISBN-13: 978-0486677231 |
| [1] Marlow W. Mathematics for Operations Research. Dover Publications. ISBN-13: 978-0486677231 |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 45 | 20 |
| Examination | Examination | 55 | 6 |