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Operations Research I

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code460-4121/03
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites
PrerequisitiesCourse Unit CodeCourse Unit Title
460-4086Biologically Inspired Algorithms
Name of Lecturer(s)Personal IDName
KRO080prof. Ing. Pavel Krömer, Ph.D.
Summary
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
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
Lectures:
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1. Introduction into operations research
2. History of operations research, impact for practical applications
3. Basic areas of operations research
4. Types of problems, application domains
5. Mathematical modelling, parameter optimization
6. Linear programming
7. Applications of linear programming
8. Traffic and distribution problems
9. Fundamentals of graph theory, graph paths, network flows
10. Bound variables, simplex algorithm
11. One dimensional cutting stock problem
12. Dantzing-Wolfe decomposition algorithm
13. Primal-dual algorithm
14. Multiobjective problems, formulation of goal programming

Seminars:
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1. Implementation of the simplex method
2. Application of the simplex method to problems with bound variables
3. Representation of a graph, adjacency matrix
4. Implementation of the  Dantzig-Wolfe algorithm
5. Implementation of the primal-dual algorithm
6. Implementation of goal programming
7. Travelling salesman problem
8. Vehicle routing problem
9. Capacitated vehicle routing problem
10. Network flow maximization problem
11. Minimum cost flow problem
12. Knapsack problem
13. Job shop scheduling problem
14. Assignment problem
Recommended or Required Reading
Required Reading:
[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:
[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
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit45 25
        ExaminationExamination55 26