460-4121/02 – Operations Research I (OV I)

Gurantor departmentDepartment of Computer ScienceCredits4
Subject guarantordoc. Ing. Lenka Skanderová, Ph.D.Subject version guarantordoc. Ing. Lenka Skanderová, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year1Semestersummer
Study languageEnglish
Year of introduction2015/2016Year of cancellation2022/2023
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
SKA206 doc. Ing. Lenka Skanderová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+0

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Tutorials

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).

Compulsory 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

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

Each student will conceive and submit five assignments on topics related to operations research. The topics of the assignments will include the application of different discussed methods to complex operations research problems. The students will work on the assignments continuously during the course of the term. There will be a possibility to consult the progress and the solutions at the lectures, seminars, individual consultations, and by email. The exam is written.

E-learning

Other requirements

Additional requirements are placed on the student.

Prerequisities

Subject codeAbbreviationTitleRequirement
460-4086 BIA Biologically Inspired Algorithms Recommended

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Operations Research (OR) is a discipline of applying advanced analytical methods to help 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 different aspects of OR. Lectures: ========= 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: ======== 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 their 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.

Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester, validity until: 2022/2023 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 45  20
        Examination Examination 55  6 3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Optional study plan
2020/2021 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Optional study plan
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Optional study plan
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Optional study plan

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