460-4121/03 – Operations Research I (OV I)

Gurantor departmentDepartment of Computer ScienceCredits5
Subject guarantordoc. Ing. Lenka Skanderová, Ph.D.Subject version guarantordoc. Ing. Lenka Skanderová, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRO080 prof. Ing. Pavel Krömer, Ph.D.
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

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 three 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

No additional requirements.

Prerequisities

Subject codeAbbreviationTitleRequirement
460-4086 BIA Biologically Inspired Algorithms Recommended

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: ========= 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: ======== 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

Conditions for subject completion

Full-time form (validity from: 2019/2020 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  25
        Examination Examination 55  26 3
Mandatory attendence participation: On the exercises, students will work on the tasks tightly related to the topic of the lecture. The tasks will be evaluated by the points. The minimal number of points is 25, the maximal 45.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (N0613A140034) Computer Science P Czech Ostrava 1 Optional study plan
2024/2025 (N0688A140014) Industry 4.0 AZD P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0688A140014) Industry 4.0 AZD P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0613A140034) Computer Science P Czech Ostrava 1 Optional study plan
2023/2024 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2022/2023 (N0613A140034) Computer Science P Czech Ostrava 1 Optional study plan
2022/2023 (N0688A140014) Industry 4.0 AZD P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2021/2022 (N0688A140014) Industry 4.0 AZD P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0688A140014) Industry 4.0 AZD P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0688A140014) Industry 4.0 AZD P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2023/2024 Summer
2022/2023 Summer
2021/2022 Summer
2020/2021 Summer