460-4121/03 – Operations Research I (OV I)
Gurantor department | Department of Computer Science | Credits | 5 |
Subject guarantor | doc. Ing. Lenka Skanderová, Ph.D. | Subject version guarantor | doc. Ing. Lenka Skanderová, Ph.D. |
Study level | undergraduate or graduate | Requirement | Optional |
Year | 1 | Semester | summer |
| | Study language | Czech |
Year of introduction | 2019/2020 | Year of cancellation | |
Intended for the faculties | FEI | Intended for study types | Follow-up Master |
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:
Recommended literature:
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
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction