Infopaket

Research of Operations

ОК.25

Обов’язкова дисципліна для ОП

First

2024/2025

4 Semester

7

LO04. Perform mathematical description, analysis and synthesis of discrete objects and systems, using the concepts and methods of discrete mathematics and algorithm theory. LO10. Have methods for choosing rational methods and algorithms for solving mathematical problems. LO02. Have basic principles and methods of mathematical, complex and functional analysis, linear algebra and number theory, analytical geometry, theory of differential equations, including partial differential equations, probability theory, mathematical statistics and random processes, numerical methods. LO14. Demonstrate the ability to self-study and continue professional development.

Be able to: 1. to study the qualitative characteristics of the constructed mathematical models. 2. formulate mathematical optimization problems for such models. 3. apply classical methods for the study of applied problems of mathematical programming. Possess: 1. skills of using classical methods of mathematical analysis and theory of linear algebra. 2. skills of formulation and algorithms for solving linear programming problems. 3. skills of search and analysis of information in open sources.

Block 1. Linear programming problem. Simplex method of solving LP problems. Topic 1. INTRODUCTION. General linear programming problem (LLP) Topic 2. Solving LP problems. Simplex method Test work Block 2. Theory of LP duality. Topic 3. Duality in the problems of LP. Topic 4. Dual simplex method. Test work Block 3. Transport task. Streams on networks. Topic 5. Transport task Topic 6. Streams on networks. Test work Block 4. Discrete and integer programming. Topic 7. Discrete programming (DP). The problem of optimal assignments. Topic 8. Methods of segments of solving problems of integer linear programming Topic 9. The method of branches and borders Block 5. Elements of game theory. Topic 10. INTRODUCTION to game theory. Matrix games. Topic 11. Mixed strategies and the relationship with PLL Test work Block 6. Nonlinear programming (NP). Topic 12. Review of methods and models of emergency. General issues of nonlinear programming. Topic 13. Convex programming (OP). Topic 14. Gradient methods and the method of possible directions Topic 15. Methods of penalty and barrier functions

1. Nefedov Yu. M. Methods of optimization in examples and problems: textbook / Yu. M. Nefedov, T. Yu. Balytska. - Київ: Кондор, 2011. - 324 с. 2. Zaichenko YP Research operations. Textbook / Yu. P. Zaichenko. - 7th ed., Reworked. and add. - Kyiv: Slovo Publishing House, 2006. - 816 p. 3. Dziuban IY Methods of research operations / IY Dziuban, OL Zhirov, OG Okhrimenko. - Kyiv: IPC "Polytechnic Publishing House", 2005. - 108 p. 4. Nakonechny SI Mathematical programming: textbook. way. / SI Nakonechny, SS Savina. - Kyiv: KNEU, 2003. - 452 pp. Research of operations in economics: textbook / ed. IK Fedorenko, OI Chernyak. - Kyiv: Knowledge, 2007. - 558 p. - (Higher education of the XXI century). 5. Hamdy A. Taha, Operations Research: An Introduction, 10th Edition,, University of Arkansas, © 2017, Pearson Additionally: 6. Yu.D. Popov, VI Tyuptya, VI Shevchenko “Optimization methods”, K., 2000

Lectures, practice work, independent work, recommended literature processing, homework.

Intermediate assesement: The maximal number of available points is 60. Personalized take-home assignment for submission. Final assessment (in the form of exam): The maximal number of available points is 40. The form of exam: writing. The types of assignments are 2 writing assignments.

Ukrainian