Optimization and Operations Research Methods

Major: System Analysis
Code of subject: 6.124.00.O.063
Credits: 5.00
Department: Information Systems and Networks
Lecturer: Ph.D., Tetiana Shestakevych
Semester: 5 семестр
Mode of study: денна
Learning outcomes: • to know the historical background and mathematical foundations of operations research, as well as their current state and the main current trends in the development of the discipline; • be able to determine the resources necessary for carrying out operations research (operational analysis); • be able to carry out a meaningful statement of the problem with the subsequent transition to the construction of a formal mathematical model, choose or construct an algorithm for solving the problem, carry out an analysis of the obtained results; • be able to determine operations research strategies applicable in the relevant subject area for the relevant business process (its modeling or optimization); • be able to collect data depending on the operation being analyzed; • be able to find the optimal parameters of the researched process and present these results in terms of the goals of operations analysis, be able to prove the possible advantages and disadvantages of using certain approaches in business processes based on the used methods of operations research.
Required prior and related subjects: Differential equations and equations of mathematical physics Functional analysis Decision making theory
Summary of the subject: Key notions of operations research. Deterministic and stochastic optimization models and the main approaches to solving them. Multiple criteria problems and their solving. Mathematical programming problem statement and classification. The notion of algorithm complexity. Simplex algorithm. Fundamental theorems of linear programming. Duality principle. Concepts of primal and dual problems. Fundamental duality theorems, Transportation theory and its usage in the information technologies. Potential theory. Integer linear programming problems. Cutting-plane method. Branch and bound algorithm and its key components. Travelling salesman problem. Network flow problems. Ford-Fulkerson algorithm. Maximum flow problem. Characteristic features of game solving methods. Matrix games, The notion of cooperative games. Decision-making under uncertainty. Dynamic programming. Bellman optimality principle. Positional games. Normal forms of the positional game. Nonlinear programming.
Assessment methods and criteria: Current control (45%): written reports on laboratory work, oral examination; Final control (55% of exam): in written, verbally.
Recommended books: 1. Selected sections of multicriteria optimization: methodical recommendations for performing control and laboratory work for students of the Faculty of Mathematics / Developer: N. E. Kondruk. – Uzhgorod: UzhNu, 2015. – 56 p. 2. Dyvak M.P. Identification of discrete models of dynamic systems with interval data: monograph/ M.P. Dyvak, N.P. Porplitsia, T.M. Eccentric. - Ternopil: VOC "Economic Thought of TNEU", 2018. - 220 p. 3. Operations research: a textbook / Anatoly Vasylovich Katrenko. — 3rd ed., ed. and additional — Lviv: Magnolia-2006, 2009. — 349 p. 4. Operations research and optimization methods: methodological recommendations for practical tasks for students of all specialties of the first (bachelor) level / comp. S. V. Prokopovich, O. V. Panasenko, L. O. Chagovets. – Kharkiv: KHNEU named after S. Kuznetsa, 2019. – 64 p.