Models and Methods of Operations Research

Teachers

Included in study programs

Teaching results

Course objective: Scientific advances in economics and operational research make it possible to model dependencies and conditions more accurately, to quantify the stochasticity of input data encountered by the solver, to implement the time aspect, and to calculate the optimal solution to complex decision problems. Modern models and methods of operational research emphasize the stochastic aspect of input data and the dynamic aspect of solved economic processes. The application dimension of operational research models is currently focused on the environmental area, the area of distribution, energy efficiency and the like. The aim of the course is to more accurately model the dependencies and conditions, quantify the uncertainty encountered by the decision maker, implement the time aspect and calculate the optimal solution to complex decision problems.
Knowledge and understanding.
After studying this course, students should:
a) understand the principles and principles of creating complex operational research models,
b) know the methodologies and relevant tools of problem analysis.
Skills, characteristics and attributes.
After studying this course, students should be able to:
a) compile appropriate mathematical programming models emphasizing data uncertainty and the dynamic aspect of decision-making tasks;
b) apply different methods using existing methodologies and approaches to the analysis of the systems under investigation;
c) be able to use practical tools to create appropriate mathematical programming models;
d) make efficient use of tools to solve corresponding mathematical programming, stochastic programming, fuzzy mathematical programming and dynamized mathematical programming problems.
Upon successful completion of the course, students will acquire the following competencies:
- practical skills and competencies with the application of methods and algorithms in mathematical modeling of complex economic processes and subsequent problem solving.

Indicative content

1. Models and methods of mathematical programming.
2. Data uncertainty in decision problems. Stochastic programming, fuzzy mathematical programming.
3. Dynamic aspect in decision problems. Dynamized problems of mathematical programming.
4. Algorithms for solving mathematical programming problems.
5. Graph theory models and methods. Graph theory algorithms.
6. Distribution models of mathematical programming and their specific character.
7. Environmental models of mathematical programming.

Support literature

1. Pekár, J. – Brezina, I. – Čičková, Z.: Synchronization of Capacitated Vehicle Routing Problem, Ekonomický časopis, 65, 2017, č. 1, s. 66 – 78
2. Jensen , P.A. - Bard, J.F.:Operations Research Models and Methods 1st Edition, Wiley; 2002
3. Vanderbei, R.J.: Linear Programming: Foundations and Extensions. 4th ed. 2014, XXII, Springer, Berlin: 2014.
4. Eiselt, H. A. – Sandblom, C-L.: Operations Research: A Model-Based Approach, 2nd ed. 2012, Springer, Berlin: 2012.
5. International Series in Operations Research & Management Science, Springer, Berlin 2021
6. Sánchez, J.M.G.: Modelling in Mathematical Programming Methodology and Techniques. Springer, Berlin, 2021

Requirements to complete the course

- 20% - part-time work
- 40% - individual project
- 40% - combined test in the form of a test and problem solving, discussion

Student workload

Total study load (in hours): 10 credits x 26 hours = 260 hours
Distribution of study load: 260 hours
Participation in consultations: 16 hours
Seminar preparation: 48 hours
Project processing: 70 hours
Final exam preparation: 126 hours

Language whose command is required to complete the course

Slovak

Date of approval: 10.02.2023

Date of the latest change: 16.05.2022