1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - pierwszego stopnia z tyt. licencjata
5. Operations Research 2

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Operations Research 2 - opis przedmiotu

Cel przedmiotu

Knowledge of selected methods, models and applications of Operations Research.

Wymagania wstępne

Zapisz zmiany

Knowledge of basic linear algebra, discrete mathematics, probability theory, linear optimization models in the field of Operations Research 1

Zakres tematyczny

Lecture:

1. Mathematical modelling in operations research. Applications of operations research. (2 h.)
2. Selected models of discrete optimization and their applications. (6 h.)
3. Methods of solving the problems of discrete optimization. (2 h.)
4. Genetic algorithms. (2 h.)
5. Maximal flow problem. Ford-Fulkerson algorithm (2 h.)
6. Project scheduling methods. CPM method. (4 h.)
7. Travelling salesman problem. Little’s algorithm. (4 h.)
8. Multicriteria programming. Interactive methods. (2 h.)
9. Dynamic programming. Decision trees. (2 h.)
10. Decision making under uncertainty. Stochastic programming. (4 h.)

Laboratory:

1. Creating mathematical models for discrete optimization problems: production problem and diet problem with integer variables, cutting and loading problems (2 h.).
2. Branch and bound algorithm for integer linear programming tasks. (2 h.).
3. Transport issue with cost and time criteria. Transport algorithm. The issue of allocation and the production line (4 h.).
4. Solving discrete and binary problems using Solver in Excel. (4 h.). Colloquium (2 h.).
5. Determining the maximum flow and minimum cross-sections in flow networks. FF-EK algorithm (2 h.).
6. The traveling salesman problem. Little's algorithm (2 h.).
7. Building a network of activities when planning projects. Determining the shortest project implementation time, critical paths (CPM method) and Gantt diagram (4 h.).
8. Multi-criteria linear optimization tasks. Determining Pareto-optimal solutions and efficient solutions. Optimal solution for the meta-criterion (2 h.).
9. Multi-objective discrete optimization tasks. Hasse diagrams and Pareto-optimal solutions. Criteria - degree of implementation of type I and II, meta-criterion (2 h.). Colloquium (2 h.).
10. Tasks related to decision-making under conditions of uncertainty and risk (2 h.).

Metody kształcenia

Lecture, laboratory classes.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

The final grade for the course takes into account the final grade for the laboratory (40%) and the final grade for the lecture (60%), assuming that the student has achieved all the expected learning outcomes to a sufficient degree.

Literatura podstawowa

1. R. J. Vanderbei, Linear Programming, Foundations and Extensions, Kluwer, Boston, 1997.
2. F.S. Hiller, G.J. Lieberman, Introduction to Operations Research, McGraw-Hill, 2005.
3. Vicas Singla, Operations Research using Excel A Case Study Approach, CRC Press, 2022.

Literatura uzupełniająca

1. Wayne L. Winston, Operations Research Applications and Algorithms, 4th edition, Thomson Brooks/Cole, 2004.
2. Hamdy A. Taha, Operations Research An Introduction, 10th edition, Pearson Education Limited, 2017.
3. Ronald L. Rardin, Optimization in Operations Research, 2nd edition, Pearson Higher Education, Inc., Hoboken, NJ 07030, 2017.
4. M. Ehrgott, Multicriteria Optimization, 2nd edition, Springer, 2005

Uwagi

Zmodyfikowane przez dr Joachim Syga (ostatnia modyfikacja: 07-02-2024 22:13)