1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2023/2024
4. Computer science and econometrics - pierwszego stopnia z tyt. licencjata
5. Operations Research 2

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Operations Research 2 - opis przedmiotu

Cel przedmiotu

Introduction of the student to the selected methods, models and applications of operations research.

 

Wymagania wstępne

Zapisz zmiany

Knowledge of Basic Linear Algebra, Discrete Mathematics (Graph Theory), Probability Theory. Knowledge of linear optimization models in terms of the subject 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. Building of mathematical models for the problems of discrete optimization: production problem and diet problem with integer variables, cutting stock and loading problems
    (2 h.).
2. Branch and bound method for the linear integer programming problems (2 h.).
3. Transportation problem with cost criterion and time criterion. Transportation algorithm. Assignment and conveyor belt problem (4 h.).
4. Solving of discrete and binary problems using Solver in Excel (4 h.). Colloquium (2 h.).
5. Finding maximal flow and minimal cuts in the flow networks. FF-EK algorithm (2 h.).
6. Travelling salesman problem. Little’s algorithm. (2 h.).
7. Building of activity networks in project scheduling. Finding minimal time of project realization, critical paths (CPM method) and Gantt diagram (4 h.).
8. Problems of linear multicriteria optimization. Finding Pareto-optimal and efficient solutions. Optimal solution for metacriterion (2 h.).
9. Problems of discrete multicriteria optimization. Hasse diagrams and Pareto-optimal solutions. Degrees of realization of criteria of the first and second type, metacriterion
   (2 h.). Colloquium (2 h.).
10. Exercises related to decision making under uncertainty and risk (2 h.).

 

Metody kształcenia

Traditional 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 from the subject takes into account grade from the laboratory (40%) and grade from the exam (60%) under the assumption that the
student has achieved all assumed educational outcomes at a sufficient degree.
 

Literatura podstawowa

1. J. Curwin, R. Slater, Quantitative Methods for Business Decisions, Cengage Learning EMEA, 1991
2. M. Q. Anderson, R. J. Lievano, Quantitative Management, Kent Pub. Co, 1986
3. S. Cooke, N. Slack, Making Management Decisions, Pearson Education Limited, 1992

Literatura uzupełniająca

1. D. A. Moore, Managerial Decision Making, Edward Elgar Publishing, 2011
2. B. Roy, Multicriteria Methodology for Decision Aiding, Springer 1996

Uwagi

Zmodyfikowane przez dr Ewa Synówka (ostatnia modyfikacja: 10-04-2024 20:12)