1. SylabUZ
2. Wydział Mechaniczny
3. semestr zimowy 2023/2024
4. WM - oferta ERASMUS - Program Erasmus
5. Operations Research

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Operations Research - opis przedmiotu

Cel przedmiotu

Transfer of basic knowledge and acquisition by students of skills and competences in the field of operations research, which will be used in the further education process and useful in future professional work.

Wymagania wstępne

Zapisz zmiany

Basic Mathematics Course, Information Technology.

Zakres tematyczny

Lecture content

L1. Preliminary issues. Basic elements and problems of operational research. Linear programming problem. Geometric method of solving the problem LP.

L2. Simplex method.

L3. Two-phase method and Big M method. Problems with Simplex.

L4. Duality and sensitivity analysis. The Dual Simplex Method.

L5. The Transportation Problem.

L6. The Assignment and Traveling Salesman Problems.

L7. Integer Programming. Gomory's cutting plane algorithm and the Branch-and-Bound Technique.

L8. Network analysis. Basic concepts of graphs. The Terminology of Networks.

L9. Shortest Path Method. Applications in technology.

L10. Project management technique. Critical path method. CPM and the Gantt chart.

L11. Time-cost analysis. PERT method. Computer aided network analysis.

L12. Components and classification of queuing systems. Kendal notation. Little's laws. Rate diagram for the birth and death process. Laws for constructing a system of equations.

L13. A single-channel system with an exponential distribution of service time and the arrival strems. Applications.

L14. Multi-channel system with a simple fluxes. Simple Streams. Applications.

L15. Computer-aided research of queuing systems. Final remarks.

Project

P1. Presentation of the course program, learning outcomes and assignment conditions. Characteristics of individual topics carried out during the project classes.

P2-3. Geometric method of solving the linear programming problem.

P4-9. Simplex Methods - maximisation and minimisation case, simplex algorithm, dual simplex method, big M method. OFC (Objective Function Coefficient) and RHS (Right Hand Side) sensitivity analysis. Integer programming.

P10-11. The transportation problem, formulation and types. The transportation problem, formulation and types. Methods of generating the basic solution. Optimization of the basic solution. Degeneracy in the transportation problem.

P12. The assignment problem.

P13-14. Project planning and scheduling - CPM and PERT techniques.

P15. Summary of completed problems. Completion of the project classes.

Metody kształcenia

Conventional lecture..

Project - individual and group work of students using literature and lecture notes.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture: exam

Grade based on a written exam that verifies the knowledge of basic issues.

Project: graded credit

The grade is determined on the basis of the component evaluating skills related to the implementation of project tasks, preparation of reports and the component for "defense" by the student of individual reports.

Final grade: arithmetic average of grades from the above-mentioned forms of classes.

Literatura podstawowa

1. Hillier F.S., Lieberman G.J., Introduction to Operations Research, McGrawHill, 2015.
2. Dantzig, George B., Thapa, Mukund N., Linear Programming 2: Theory and Extensions, Springer, 2003.
3. Thomopoulos N.T.: Fundamentals of Queuing Systems, Springer, New York, 2012.
4. P. Rama Murthy: Operations Research, New Age International Publishers, 2007.
5. Wayne L. Winston: Operations Research. Applications and algorithms. Thomson Brooks/Cole, 2004.
6. Electronic help of programs

Literatura uzupełniająca

1. Halidi Lyeme, Mohamed Seleman:  Introduction to Operations Research: Theory and Applications. LAP LAMBERT Academic Publishing, 2012.
2. Ignasiak E. (red.), Badania operacyjne, PWE, Warszawa, 2001. (in Polish)
3. Kukuła K. (red.), Badania operacyjne w przykładach i zadaniach, Warszawa, PWN, 2001. (in Polish)

Uwagi

Zmodyfikowane przez dr inż. Tomasz Belica (ostatnia modyfikacja: 06-02-2024 18:42)