Operations Research and Mathematical Models in Technology

Course guarantor:

Jana Kučerová

Lecturer:

Jana Kučerová

Tutor:

Jana Kučerová

Supervisor:

Department of Applied Informatics

Synopsis:

An introduction to optimization methodologies with the emphasis on linear

optimization, stochastic modelling and multiple criteria optimization including algorithms and computations. Applications will be introduced as appropriate in seminars.

Requirements:

no prerequisities

Syllabus of lectures:

1. Survey of optimization methods in Operations Research. Principles of model building. Formulation of optimization problems.

2. Methods for linear optimization with one criterion. Simplex method.

3. Parametrical and integer linear programming.

4. Formulation of practical transporation problems. Initial feasible solution and optimal solution of transportation problem. (MODI method)

5. Stochastic processes.

6. Queuing theory. Applications of queuing theory.

7. Random number generation. Generation of the values of random variable with a given distribution.

8. Simulation modelling.

9.Deterministic models of inventory control. Stochastic modelsof inventory control.

10. Models of selection and replacement and their applications.

11. Dynamic programming. Bellmans principle of optimality.

12. Classification of decision situations. Optimization with one criterion and multiple criteria. Game theory.

13. Multiple criteria decision making

Syllabus of tutorials:

1. Formulation of optimization problems with the emphasis on civil engineering.

2. Graphical method

3. Simplex method.

4. Examples of transportation problems. Initial feasible solution and optimal solution of transportation problem. (MODI method)

5. Examples in queuing theory. Applications of queuing theory.

6. Examples of random number generation. Generation of the values of random variable with a given distribution.

7. Examples of simulation modelling.

8. Deterministic models of inventory control. Stochastic modelsof inventory control.

9. Models of selection and replacement and their applications.

10. Dynamic programming. Bellmans principle of optimality.

11. Formulation of multiple criteria problems

12. Compromise solution of multiple criteria problem

13. Multiple criteria decision making

Study Objective:

The goal of the study is to introduce the standard optimization models and the approaches in model buildingto to students. The emphasis is on the application of these models in practice.

Study materials:

Demel, J.: Operační výzkum. kix.fsv.cvut.cz/~demel/ped, Praha 2022

Jablonský, J.: Operační výzkum. Professional Publishing, Praha 2011, ISBN 978-80-86946-44-3

Hillier, F.S., Lieberman, G.J.: Introduction to Operations Research (tenth edition). McGraw-Hill 2015, ISBN 978-1-259-25318-8

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Stavitelství - příprava, realizace a provoz staveb (compulsory elective course)