Operations Research and Mathematical Methods in Technology
Code  Completion  Credits  Range  Language 

128OPMT  Z,ZK  5  2P+2C  Czech 
 Garant předmětu:
 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 9788086946443
Hillier, F.S., Lieberman, G.J.: Introduction to Operations Research (tenth edition). McGrawHill 2015, ISBN 9781259253188
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 obor Příprava, realizace a provoz staveb (compulsory course)