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Optimization of network flows
Rychtář, Adam ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This bachelor thesis focuses on the assigment of waste flows to specific producer for each edge andaplication on real model which maps the Czech Republic and the model is applied to real data of the Czech Republic. The goal is to determine variance of the expenses for each producer subject to changes in waste processing requirements. Then, the solution impacts and bottlenecks are analysed. The suitable optmization models is formulated and computations are realizaed in GAMS.
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Implemenation of a Game Theory Library
Židek, Stanislav ; Peringer, Petr (referee) ; Hrubý, Martin (advisor)
Game theory has become very powerful tool for modelling decision-making situations of rational players. However, practical applications are strongly limited by the size of particular game, which is connected to the computational power of computers nowadays. Aim of this master's thesis is to design and implement a library, which would be able to find correlated equilibria in as complex non-cooperative games as possible.
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Advanced Optimization of Network Flows
Cabalka, Matouš ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
The master’s thesis focuses on the optimization models in logistics with emphasis on the network interdiction problem. The brief introduction is followed by two overview chapters - graph theory and mathematical programming. Important definitions strongly related to network interdiction problems are introduced in the chapter named Basic concepts of graph theory. Necessary theorems used for solving problems are following the definitions. Next chapter named Introduction to mathematical programming firstly contains concepts from linear programming. Definitions and theorems are chosen with respect to the following maximum flow problem and the derived dual problem. Concepts of stochastic optimization follow. In the fifth chapter, we discuss deterministic models of the network interdiction. Stochastic models of the network interdiction follow in the next chapter. All models are implemented in programmes written in the programming language GAMS, the codes are attached.
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Network flows and their modifications
Bitara, Matúš ; Hošek, Jaromír (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems. Brief introduction to graph theory and linear programming is followed by transportation problem of waste transport. Then there is a part with real data applied to the territory of the Czech Republic. After that the user interface created in Visual Basic programming language is explained. In conclusion computational results are discussed as well as their possible improvement.
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Optical switching and traffic grooming
Foldyna, Petr ; Havliš, Ondřej (referee) ; Horváth, Tomáš (advisor)
This bachelor thesis is about problematics of optimalization wavelenght usage in optical networks. First part theoreticaly explains optical networks and problems when using them, switching in optical networks and traffic grooming. In second part mathematical equations of given problems are realized and also simulations using GLPK are realized. From results of simulation resolutions are given and usage of methods in real networks is explained.
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Network simplex method
Khýr, Lukáš ; Janošťák, František (referee) ; Popela, Pavel (advisor)
This thesis is focused on summary knowledges relating to mathematical modeling in optimization area. We will deal with simplex method in detail and especially its network modification, which is used in various practical applications. We will solve tasks of various sizes and compare their solutions using implementation these two methods in Matlab. There is solved a task with real data provided by the Institute of Process Engineering at the end of the work.
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Optimization in Logistics
Huclová, Alena ; Škapa, Stanislav (referee) ; Popela, Pavel (advisor)
The thesis is focused on the optimization of models of transportation and transshipment problem with random demand, additional edges, and dynamic pricing. The theoretical part of the thesis introduces mathematical models of transportation. The software GAMS, which is used for the solution, is all so described. The practical part is a split among chapters and implements the described models by using real data.
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Selected optimization models in logistics
Málek, Martin ; Pavlas, Martin (referee) ; Popela, Pavel (advisor)
The bachelor thesis focuses on optimization models in logistics, which are solved by linear programming. Theoretical part introduces basic terms of graph theory, optimization, linear programming and network flows. Practical part contains mathematical models, their implementation, and obtained results. Furthermore, real-world application is solved at the end.
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Advanced Stochastic Programming Models in Power Engineering
Pavelka, Ondřej ; Štětina, Josef (referee) ; Popela, Pavel (advisor)
This diploma thesis applies stochastic optimization in the field of the power engineering. In the thesis first part, the needed mathematical theory is described, specifically mathematical, linear, nonlinear, integer and stochastic programming. The second part deals with the heating plant, in which heat is generated by gas and biomass boilers. The aim of this thesis is to design a model for the schedule planning of these boilers. The model is based on two stage stochastic programming with scenario approach. Then the model is solved by GAMS software. In the final part of the text, the focus is on the model sensitivity analysis and suggestions for future improvement.
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