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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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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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Optimalizace výrobní struktury ve firmě Jelínek lahůdky z Hané s. r. o.
Zatloukal, David
Zatloukal, D. Optimalization of production structure in Jelínek lahůdky z Hané s. r. o. company. Bachelor thesis. Brno: Mendel University, 2019. This these is focused on optimalization of production in Jelínek lahůdky z Hané s. r. o. company while respecting all requirements set by the management of the company, limiting conditions and for the purpose of maximizing profit or minimizing costs. The introduction and the aim of the these are described in the introduction. The following is the table of contents and a list of images and tables that were used to create the these. In the second part, the problems and theoretical aspects of operational research are explained. Then the company itself, it’s history and operations are introduced. In the practical part, several mathematical models maximizing profit, minimizing costs and a model based on a one-time higher order are created. The following are recommendations not only for a specific company, but also general recommendations for similar companies engaged in similar production.
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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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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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Origin of linear programming as a scientific discipline
Fišmon, Petr ; Šindelářová, Irena (advisor) ; Kuncová, Martina (referee)
This thesis deals with the origin and extension of linear programming. It describes various influences that have participated in its formation. The first part of thesis describes military influences, which stimulated governments of great powers to support mathematical modelling and development of linear programming. Next point of the bachelor paper is development of general linear model that was based on economics models. The thesis deals with mathematic theory, which gave the foundation to the Simplex method and with computer technology, which was able to solve linear models and put them into practice.
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Alternative rules for determining pivot columns and pivot rows in the simplex method
Leontiev, Andrey ; Kalčevová, Jana (advisor) ; Skočdopolová, Veronika (referee)
In my thesis I tried to describe the problems of choice of a pivot in the simplex method. The first part is devoted to the mathematical model of linear programming and simplex method in general. Here are explained the key concepts and principles of this method. There is the description of alternative rules for choosing a pivot using the simplex method in the second part. The description of each method is supported by example. I emphasize here the proofs of finite algorithm for each rule. In the last part of my thesis I have placed my own examples to show the different effects using different methods.
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