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Optimizing the line-up of a sports team in a sallary capped league
Sabo, Adam ; Popela, Pavel (referee) ; Hrabec, Pavel (advisor)
This thesis is focused on the optimization of the lineup of a professional sports team operating under a salary cap condition. In the first part of the thesis, the theoretical foundations necessary for a proper understanding of the issue are introduced. Further, mathematical statistics and optimization methods are explained here and used in data analysis and in the creation of the relevant model. Particular emphasis is put on the methods of principal component analysis and linear programming. In the second part of the thesis, the problem of the optimization task, which takes into account the relevant NHL rules of competition and the salary cap together with performance characteristics of players, is formulated. The formulation was used to develop an optimization model that simulates real conditions in the NHL. This section also presents the application of the model based on historical data. Results obtained from calculations using the Python programming language are presented in the form of graphs, tables, and commentaries, showcasing the optimal team lineups, their characteristics, and respective rankings.
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Advanced Budget Optimization
Golasowski, Martin ; Janíček, Ladislav (referee) ; Popela, Pavel (advisor)
The aim of this diploma thesis is to show possibilities of mathematical modeling of creating budget of public universities in Czech republic based on a deeper study of the issue. In the first part of the work, the financing of universities in the Czech Republic is explained and according to what rules and patterns money is distributed to universities. In the next part, the basic knowledge regarding mathematical optimization and stochastic programming, including the creation of models, is presented. Subsequently, a model of stochastic nonlinear programming is compiled to optimize the distribution of funds from some funding sources to universities. In the last chapter, the model is implemented in the GAMS software and the obtained results are evaluated.
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Statistical analysis of COVID-19
Zapoměl, Jakub ; Popela, Pavel (referee) ; Žák, Libor (advisor)
This thesis deals with the statistical analysis of COVID-19 disease. The thesis focuses on data processing related to the disease, the formulation and verification of statistical hypotheses, the application of piecewise linear regression, the prediction of the further development of the disease, and the verification of predictions presented in the media. Specific analyses are conducted using Python.
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Airborne wind energy system
Killioglu, Can ; Popela, Robert (referee) ; Zikmund, Pavel (advisor)
The master's thesis deals with the issue of flying wind turbines, which is an innovative area of renewable energy. The main advantage of these power plants over conventional wind turbines is their ability to reach higher altitudes and thus take advantage of stronger wind conditions. An important part of the thesis is the aerodynamic analysis of the rotor in autorotation mode, which investigates the behaviour of the propeller rotor. Furthermore, the conceptual and structural design of a selected type of flying wind turbine is carried out.
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Optimization in selected engineering problems
Přikryl, Tomáš ; Popela, Pavel (referee) ; Mrázková, Eva (advisor)
The goal of this paper is a basic understanding of elementary concepts of the mathematical programming field and an aplication of such concepts for the optimization of machine design. The subject of nonlinear optimization is put under deeper scrutiny and so are solution methods of nonlinear problems. This paper also contains essential findings about shafts in the context of engineering components. In the practical part these findings are applied for an optimization of a shaft where the goal is to minimize the shaft’s weight.
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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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Risk Analysis of Important Factors of Company Using Statistical Methods
Genčurová, Lucie ; Popela, Pavel (referee) ; Karpíšek, Zdeněk (advisor)
This diploma thesis is focusing on the analysis of individual financial indicators of company MARLENKA international s.r.o. using the methods of financial analysis and statistical methods. The financial situation of the company is evaluated based on the results of analyzes. Then the prediction of the evolution of the selected indicators is calculated for the next two years using regression analysis and interval regression analysis. The diploma thesis also addresses potential risk for the company and recommendations for the risk reduction. Following the analyzes, a summary of the company’s financial situation is created.
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Statistical analysis of samples from the generalized exponential distribution
Votavová, Helena ; Popela, Pavel (referee) ; Michálek, Jaroslav (advisor)
Diplomová práce se zabývá zobecněným exponenciálním rozdělením jako alternativou k Weibullovu a log-normálnímu rozdělení. Jsou popsány základní charakteristiky tohoto rozdělení a metody odhadu parametrů. Samostatná kapitola je věnována testům dobré shody. Druhá část práce se zabývá cenzorovanými výběry. Jsou uvedeny ukázkové příklady pro exponenciální rozdělení. Dále je studován případ cenzorování typu I zleva, který dosud nebyl publikován. Pro tento speciální případ jsou provedeny simulace s podrobným popisem vlastností a chování. Dále je pro toto rozdělení odvozen EM algoritmus a jeho efektivita je porovnána s metodou maximální věrohodnosti. Vypracovaná teorie je aplikována pro analýzu environmentálních dat.
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Optimization in engineering problems
Čepl, Ondřej ; Popela, Pavel (referee) ; Mrázková, Eva (advisor)
This bachelor's work engages optimization and its improvement in engineering cases. There are defined basic terms and optimization's cases, basic characteristics of the optimization case are accounted and basic methods of their solutions are understated. These teoretic findings are availed by optimization of the measurements of three-bar truss, whereas there are solved two options of optimization's case. Mathematical models are implemented to programm GAMS and at the conclusion is accomplished disccusion of accomplishments.
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