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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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Production planning under uncertainty
Grulich, Martin ; Popela, Pavel (referee) ; Dvořák, Jiří (advisor)
This diploma work deals with a dynamic multi-level multi-item lot sizing problem in a general production-assembly structure represented by a directed acyclic network, where each node may have several predecessors and successors. We assume stochastic demand, finite planning horizon consisting of discrete time periods, dynamic lot sizes, multiple constrained resources and time-varying cost parameters. The objective is to minimize the total costs over the planning horizon. This thesis includes overview of models with stochastic demand and also general description of genetic algorithm. Using different modifications of genetic algorithm I have proposed and implemented methods for solving a chosen model. Then I have made an experimental comparison of these method on selected problems.
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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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Stochastic Programming Methods for Investment Decisions
Kubelka, Lukáš ; CFA, Tomáš Menčík, (referee) ; Popela, Pavel (advisor)
This thesis deals with methods of stochastic programming and their application in financial investment. Theoretical part is devoted to basic terms of mathematical optimization, stochastic programming and decision making under uncertainty. Furter, there are introduced basic principles of modern portfolio theory, substantial part is devoted to risk measurement techniques in the context of investment, mostly to the methods Value at Risk and Expected shortfall. Practical part aims to creation of optimization models with an emphasis to minimize investment risk. Created models deal with real data and they are solved in optimization software GAMS.
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Chess preparation optimization
Walica, Roman ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
This work is focused on the preparation for the chess game, the issue of Elo rating system and optimization of the problem associated with the preparation for the chess tournament. You can find here how to obtain and modify appropriate information about potential opponents behind the chessboard. Result of this work is an optimization model which, if you enter relevant data, calculates how much time to spend on preparations for chess variants.
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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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Fossil fuels substitution in large combustion plant
Hájek, Zdeněk ; Popela, Pavel (referee) ; Touš, Michal (advisor)
The thesis aims at current issues of using renewable resources here in the Czech Republic, mainly on biomass co-firing with fossil fuels in large combustion plant. The introduction provides an overview of systems for biomass co-firing. Further the using of optimization for solution problem of integration biomass fuels into existing large combustion plants and planning its operation conditions is presented. The main point of this thesis lies in creating of a user interface for modeling and optimization tool. Its functionality will be proved by solving a case study involving the analysis of possibilities for replacing fossil fuels due to the limited availability of coal in the market.
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