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Risk modelling for production processes
Ftáčnik, Peter ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The processes and procedures covered the main core of the professional operations in the manufacturing plant. The enterprise should focus on the efficient running of the main processes and risks associated with these procedures. My thesis deals with the risk analysis of selected manufacturing processes particular company from qualitative and quantitative point of view. First, the results are presented from qualitative risk analysis, especially in scope of failures of the machines or in the sequences of production. Second part focus on the problems of optimization sequence batches that the total time required for pre-setting of machines between doses should be minimal. The thesis also takes random waiting period into the consideration and applies wait-and-see approach of stochaistic programming applied in task traveling salesman. Calculations are processed by the GAMS. The results from the GAMS are refered in MS Excel, they are further discussed and interpreted by using descriptive statistics.
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Advanced Decomposition Methods in Stochastic Convex Optimization
Kůdela, Jakub ; Fabian, Csaba (referee) ; Šmíd,, Martin (referee) ; Popela, Pavel (advisor)
Při práci s úlohami stochastického programování se často setkáváme s optimalizačními problémy, které jsou příliš rozsáhlé na to, aby byly zpracovány pomocí rutinních metod matematického programování. Nicméně, v některých případech mají tyto problémy vhodnou strukturu, umožňující použití specializovaných dekompozičních metod, které lze použít při řešení rozsáhlých optimalizačních problémů. Tato práce se zabývá dvěma třídami úloh stochastického programování, které mají speciální strukturu, a to dvoustupňovými stochastickými úlohami a úlohami s pravděpodobnostním omezením, a pokročilými dekompozičními metodami, které lze použít k řešení problému v těchto dvou třídách. V práci popisujeme novou metodu pro tvorbu “warm-start” řezů pro metodu zvanou “Generalized Benders Decomposition”, která se používá při řešení dvoustupňových stochastických problémů. Pro třídu úloh s pravděpodobnostním omezením zde uvádíme originální dekompoziční metodu, kterou jsme nazvali “Pool & Discard algoritmus”. Užitečnost popsaných dekompozičních metod je ukázána na několika příkladech a inženýrských aplikacích.
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Integer Optimization for Transportation Problems
Cabalka, Matouš ; Žák, Libor (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems with emphasis on traveling salesman problem. Brief introduction to the history is followed by theoretical part describing linear programming, integer programming and formulation of traveling salesman problem. Description of data preprocessing is included. Finally computational results are discussed and evaluated.
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Optimization Models of Financial Risk
Danko, Erik ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with optimization models of financial risks. The first part, which is devoted to the theoretical background, introduces the basic concepts of optimization, modern portfolio theory, fundamental and technical analysis and statistical background. The basic principles of operation of modern portfolio theory are presented. The methods for analysis and selection of assets called Growth at A Reasonable Price and portfolio optimization approach according to Harry Markowitz were used with selected methods. The practical part is focused on the data analysis, selection of assets and design of a portfolio optimization model according to selected conditions with an emphasis on minimizing investment risk. The used models examine the selected data and are solved using the MS Excel add-in Solver version.
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Modelling of logistics of inter-municipal waste transport
Kučera, Jiří ; Popela, Pavel (referee) ; Nevrlý, Vlastimír (advisor)
This diploma thesis focuses on the issue of inter-municipal waste transport. The main part of the thesis focuses on the development of a computing core designed to create a collection plan for selected municipalities forming a union. The computing core was created so that it could be integrated into a user-friendly web application. The creation of a computational tool is based on the theoretical foundations of graph theory, mathematical programming and heuristic algorithms. In this thesis, consecutive algorithms for clustering of address points, collection design for several types of waste with a heterogeneous vehicle fleet and for creating collection proposal for a several-week long collection plan were developed. The presented approach was tested on real data from an existing union of municipalities in the South Moravian Region.
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Implementation of KDE+ statistic method
Svoboda, Tomáš ; Popela, Pavel (referee) ; Bíl,, Michal (advisor)
In this master's thesis I presented a new statistical method KDE+ (Kernel Density Estimation plus) that allows detecting clusters of points on the linear data. I created a self-standing application that enables anybody to try the method and apply it on their own data. One possible usage of the method and application is for the detection of critical roads sections with a high concentration of traffic accidents. Development of the application includes analysis of KDE+ statistical method, design of appropriate program structures and the implementation. Optimization were carried out to achieve higher performance after creating the prototype. At the end the software was validated by analysing vehicle collision data from the police database of the Czech Republic.
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Mathematical models in strategic decision-making
Khýr, Lukáš ; Popela, Pavel (referee) ; Pavlas, Martin (advisor)
This master thesis deals with various mathematical models, which can be used for designing the location of collection points for various fractions of municipal waste with consideration of walking distance, economic demands and utilization of allocated capacities. Scripts for generating input datasets for applied models from basic input data, which are address points with population and GPS coordinates, is also included in the thesis. The model was implemented in GAMS and the script was written in VBA in Microsoft Excel. Model was used in case study. Results of single and multi-criteria approaches are analyzed and compared.
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Operational research in waste recycling
Camara, Assa ; Popela, Pavel (referee) ; Pavlas, Martin (advisor)
The bachelor thesis is aimed at finding and describing a mathematical model that reconstructs the actual current financial costs of collecting and collecting waste at the level of municipalities with expanded scope, which are not easily available and are needed for further planning in waste management. In order to create the model, the knowledge of optimization, statistics and graph theory are summarized in the text. The model is applied to real data in the GAMS environment. The results of the application are commented on and analysed. Based on this analysis, there are also possibilities to develop this model.
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Optimization in Financial Applications
Večeřa, Tomáš ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
The main purpose of this thesis is to create an efficient stock portfolio, specifically to optimize current distribution of stock index S&P 500. The building process consist of well-established mathematical-economical methods, which are then improved by applying mathematical models from statistics and optimization. Firstly, we define essential terms in order to reach deeper understanding of used methods. Afterwards, process of thorough selection of stocks and sectors comes to place. Data are then processed in program GAMS in three different ways, depending on investors preference. Although this approach was applied to current era, its principles are applicable to any given timeline.
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