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Stochastic optimization in AIMMS
Kůdela, Jakub ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
Tato diplomová práce uvádí základní poznatky matematického a především stochastického programování. Navíc se zabývá použitím softwaru AIMMS při vytváření a řešení optimalizačních problémů. Naším hlavním cílem je naprogramovat v softwaru AIMMS několik metod řešení problémů stochastického programování a ukázat jejich použití a užitečnost na vybraných problémech. Jedním z problémů, který jsme si zvolili, je model spalovny. Všechny AIMMS programy, které v našem textu použijeme a popíšeme, a jejich zdrojové kódy budou přiloženy v dodatcích.
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Selected Optimization Models for Risk Reduction in Air Transport
Schwarz, Ondřej ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with mathematical modeling of the situation when due to the increased risks occurring around Europe there is a need of immediate transport of Czech citizens back to the Czech Republic. The model takes into account the general level of random fluctuations in demand and transportation costs. The optimization model is then built on the ideas of stochastic programming and includes real and expert data in the field of air transportation, which are later implemented into GAMS. The results are discussed. The survey part of the diploma thesis is devoted to the possibility of applying linear and stochastic programming, the interpretation of the mathematical transportation theory. It describes the basic tools and development environment and the realization of mathematical model based on real data in GAMS. The second part of the thesis deals with a proposal of possible improvements in aviation by applying the real data into the model and by analyzing the obtained results.
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Stochastic programming models with applications
Novotný, Jan ; Michálek, Jaroslav (referee) ; Popela, Pavel (advisor)
Diplomová práce se zabývá stochastickým programováním a jeho aplikací na problém mísení kameniva z oblasti stavebního inženýrství. Teoretická část práce je věnována odvození základních přístupů stochastického programování, tj. optimalizace se zohledněním náhodných vlivů v modelech. V aplikované části je prezentována tvorba vhodných optimalizačních modelů pro mísení kameniva, jejich implementace a výsledky. Práce zahrnuje původní aplikační výsledky docílené při řešení projektu GA ČR reg. čís. 103/08/1658 Pokročilá optimalizace návrhu složených betonových konstrukcí a teoretické výsledky projektu MŠMT České republiky čís. 1M06047 Centrum pro jakost a spolehlivost výroby.
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Modelling of energy producing system and its operation planning applying advanced mathematical methods
Benáčková, Jana ; Karpíšek, Zdeněk (referee) ; Pavlas, Martin (advisor)
This master's thesis deals with the proposal of the cost-effective biomass and coal combustion concept for a real generation plant. The optimization of the current fuel basis exploitation and annual operation scheduling was the main goal. Applying the regression analysis and stochastic programming the mathematical model was constructed based on the operating data. The overall energy source model was implemented to the concept of the optimal operation scheduling considering the economic aspects. The fuel utilization and energy production planning are the main applications of this design.
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Effective Investment Planning in Waste-to-Energy Systems
Šomplák, Radovan ; Klemeš,, Jiří (referee) ; Žaloudík, Petr (referee) ; Stehlík, Petr (advisor)
PhD thesis deals with the application of the simulation and optimization methods in the waste-to-energy field. An introduction describes the current state of the waste management in the EU with the focus on the Czech Republic. In the following chapter the evaluation criteria for investment intentions and the basic principles of stochastic programming are discussed. The core of the work lays in the mathematical models for the planning and operation of the process plants as well as in the mathematical models for the waste collection. The transportation problem involves all considered technological elements and therefore it is possible to simulate the waste streams between the producers and processors. This approach is demonstrated with five case studies. In the first three studies the calculations for the potential investor are presented. The main outcome of these case studies is the determination of the level of attractiveness of investment and the identification the greatest risks. Another case study is devoted to an analysis with the focus on perspective of government policies and in the last case study the issue of the waste management is analyzed in detail from the perspective of the waste producers. Developed computational tools are flexible and can be further developed and adapted based on the objectives of the specific tasks.
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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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Modelling of Selected Risks in Healthcare
Nováková, Pavlína ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with the modeling of selected risks in healthcare. Motivated by the current pandemic situation, it focuses on analysis of risks associated with the vaccination center in Brno. The theoretical part is mainly devoted to the issue of risk management with a focus on risks in healthcare, where the methods that are used in the practical part are defined. Furthermore, the thesis presents selected topics of mathematical programming. Especially, the newsvendor problem is introduced as inspiring case for further modelling. The brief description of the covid-19 pandemic situation later serves as one of the data sources. The practical part deals with the description and risk analysis of the vaccination process using the methods "What If?" and the FMEA method. Appropriate decisions are then proposed for selected risk situations using the GAMS optimization system. Based on the results of the calculations, specific recommendations are proposed.
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Asset-Liability Management:Application of Stochastic Programmingwith Endogenous Randomness andContamination
Rusý, Tomáš ; Kopa, Miloš (advisor) ; Consigli, Giorgio (referee) ; Branda, Martin (referee)
Title: Asset-Liability Management: Application of Stochastic Programming with Endogenous Randomness and Contamination Author: RNDr. Tomáš Rusý Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, PhD., Department of Probability and Mathematical Statistics Abstract: This thesis discusses a stochastic programming asset-liability management model that deals with decision-dependent randomness and a subsequent contamination analysis. The main model focuses on a pricing problem and the connected asset- liability management problem describing the typical life of a consumer loan. The endogeneity stems from the possibility of their customer rejecting the loan, the possibility of the customer defaulting on the loan and the possibility of prepay- ment which are all affected by the company's decision on interest rate of the loan. Another important factor, which plays a major role for liabilities, is the price of money in the market. There, we focus on the scenario generation procedure and develop a new calibration method for estimating the Hull-White model [Hull and White, 1990] under the real-world measure. We define the method for the gen- eral class of one-factor short-rate models and perform an extensive analysis to assess the estimation performance and...
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Selected Advanced Stochastic Programming Models
Brzobohatý, Jan ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with stochastic dominance. The goal is to lay the foundations for defining stochastic dominance, to describe its properties and to explain this concept on simple examples. Another goal is to apply this concept to network problems with random price. Examples in this thesis also contain solutions and python code how to find them.
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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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