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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 Optimization Models in Energy Industry
Studený, Vojtěch ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
This diploma thesis addresses the modeling of electricity production from rooftop photovoltaic power plants. The aim of the work was to find out how the input parameters affect the return and to find out the optimal conditions for achieving the shortest return time. The model is created in Microsoft Excel and GAMS. The inputs include the current conditions of the New Green Savings grant program. The work separately examines systems without energy storage and systems with batteries. Both systems are optimized and then the change in return depending on random variables is determined. The results show a lower payback period for battery systems, while meeting the subsidy conditions at the same time with lower acquisition costs.
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Optimization in engineering design problems
Sýkora, Zdeněk ; Cabalka, Matouš (referee) ; Mrázková, Eva (advisor)
This bachelor thesis deals with the use of optimization in the problems of beam loading and buckling stability. The problems were solved in the GAMS software. The solutions of the first two problems is compared with results obtained using software Ansys. It also contains chapters on basic optimization theory, the theory of ordinary differential equations and a chapter on selected concepts in mechanics of materials.
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Optimization in logistics with pricing
Langr, Tomáš ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
This bachelor thesis concerns itself with dynamic pricing and its application in network transport models in order to optimize the prices that play an important role in these models. In the theoretical part, we deal with the basic concepts of optimization, linear programming, graph theory and theory related to dynamic pricing. Emphasis is put on linking all this knowledge and its application in solving logistics models.
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Optimization Models of Risk in Energy Systems
Tetour, Daniel ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with mathematical modeling of the resource allocation problem in an energy system with respect to technical parameters of the used resources. The model includes random input variables affecting the amount of demand and constraints related to associated risks. The thesis addresses control of the operation of various types of boilers and also extends the system with a heat storage tank examining its impact on the behavior of the system and achieved results. The optimization model is based on a multi-period two-stage scenario model of stochastic programming and works with simulated data, which combines real data, statistically determined estimates, and the use of logistic regression. The implementation utilizes GAMS software. When comparing the achieved results with the current state, it was found that the heat storage tank has a positive effect on the function of the system as it allows for extended usage of the cheaper unregulated sources by storing surplus heat, and thus helps to reduce the overall costs of the system.
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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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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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Optimization models in population protection
Mihálová, Veronika ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
This master thesis utilizes operational research principles to model and address emergency events, with a focus on rapidly and effectively making decisions related to population sheltering and the allocation of security forces during such crises. The theoretical section provides fundamental information about the current state and application of risk management in civil security while defining terms directly associated with population protection and crisis management. Moreover, it explores the historical application of mathematical programming and optimization in crisis management processes. In the practical segment of the thesis, the fundamental traffic problem is adapted to address the issue of establishing permanent civil protection shelters in the Brno-Židenice district. The models are solved using the GAMS program, building upon a comprehensive risk analysis that meticulously identifies key components of the population protection system. Furthermore, potential risk scenarios for the system are formulated using the FMEA method. The results obtained, which outline optimal allocation strategies for residents and security forces, are visually presented on maps. Recommendations are provided for future planning and crisis management in emergency events.
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Stochastic Optimization Models in Energy Industry
Studený, Vojtěch ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
This diploma thesis addresses the modeling of electricity production from rooftop photovoltaic power plants. The aim of the work was to find out how the input parameters affect the return and to find out the optimal conditions for achieving the shortest return time. The model is created in Microsoft Excel and GAMS. The inputs include the current conditions of the New Green Savings grant program. The work separately examines systems without energy storage and systems with batteries. Both systems are optimized and then the change in return depending on random variables is determined. The results show a lower payback period for battery systems, while meeting the subsidy conditions at the same time with lower acquisition costs.
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