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Modelling of Individual Investment Risks
Freml, Josef ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with modeling of individual investment risks. The first part is devoted to the approach of the basic concepts in the area of investment risks, assets, portfolio and its components. The basic principles of optimization, stochastic programming including the problems of modern theory of the portfolio are presented. The analysis of the current situation is divided into two parts, where the first part contains analysis of the investor profile. In the second part, the selection and analysis of assets suitable for combination in the portfolio are made. The practical part is focused on the creation of the Markowitz model of optimal portfolio of determined assets. The model works with real data and is programmed through the GAMS mathematical program.
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Models and methods for routing problems
Nevrlý, Vlastimír ; Žák, Libor (referee) ; Popela, Pavel (advisor)
This master's thesis deals with mathematical model building for routing problems and ways to solve them. There are discussed and implemented deterministic and heuristic approaches that are suitable to be utilized. A big effort is put into building of the mathematical model describing a real world problem from the field of waste management. Appropriate algorithms are developed and modified to solve a particular problem effectively. An original graphical environment is created to illustrate acquired results and perform testing computations.
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Optimization Risk Models in Fish Production
Franěk, Martin ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with the risk associated with fish production. Selected risks are further taken into account. The risks are further described and addressed using the FMEA matrix. The thesis contains a mathematical model that solves the optimal population of the pond in order to maximize profits. The model includes fixed input parameters, which includes the price of hatchery material and the market price of fish. Furthermore, the model contains random input parameters that are limited by the intervals and includes the growth coefficient and the size of the population in the pond. The optimization model is based on simulated data, which are based on real data and statistically determined estimates. The used data are processed into tables in MS Excel for better visualization. GAMS software is used for software implementation of the model.
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Engineering Optimization
Kokrda, Lukáš ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
The bachelor thesis deals with convex optimization and in particular, it processes a design of the optimal support of a loaded beam. For better understanding of the terms used, the bachelor thesis contains the brief introduction to the convex optimization problems, explanation of the basic therms of ordinary dierential equations and theory of elasticity. When the original model is built, then the results are obtained by computations in the MATLAB software.
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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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Modelling Languages for Optimization Problems
Talpa, Jaroslav ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
This bachelor thesis is concerned with the area of modeling and solving of optimization problems, mainly by the use of modeling languages. For the solving of two selected types of complex optimization problems, sensitivity analysis and multistage optimization, two original software solutions in Java using the GAMS modeling language, are described in the paper, which are further tested and applied to real problems. The thesis also describes the issue of parallelism which is implemented by the proposed programs.
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Mathematical Programming Models for Optimal Control Problems
Dražka, Jan ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
This thesis deals with optimization of a vehicle’s (racing) drive on a track. The model of a vehicle and a track is built in this thesis. The first chapter is devoted to the fastest pass problem formulation. The problem optimizes (in the least time) the vehicle’s drive from a start line to a finish line. The problem is formulated as an optimal control theory problem. In the second chapter the optimal control theory problem is suitably discretised and transformed into a nonlinear programming problem. The transformation of the fastest pass problem into nonlinear programming problem, its detailed and illustrative derivation and reformulation form the main part of the thesis. Third chapter presents the implementation and solution of the problem using GAMS and MATLAB. This thesis is a part of a specific research project on which the author has participated. The main contribution of the author is an original formulation of the fastest pass problem as a nonlinear programming problem and its implementation and solving using GAMS.
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Correlation coefficients and their field of application
Rudžík, Matej ; Popela, Pavel (referee) ; Žák, Libor (advisor)
This bachelor’s thesis deals with different types of correlation coefficients and their properties depending on the data layout. The theoretical part of this work contains definitions of various types of correlation coefficients and tests related with this issue. The practical part compares the behaviour of parametric and nonparametric correlation coefficients in different situations. This comparison is realised in program MATLAB.
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Engineering optimization models
Tydlačka, Martin ; Plšek, Jan (referee) ; Popela, Pavel (advisor)
A cross-section of a girder made out of profile I is designed with respect to random loads, to which a girder will face during life time. Because the random loads are there, we need another aaproach to solving this exercise. Acceptable aproach is usage of optimisation and four choosen models, solving random loads. The cross-section has been to optimize with respect to minimal weight subject the safety constraint. Goal of this thesis is to present method of transfer structural exercise to exercise of mathematical optimisation, present four choosen models and apply this to exercise with random loads.
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