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Selected financial optimization models
Bujnovský, Daniel ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This work is focused on models of optimal asset and liability management. The practical section illustrates various ways of modelling strategies depending on the problem formulation, chosen set of assets and the type of the used optimization technique. The main examples are portfolio immunization and the Yasuda-Kasai model together with the extended version of Markowitz model. The author provides across the work an overview of different financial risks and various tools for their measurement together with possible formulations of expected returns relevant to the studied models. The individual models are compared and often extended by other constraints in order to improve their practical applicability. From the point of view of the mathematical optimization several ways of input data generation are described for example by using the extended Brownian motion. All practical parts go hand in hand with illustrative pictures and codes. The necessary financial and mathematical theory is included as well.
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Modeling of scoring probability in sport
Hilscher, Ondřej ; Bednář, Josef (referee) ; Hrabec, Pavel (advisor)
This thesis aims for modelling of scoring probability in football. It describes necessary mathematical methods used in logistic regression model building and in basic statistical hypothesis tests. Afterwards the mathematical methods are used on available data from professional football matches. Resulting model uses shooting method, pitch location and simplified match situation as predictors.
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Optimization of EDM process control parameters
Prokeš, Tomáš ; Beneš, Libor (referee) ; Bednář, Josef (referee) ; Matoušek, Radomil (advisor)
The dissertation thesis is focused on the optimization of control parameters of an EDM machine; the subject of optimization is cutting speed and surface topography. The first part of the thesis contains a research study on the technology of electrical discharge machining with the attention paid to the optimization methods use for control parameters of this process. The second part of the thesis is focused on real application of knowledge gained from studied sources. Here, a design of experiment aim at optimizing the parameters of the EDM machine is designed and carried on to maximize the cutting speed with the highest possible surface quallity. The result of the work is to build adequate regression models and find the optimal setting of machine control parameters.
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Optimization Risk Modelling in GAMS
Kutílek, Vladislav ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with the possibilities of using the optimization modelling software system GAMS in risk management. According to the assignment, emphasis is placed on a detailed approach to the program for those, who are interested in its use in the field of risk engineering applications. The first part of the thesis contains the knowledge to understand what the GAMS program is and what it is used for. The next part of the work provides instructions on how to download, install, activate the program and what the user interface of the program looks like. Thanks to mathematical programming, it will be explained on a project on the distribution of lung ventilators, what basic approaches may be used in risk modelling in the GAMS program on a deterministic model. The following are more complex wait-and-see models, which contains the probability parameters and here-and-now models, where we work with demand scenarios and verify whether if they meets the requirements of other scenarios or calculate costs for the highest demands. The two-stage model is also one of the here-and-now models, but it is significantly more complex in its size and range of input data, it includes additional price parameters for added or removed pieces of lung ventilators from the order.
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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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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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Optimization Models in Energy Production
Němcová, Lucie ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This bachelor's thesis focuses on optimization of a boiler's size of a waste incineration plant from an economic point of view. The problem was approximated by discretization because random parameters with normal distribution occured in the incineration plant model. To evaluate the quality of such approximation there were created confidence intervals using random sample information, independent random number streams method and common random number streams method. Used methods were compared and the smallest number of scenarios that aproximates the problem "well enough" was proposed in the last part of this thesis.
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Sports data analysis
Horák, Patrik ; Bednář, Josef (referee) ; Hrabec, Pavel (advisor)
The main preoccupation of this thesis is analysis of ice hockey statistics. The first section describes widely used elementary and advanced ice hockey statistics. The second part contains selected comparable studies working with similar hypotheses. The third section introduces necessary mathematical tools, such as, Two-sample t-test, correlation, Two-way analysis of variance with no interaction and their nonparametric equivalents. In the last section described statistical hypotheses tests are applied to ice hockey dataset. Results interpretation is also included.
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Statistical properties of control charts and capability models
Vidová, Katarína ; Jankových, Róbert (referee) ; Bednář, Josef (advisor)
The diploma thesis is focused on process stability and capability assessment. It describes certain types of control charts, basic capability indices as well as Box-Cox transformation. The practical part of the study is concerned with applying control charts on generated data and consequently on real data. By this, it focuses on comparing various methods of estimating sample standard deviation and on the impact of non-compliance with the assumption of normal distribution of process variable on process stability and capability assessment.
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Determination of capability and stability of a chosen technical process
Šváchová, Mariana ; Blecha, Petr (referee) ; Bednář, Josef (advisor)
This diploma thesis deals with the evaluation of the capability of a specific production process. The theoretical part of the work contains a description of statistical process control, types of control charts and evaluation of process capability. The practical part is focused on evaluating the capability of a specific process. The method of dataset collection is described at first, then this data are analyzed and the capability of this process is evaluated.
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