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Vertex coloring algorithms in scheduling problems under uncertainty
Hájek, Štěpán ; Branda, Martin (advisor) ; Lavička, Karel (referee)
This thesis concerns solutions to problems that arise in optimizing fixed interval scheduling under situations of uncertainty such as when there are random delays in job process times. These problems can be solved by using a vertex coloring with random edges and problems can be formulated using integer linear, quadratic and stochastic programming. In this thesis is propo- sed a new integer linear formulation. Under certain conditions there is proved its equivalence with stochastic formulation, where is maximized the schedule reliability. Moreover, we modified the proposed formulation to obtain bet- ter corresponding to real life situations. In a numerical study we compared computational time of individual formulations. It turns out that the propo- sed formulation is able to solve scheduling problems considerably faster than other formulations. 1
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Normality and its testing
Hájek, Štěpán ; Bašta, Milan (advisor) ; Klebanov, Lev (referee)
This thesis is concerned with normality and its testing. We often encounter with this topic when using statistical tests and models. Among others, examples such as t tests, analysis of variance and linear regression might be given. In this thesis these tests and models are overviewed and the consequences of the violation of the normality assumption are briefly mentioned. The following section describes statistical tests of normality. For example Shapiro-Wilk test or Anderson-Darling test are explored. For each test of normality is given test statistic and conditions for rejection of the null hypothesis. The last section provides a simulation study. The first part of this study is devoted to exploring whether the empirical relative frequency of Type I error corresponds to the nominal significance level of the test. The second part of the simulation study explores the power of normality tests against various alternatives. The results are summarized and discussed. 1
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Application of the Fibonacci sequence in asset markets
Hájek, Štěpán ; Soukup, Alexandr (advisor)
This bachelor thesis deals with ,how says the title ,Application of the Fibonacci sequence in asset markets. Aim of the thesis itself is preview of the main technics of aúplication of the Fibonacci sequence on real markets.
In the teoretic part of thesis is eplained Fibonacci sequence everywhere around us, not only on markets. Explaind are also basic applications of Fibonacci sequence on various markets.
In the solution of particular problem were attached technics used by proffesional traders and verified by myself. We will be able to identify levels ,which markets tend to use as a support or resistance. We will review the reasearch´s productivness of particular Aápplication of the Fibonacci sequence.
Based on the reasearch ,we will have basic idea about tool, that is beinng used by traders all around the world. Goal of the thesis is to provide knowledge about Fibonacci sequence and also the application of it.
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