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Decision Problems and Empirical Data; Applications to New Types of Problems
Odintsov, Kirill ; Kaňková, Vlasta (advisor) ; Lachout, Petr (referee)
This thesis concentrates on different approaches of solving decision making problems with an aspect of randomness. The basic methodologies of converting stochastic optimization problems to deterministic optimization problems are described. The proximity of solution of a problem and its empirical counterpart is shown. The empirical counterpart is used when we don't know the distribution of the random elements of the former problem. The distribution with heavy tails, stable distribution and their relationship is described. The stochastic dominance and the possibility of defining problems with stochastic dominance is introduced. The proximity of solution of problem with second order stochastic dominance and the solution of its empirical counterpart is proven. A portfolio management problem with second order stochastic dominance is solved by solving the equivalent empirical problem. Powered by TCPDF (www.tcpdf.org)
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Solving Canadian Traveller Problem
Filip, Sebastián ; Matoušek, Radomil (referee) ; Dvořák, Jiří (advisor)
This thesis deals with Canadian traveller problem (CTP), which can be defined as the shortest path problem in a stochastic environment. The overview of different CTP variants is presented in theoretical part of this thesis, as well as known solutions to these variants. In the next parts, the thesis focuses on the stochastic variation of CTP (SCTP). For this variant chosen solutions (strategies) are discussed more in depth. At the same time, the original strategies named UCTO and UCTP are presented. Further, the thesis deals with the description of a window application implemented in Java, which has been developed to validate and test the functionality of selected strategies. The final part contains experiments and comparison of selected strategies.
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Stochastic activity networks
Sůva, Pavel ; Dupačová, Jitka (advisor) ; Kaňková, Vlasta (referee)
In the present work, stochastic network models representing a project as a set of activities are studied, as well as different approaches to these models. The critical path method, stochastic network models with probability constraints, finding a reference project duration, worst-case analysis in stochastic networks and optimization of the parameters of the probability distributions of the activity durations are studied. Use of stochastic network models in telecommunications networks is also briefly presented. In a numerical study, some of these models are implemented and the~related numerical results are analyzed.
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Risk modelling in transportation
Lipovský, Tomáš ; Pavlas, Martin (referee) ; Popela, Pavel (advisor)
This thesis deals with theoretical basics of risk modelling in transportation and optimization using aggregated traffic data. In this thesis is suggested the procedure and implemented the application solving network problem of shortest path between geographical points. The thesis includes method for special paths evaluation depending on the frequency of traffic incidents based on real historical data. The thesis also includes a~graphical interface for presentation of the achieved results.
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Optimization of building constructions with probability constraints
Kokrda, Lukáš ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with penalty approach to stochastic optimization with chance constraints which are applied to structural mechanics. The problem of optimal design of beam dimensions is modeled and solved. The uncertainty is involved in the form of random load. The corresponding mathematical model contains a condition in the form of ordinary differencial equation that is solved by finite element method. The probability condition is approximated by several types of penalty functions. The results are obtained by computations in the MATLAB software.
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Optimization Models for Waste-to-Energy Problems
Hošek, Jaromír ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The main aim of this thesis is to create a sequence of mathematical optimization models with different levels of complexity for the efficient management and waste energy utilization. Stochastic programming approach was utilized to deal with random demand and uncertain heating values. Hence, more applicable model of the waste-to-energy plant has been developed. As the next step, the model is enhanced by heating plant extension. Computations are realized for real-world data and optimal solution is found by using GAMS implementation.
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Optimization of Thermal Field with Phase Change
Pustějovský, Michal ; Klimeš, Lubomír (referee) ; Popela, Pavel (advisor)
This thesis deals with modelling of continuous casting of steel. This process of steel manufacturing has achieved dominant position not only in the Czech Republic but also worldwide. The solved casted bar cross-section shape is circular, because it is rarely studied in academical works nowadays. First part of thesis focuses on creating numerical model of thermal field, using finite difference method with cylindrical coordinates. This model is then employed in optimization part, which represents control problem of abrupt step change of casting speed. The main goal is to find out, whether the computation of numerical model and optimization both can be parallelized using spatial decomposition. To achieve that, Progressive Hedging Algorithm from the field of stochastic optimization has been used.
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On quantile optimization problem with censored data
Volf, Petr
In the framework of stochastic optimization the criterion based on selected quantiles is considered. Further, stochastic characteristics are estimated from censored data. Therefore, certain theoretical results concerning estimators of distribution function and quantiles under censoring are recalled and utilized to prove consistency of solution based on estimates. Behavior of solutions for finite data sizes is studied with the aid of randomly generated example.
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A Simple Decision Problem of a Market Maker
Šmíd, Martin
We formulate a simple decision model of a market maker maximizing an utility from his consumption. We reduce the dimensionality of the problem to one. We nd that, given our setting, the quotes set by the market maker depend on the inventory of the traded asset but not on the amount of cash held by the market maker.
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Poznámka k empirickým odhadům v ekonomických úlohách
Kaňková, Vlasta
Optimization problems depending on a probability measure correspond to many economic applications. Since the ``underlying" measure is usually unknown the decision is mostly determined on the data basis, it means on statistical (mostly empirical) estimates of the probability measure. Properties of the optimal value (and solution) estimates have been investigated many times. There were introduced assumptions under which the asymptotic distribution is normal and the convergence rate is at least exponential. We generalize the assertions concerning rate convergence. Especially we shall consider distribiotions with the Pareto tails. The introduced assertions are focus on optimal value estimates.
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