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Production planning under uncertainty
Grulich, Martin ; Popela, Pavel (referee) ; Dvořák, Jiří (advisor)
This diploma work deals with a dynamic multi-level multi-item lot sizing problem in a general production-assembly structure represented by a directed acyclic network, where each node may have several predecessors and successors. We assume stochastic demand, finite planning horizon consisting of discrete time periods, dynamic lot sizes, multiple constrained resources and time-varying cost parameters. The objective is to minimize the total costs over the planning horizon. This thesis includes overview of models with stochastic demand and also general description of genetic algorithm. Using different modifications of genetic algorithm I have proposed and implemented methods for solving a chosen model. Then I have made an experimental comparison of these method on selected problems.
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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 Programming Methods for Investment Decisions
Kubelka, Lukáš ; CFA, Tomáš Menčík, (referee) ; Popela, Pavel (advisor)
This thesis deals with methods of stochastic programming and their application in financial investment. Theoretical part is devoted to basic terms of mathematical optimization, stochastic programming and decision making under uncertainty. Furter, there are introduced basic principles of modern portfolio theory, substantial part is devoted to risk measurement techniques in the context of investment, mostly to the methods Value at Risk and Expected shortfall. Practical part aims to creation of optimization models with an emphasis to minimize investment risk. Created models deal with real data and they are solved in optimization software GAMS.
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Chess preparation optimization
Walica, Roman ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
This work is focused on the preparation for the chess game, the issue of Elo rating system and optimization of the problem associated with the preparation for the chess tournament. You can find here how to obtain and modify appropriate information about potential opponents behind the chessboard. Result of this work is an optimization model which, if you enter relevant data, calculates how much time to spend on preparations for chess variants.
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Network flows and their modifications
Bitara, Matúš ; Hošek, Jaromír (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems. Brief introduction to graph theory and linear programming is followed by transportation problem of waste transport. Then there is a part with real data applied to the territory of the Czech Republic. After that the user interface created in Visual Basic programming language is explained. In conclusion computational results are discussed as well as their possible improvement.
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Fossil fuels substitution in large combustion plant
Hájek, Zdeněk ; Popela, Pavel (referee) ; Touš, Michal (advisor)
The thesis aims at current issues of using renewable resources here in the Czech Republic, mainly on biomass co-firing with fossil fuels in large combustion plant. The introduction provides an overview of systems for biomass co-firing. Further the using of optimization for solution problem of integration biomass fuels into existing large combustion plants and planning its operation conditions is presented. The main point of this thesis lies in creating of a user interface for modeling and optimization tool. Its functionality will be proved by solving a case study involving the analysis of possibilities for replacing fossil fuels due to the limited availability of coal in the market.
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Wing leading edge active flow concept analysis
Mahdal, Vít ; Zikmund, Pavel (referee) ; Popela, Robert (advisor)
This research is focused on substitution of commonly used High-Lift devices by active flow control on the wing leading edge. The analysis is done by CFD tools with use of Reynolds-Averaged Navier-Stokes (RANS) method. In the beginning of the research, commonly used High-Lift devices are described. Solver setting and its explanation together with verification and validation is described in the following chapters. An active flow control concept is testing at the LS(1)-0413 airfoil, for 5 different positions of slots, two different slots widths (h/c= 0,0025 and 0,005) and two different blowing velocities (v_Jv_=2,22 and 4,44). In the end of this paper, physical phenomena of blowing is described together with evaluation of different cases. The best case is compared with Fowler and slotted flap at Reynolds number 2,2 million.
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Investment Optimization
Bujnovský, Daniel ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This work is focused on description of two models of mathematical programming - the network model and the Markowitz portfolio model, their connection and application in transportation problems. The goal of the practical section is to approach the description of these problems to the real situations and look for their efficient solutions at the same time. All of that is accompanied by examples on real data from capital market or own model data. The theoretical considerations and thoughts are implemented in programming language Matlab. All results are explained in context to both models. The thesis also includes the introduction to economical and statistical theory which is necessary to understand the problem.
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