Stochastické programování a optimalizace jsou velmi užitečné nástroje pro řešení široké škály inženýrských úloh zahrnujících neurčitost. Diplomová práce se zabývá stochastickým programováním a jeho aplikací při řešení logistických úloh. Teoretická část práce je věnována jak základním pojmům z teorie grafů, tak pojmům souvisejících s matematickým, lineárním, celočíselným a stochastickým programováním. Pozornost je věnována také návaznosti zmíněných pojmů na logistiku. Druhá část se zabývá tvorbou vlastních úloh prezentujících stochastické logistické modely, jejich implementací a výsledky.

The diploma thesis deals with mathematical modeling of the situation when due to the increased risks occurring around Europe there is a need of immediate transport of Czech citizens back to the Czech Republic. The model takes into account the general level of random fluctuations in demand and transportation costs. The optimization model is then built on the ideas of stochastic programming and includes real and expert data in the field of air transportation, which are later implemented into GAMS. The results are discussed. The survey part of the diploma thesis is devoted to the possibility of applying linear and stochastic programming, the interpretation of the mathematical transportation theory. It describes the basic tools and development environment and the realization of mathematical model based on real data in GAMS. The second part of the thesis deals with a proposal of possible improvements in aviation by applying the real data into the model and by analyzing the obtained results.

[pt] A natureza incerta e a importância do mercado da soja para economia do Brasil são forças motrizes para melhorias no processo de planejamento da cadeia logística da soja. Esta tese apresenta um novo modelo matemático de programação estocástica para auxiliar no planejamento tático da cadeia logística da soja. Os principais componentes espaciais e temporais da indústria da soja, sob o ponto de vista do embarcador, são abordados no modelo. A função objetivo do modelo maximiza o lucro obtido com base na diferença entre a receita da venda de grãos, farelo e óleo de soja e os custos de transporte, processamento, armazenamento e venda de grãos, farelo e óleo de soja. As decisões relacionadas ao planejamento tático encontram-se dentro de um horizonte temporal de um ano. Aspectos inerentes aos contratos de transportes e de compra de soja em grão são incorporados no modelo. O modelo de programação estocástica proposto é linear de dois estágios com estrutura de recurso fixo. O modelo foi aplicado a um exemplo real com 21 pontos de origem, 11 silos, 6 fábricas de processamento, 5 pontos de mercado interno, 6 portos e 225 arcos de transportes, considerando 243 cenários, oriundos da combinação de quatro fontes de incertezas: preço de compra e venda da soja em grão, a demanda externa da soja em grão e a quebra de safra. / [en] The uncertain nature and importance of the soybean market for Brazils economy are driving forces for improvement in the planning process of soybeans supply chain. This thesis presents a new stochastic programming mathematical model to assist in tactical planning of the soybean logistics chain. The model was conceived as a tool to assist the decision making of any trader involved in this highly complex market. The main spatial and temporal components of the soybean industry are addressed in the model. The objective function of the model maximizes the profit achieved based on the difference between the revenue from the sale of grain, meal and oil and the costs of transportation, processing, storage and the sale of grain, meal and oil. The model is intended to be applied for decisions related to tactical planning within a time horizon of one year. Aspects related to transport and purchase of soybeans contracts are incorporated in the model. The stochastic programming model is linear of two-stage with fixed resource structure. The model was applied to a real example with 21 points of origin, 11 silos, 6 processing plants, 5 points of the internal market, 6 ports and 225 arcs of transport, considering 243 scenarios, derived from the combination of four sources of uncertainty: purchase price and sale price of soybeans, foreign demand of soybeans and crop failure.

This thesis deals with the multi-stage stochastic programming problems. In the first part, there are introduced two-stage and multi-stage stochastic programming problems. Next, two methods how to generate scenarios are described in detail - the moment method and paths-based methods. The second chapter describes the flower-girl problem, its various formulations and other extensions using ro- bustness and endogenous randomness. The practical part follows, where several different formulations of the flower-girl problem are solved. First, the problem when the florist sells roses with an unlimited life for one week is solved. Then this problem is reformulated as a two-stage problem and the results are compared. Then a formulation with a limited rose life of 2 days is presented. The greatest attention is paid to the problem with a limited rose life of 4 days - the basic formulation of the problem and several extended formulations are solved. 1

This thesis focuses on the stability of ALM models formulated as problems of multistage stochastic programming, with respect to reductions in scenario tree. In the first chapter, we introduce multistage stochastic programming problem and the chosen approach of the master scenario tree generation. The second chapter describes models of asset price evolution in time and clustering algo- rithm used for generation of the master tree. In the third chapter, we describe three random and three deterministic scenario tree reduction algorithms. In the fourth chapter, we formulate two pension fund ALM problems - the first one is four-stage problem, the second one is seven-stage problem. The fifth chap- ter is dedicated to the description of the practical part of the thesis, in which we study and compare the stability of the objective function and the solutions in individual stages with respect to scenario tree reductions obtained from the algorithms described in the third chapter. 1

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Electrical energy is the basic necessity for the economic development of human societies. In recent decades, the electricity industry is undergoing enormous changes, which have evolved into a large-scale and competitive industry. The integration of volatile renewable energy, and the emergence of transmission switching (TS) techniques bring great challenges to the existing power system operations problems, especially security-constrained unit commitment (SCUC) solution engines. In order to deal with the uncertainty of volatile renewable energy, scenario-based stochastic optimization approach has been widely employed to ensure the reliability and economic of power systems, in which each scenario would represent a possible system situation. Meanwhile, the emergence of TS techniques allows the system operators to change the topology of transmission systems in order to improve economic benefits by mitigating transmission congestion. However, with the introduction of extra scenarios and decision variables, the complexity of the SCUC model increases dramatically and more computational efforts are required, which might make the power system operation problems difficult to solve and even intractable. Therefore, an advanced solution technique is urgently needed to solve both stochastic SCUC problems and TS-based SCUC problems in an effective and fast way. In this dissertation, a decomposition framework is presented for the optimal operation of the large-scale power system, which decomposes the original large-size power system optimization problem into smaller-size and tractable subproblems, and solves these decomposed subproblems in a parallel manner with the help of high performance computing techniques. Numerical case studies on a modified I 118-bus system and a practical 1168-bus system demonstrate the effectiveness and efficiency of the proposed approach which will offer the power system a secure and economic operation under various uncertainties and contingencies.

This dissertation considers sheltering network planning and operations for natural disaster preparedness and responses with a two-stage stochastic program. The first phase of the network design decides the locations, capacities and held resources of new permanent shelters. Both fixed costs for building a new permanent shelter and variable costs based on capacity are considered. Under each disaster scenario featured by the evacuee demand and transportation network condition, the flows of evacuees and resources to shelters, including permanent and temporary ones, are determined in the second stage to minimize the transportation and shortage/surplus costs. Typically, a large number of scenarios are involved in the problem and cause a huge computational burden. The L-shaped algorithm is applied to decompose the problem into the scenario level with each sub-problem as a linear program. The Sheltering Network Planning and Operation Problem considered in this dissertation also has a special structure in the second-stage sub-problem that is a minimum cost network flow problem with equal flow side constraints. Therefore, the dissertation also takes advantages of the network simplex method to solve the response part of the problem in order to solve the problem more efficiently. This dissertation investigates the extending application of special minimum cost equal flow problem. A case study for preparedness and response to hurricanes in the Gulf Coast region of the United States is conducted to demonstrate the usage of the model including how to define scenarios and cost structures. The numerical experiment results also verify the fast convergence of the L-shaped algorithm for the model.

[pt] A seleção de um portfolio de renda fixa é um problema comumente enfrentado pelos agentes do mercado financeiro. A alocação ótima destes ativos melhora o nível de rentabilidade e lucratividade da instituição. Um dos trade-offs rotineiramente encontrado pelos gestores destas carteiras é decidir entre a compra de títulos pré-fixados e pós-fixados de curto prazo ou longo prazo, sendo que estes últimos no geral rendem mais devido ao prêmio de risco. Tais títulos, apesar de terem a sua rentabilidade já definida no momento da compra, podem ser vendidos a qualquer momento e sua nova rentabilidade estará sujeitas às marcações a mercado. O retorno da carteira composta por estes títulos é portanto uma variável aleatória que torna necessário o controle dos riscos de perda deste portfolio. O presente estudo teve por objetivo desenvolver um modelo de otimização da rentabilidade de uma carteira composta somente por títulos prefixados do tesouro nacional, com restrições ao nível de risco expresso através do Conditional Value at Risk. Após tal, foram realizados backtests para medir o desempenho do modelo e comparar a sua rentabilidade com o índice CDI. Os testes mostraram que o modelo apresenta resultados bons em rentabilidade e resultados satisfatórios em termos de controle de risco. / [en] Fixed-income portfolio selection is a common problem faced by financial market agents. The optimal allocation of these assets improves the profitability of institutions. A trade-off routinely found by the managers of these portfolios is deciding between buying floating rate securities or short-term or long-term fixed-rate securities, while the latter generally has a higher yield due to risk premium. Despite fixed rate securities have their return already set at the moment of purchase, they can be sold at any time and the new return will be subject to the current market prices. Since the return of a portfolio holding these securities is a random variable, we argue for the importance of a risk assessment and control a fixed income security portfolio. This study aimmed to develop an optimization model of return with a portfolio composed only on fixed and floating rate bonds from Brazil s sovereign treasury, using risk restrictions expressed on the Conditional Value at Risk measure. After that, backtestswere performed to measure model efficiency and compare its return to the Brazilian s Interbank rate. The tests have shown good results in profitability and risk control.