Le système étudié durant cette thèse est un véhicule électrique hybride avec deux sources d’énergies (Pile à combustible et Super-capacité). L’objectif fixé est de minimiser la consommation du carburant tout en satisfaisant la demande instantanée en puissance sous des contraintes de puissance et de capacité et de stockage. Le problème a été modélisé sous la forme d’un problème d’optimisation globale. Nous avons développé de nouvelles méthodes heuristiques pour le résoudre et proposé le calcul d’une borne inférieure de consommation, en apportant de meilleurs résultats que ceux trouvés dans la littérature. En plus, une étude de robustesse a été réalisée afin de minimiser la consommation de pire-cas suite à une perturbation ou du fait d’incertitudes sur les données d’entrée, précisément sur la puissance demandée. Le but de cette étude est de prendre en compte les perturbations dès la construction des solutions afin d’éviter l’infaisabilité des solutions non robustes en situation perturbée. Les heuristiques de résolution du problème robuste modélisé sous la forme d’un problème de Minimax ont fourni des solutions moins sensibles aux perturbations que les solutions classiques. / The system studied in this thesis is a hybrid electrical vehicle with two energy sources (fuel cell system and super-capacitor). The first goal is to minimize the fuel consumption whilst satisfying the requested power for each instant, taking into account constraints on the availability and the state of charge of the storage element. The system was modeled as a global optimization problem. The heuristics developped for obtaining the best power split between the two sources and the lower bound consumption computation proposed provide better results than those found in the literature. The second goal of the thesis is the study of the robustness of the solutions in order to minimize the worst-case consumption when perturbation happens or uncertainty is added to the input data. In this study the uncertainty concerns the power required for traction. The objective is to maintain the feasibility of solutions and limit the worst consumption that can happen due to a demand fluctuation. Dedicated heuristics are proposed for solving the identified robust variant of the problem, modeled as a Minimax problem. The solutions provided are less sensitive to the perturbations than the previous ones.

This dissertation considers radar detection and tracking of weak fluctuating targets using dynamic programming (DP) based track-before-detect (TBD). TBD combines target detection and tracking by integrating data over consecutive scans before making a decision on the presence of a target. A novel algorithm is proposed which employs order statistics in dynamic programming based TBD (OS-DP-TBD) to detect weak fluctuating targets. The well-known Swerling type 0, 1 and 3 targets are considered with non-Gaussian distributed clutter and complex Gaussian noise. The clutter is modeled using the Weibull, K and G0 distributions. The proposed algorithm is shown to provide better performance than well-known techniques in the literature. In addition, a novel expanding window multiframe (EW-TBD) technique is presented to improve the detection performance with reasonable computational complexity compared to batch processing. It is shown that EW-TBD has lower complexity than existing multiframe processing techniques. Simulation results are presented which confirm the superiority of the proposed expanding window technique in detecting targets even when they are not present in every scan in the window. Further, the throughput of the proposed technique is higher than with batch processing. Depending on the range and azimuth resolution of the radar system, the target may appear as a point in some radar systems and there will be target energy spillover in other systems. This dissertation considers both extended targets with different energy spillover levels and point targets. Simulation results are presented which confirm the superiority of the proposed algorithm in both cases. / Graduate

[pt] Ao tomar suas decisões, o gerente se vê frente a frente com diferentes tipos de incertezas, entre elas, o tempo para se concluir um projeto. As características de inovação e ineditismo dos projetos de Pesquisa e Desenvolvimento aplicados à tecnologia reforçam ainda mais os cuidados a serem tomados com a dimensão tempo no momento da decisão, pois a penalidade pode ser até mesmo a perda de uma oportunidade valiosa de negócio. Para quantificar o impacto do esforço aplicado em um Projeto de Pesquisa e Desenvolvimento Tecnológico no valor de um empreendimento, conduzido em um contexto onde o tempo é representado por uma variável aleatória, desenvolvemos o modelo que apresentamos neste trabalho. Para tanto utilizamos a Teoria das Opções Reais, considerando que o projeto se desenvolve seqüencialmente e que pode ser abandonado em qualquer estágio de desenvolvimento. O modelo utiliza uma treliça para captar a incerteza técnica própria do desenvolvimento do desempenho da tecnologia e considera como variável aleatória o tempo de conclusão de cada uma das fases do projeto. O valor esperado do projeto, com a flexibilidade propiciada pela opção de abandono embutida no projeto de Pesquisa e Desenvolvimento, é calculado combinando a Simulação de Monte Carlo e a técnica da Programação Dinâmica. Aplicamos o modelo para tratar o caso de uma planta Gas-to-liquid (GTL). A função payoff do projeto de Pesquisa e Desenvolvimento foi construída a partir de diversas contribuições geradas no bojo de um convênio firmado entre o Departamento de Engenharia Industrial da PUC-RJ e a Petrobras S.A., com o objetivo de avaliar economicamente uma planta GTL. / [en] When making decisions, the figure of the manager comes across different types of uncertainties. Among them, the time to conclude a project. The characteristics of innovation and novelty in Research and Development Projects applied to technology, further reinforces the caution to be taken regarding the time dimension at the moment of the decision, since the penalty could culminate in the loss of a valuable business opportunity. In order to quantify the impact of the effort applied in a Research and Technological Development Project, in the value of an entrepreneurship conducted according to a context in which time is represented by a random variable, this study presents a pertinent model. Considering that a project sequentially evolves and can be abandoned during any stage of its development, the Theory of Real Options was the chosen theoretical framework. The model utilizes a lattice to capture the technical uncertainty, characteristics of the development of technology performance, and takes in account as a random variable the time of the conclusion of each stage of the project. The expected value of the project with the flexibility provided by the option to abandonment built in the Research and Development Project, is calculated through a combination of the Monte Carlo Simulation and the technique of Dynamic Programming. The proposed model was applied in the case of a Gas-to-liquid (GTL) plant. The payoff function of the Research and Development Project was built through several contributions stemmed from an agreement between the Industrial Engineering Department of PUC-RJ and Petrobras S.A., in order to assess the economic value of a GTL plant

O planejamento operacional de um sistema de transporte de longa distância implica resolver um problema de otimização de rede dinâmica, visando a efetuar, de forma eficaz e eficiente, o atendimento às demandas de cargas, utilizando a capacidade de transporte disponível. A metodologia de solução proposta utiliza a abordagem de Rede de Filas Logísticas, a qual substitui o processo de otimização global da rede (usualmente utilizando Programação Linear Inteira) por um modelo de Programação Dinâmica Estocástica, Aproximada e Adaptativa, que permite a resolução de uma série de subproblemas delimitados no tempo, reduzindo sensivelmente a quantidade de variáveis envolvidas. Este método permite a utilização de modelos matemáticos mais realistas em horizontes de planejamento mais amplos. O presente trabalho estende os modelos encontrados na Literatura, aplicando o método a problemas de maior complexidade, incluindo a consideração de frotas heterogêneas de veículos, janelas de início de atendimento, utilização de terceiros transportadores e penalidades pelo não atendimento das demandas. São apresentados exemplos de problemas experimentais submetidos com sucesso à técnica desenvolvida. O trabalho inclui ainda o delineamento de um Sistema de Apoio à Decisão incorporando a metodologia proposta. / Operational planning of a long haul transportation system implies to solve a dynamic network optimization problem, aiming to perform the freight movements in an efficient and effective way, while utilizing the available transportation capacity. The proposed solution methodology utilizes the Logistic Queueing Network approach, replacing the network global optimization process through Integer Linear Programming by a model of Stochastic, Approximate and Adaptive Dynamic Programming, which allows the resolution of a sequence of sub- problems delimited in time, strongly reducing the quantity of variables involved. This method allows the utilization of more realistic mathematical models in a broader planning horizon. The research extends models found in the literature to solve more complex problems, including the consideration of heterogeneous fleet of vehicles, time windows, third party vehicles and penalties for not attendance of demands. Experimental problems solved successfully with the developed technique are presented. The work also presents the delineation of a Decision Support System incorporating the proposed methodology.

Buscando-se a aplicação prática da teoria de Wave Field Synthesis (WFS) na música, foi feita uma pesquisa visando à modelagem de um sistema de sonorização capaz de criar imagens sonoras espaciais com a utilização desta técnica. Diferentemente da maioria das outras técnicas de sonorização, que trabalham com uma região de escuta pequena e localizada, WFS permite projetar os sons de cada fonte sonora - como instrumentos musicais e vozes - em diferentes pontos do espaço de audição, em uma região de escuta que pode abranger quase toda a área compreendida por este espaço, dependendo da quantidade de alto-falantes instalados. O desenvolvimento de um código de estrutura modular para WFS foi baseado na plataforma orientada a patches Pure Data (Pd), e no sistema de auralização AUDIENCE, desenvolvido na USP, sendo integrável como ferramenta para espacialização sonora interativa. A solução emprega patches dinâmicos e uma arquitetura modular, permitindo flexibilidade e manutenabilidade do código, com vantagens frente a outros software existentes, particularmente na instalação, operação e para lidar com um número elevado de fontes sonoras e alto-falantes. Para este sistema também foram desenvolvidos alto-falantes especiais com características que facilitam seu uso em aplicações musicais. / Seeking the practical application of the theory of Wave Field Synthesis (WFS) in music, a research aimed at modeling a sound system capable of creating spatial sound images with the use of this technique was made. Unlike most other techniques for sound projection that work with a small, localized listening area, WFS allows projecting the sounds of each sound source - such as musical instruments and voices - at different points within the hearing space, in a region that can cover almost the entire area comprised by this space, depending on the amount of installed speakers. The development of a modular structured code for WFS was based on the patch-oriented platform Pure Data (Pd), and on the AUDIENCE auralization system developed at USP, and it is integrable as a tool for interactive sound spatialization. The solution employs dynamic patches and a modular architecture, allowing code flexibility and maintainability, with advantages compared to other existing software, particularly in the installation, operation and to handle a large number of sound sources and speakers. For this system special speakers with features that facilitate its use in musical applications were also developed.

O planejamento da operação energética de sistemas hidrotérmicos de potência tem como objetivo determinar a participação de usinas termoelétricas e hidrelétricas de forma a garantir o suprimento desta energia ao menor custo operacional possível, dentro de restrições técnicas. Alguns fatores tornam a solução desse problema bastante complexa destacando a não linearidade, presente na equação de geração hidráulica; a não separabilidade espacial, devido ao fato da decisão de quanto gerar em uma usina interferir em outra usina do sistema; a separabilidade temporal aditiva, devido a interferência de uma decisão atual em uma decisão futura e, como no caso brasileiro, de grande porte. O objetivo deste trabalho é apresentar uma nova abordagem para o planejamento da operação de sistemas hidrotérmicos de potência, com Programação Dinâmica, de forma que as usinas hidrelétricas possam ser representadas e otimizadas individualmente, completamente desacopladas. Essa aplicação é possível através da utilização de uma função objetivo modificada, considerando-se não apenas os custos, mas também os dados de afluências das usinas imediatamente a jusante. O modelo proposto, como função objetivo modificada, foi aplicado em cascatas de usinas hidrelétricas brasileiras, cujos resultados puderam ser comparados com os comportamentos ótimos obtidos de forma direta, ou seja, com a otimização de todo o sistema em conjunto. Com base nos resultados obtidos, pôde-se observar o bom comportamento do modelo implementado. / The energetic operation planning in hydrothermal power systems aims to determine the participation of hydroelectric power plants and thermoelectric power plants to ensure the supply of electricity at the lowest operating cost possible, between technical constraints. Some factors make the solution of this problem quite complex highlighting the nonlinearity, present in the equation of hydraulic generation, non-spatial separability, due the fact that the decision of the amount of energy generated in a plant interfere in another plants of the system, the additive time separability, because of the interference from an actual decision on a future decision and, as in the Brazilian case, large. The proposal of this work is to present a new approach to hydrothermal power systems, with Dynamic Programming, so that hydroelectric power plants can be represented and optimized individually, completely decoupled. This application is possible through the use of a modified objective function, considering not only costs but also the inflow data immediately on the downstream plants. The proposed model was applied in a Brazilian cascade of hydroelectric plants, comparing the optimal behavior obtained directly, by optimizing the whole system together and the new technique behavior. Based on the results obtained, we can observe the good results of the implemented model.

Le problème de routage de véhicules avec fenêtres de temps et routes multiples (MTVRPTW) est une généralisation du problème de routage de véhicules avec fenêtres de temps (VRPTW). Dans le MTVRPTW, on autorise un véhicule à effectuer plusieurs routes durant une période de planification, ce qui permet d'optimiser les transports lorsque le nombre de véhicules est limité et peu élevé. Nous proposons dans cette thèse la première méthode exacte permettant de résoudre ce problème. Notre modélisation prend la forme d'un problème de couverture des clients dont les variables sont des routes. Des contraintes d'exclusion mutuelle expriment la disponibilité des véhicules. Nous utilisons la Génération de Colonnes, avec un sous-problème effectuant, par programmation dynamique, une recherche de plus court chemin élémentaire contraint en ressources. Notre méthode de programmation dynamique tient compte des dépendances de plusieurs ressources grâce à la notion de label représentatif, et est ainsi plus efficace qu'une approche classique. La méthode de Génération de Colonnes est incluse dans un schéma de Branch and Price composé de deux types de branchement, l'un basé sur les arcs, l'autre sur la résolution d'un VRPTW. Nous avons mis en place diverses méthodes accélératrices spécifiques du MTVRPTW. Nous donnons les résultats de l'algorithme sur les instances de Solomon. Des résultats issus de méthodes exactes étaient disponibles dans la littérature pour le MTVRPTW avec durée limite sur les routes. Nous avons proposé un nouvel algorithme plus performant, et basé sur nos méthodes, pour cette variante du problème. / The multi-trip vehicle routing problem with time windows (MTVRPTW) is a generalization of the vehicle routing problem with time windows (VRPTW). In the MTVRPTW, one vehicle can perform several trips during a planning period. This allows optimizing the transport when the number of vehicles is limited and small.We propose here the first exact method for solving this problem.Our model is designed as a coverage problem for customers where the variables are trips. Mutual exclusion constraints express the availability of vehicles. We use a column generation scheme in which the sub-problem is an elementary shortest path problem with resource constraints (ESPPRC). Our dynamic programming method for ESPPRC takes into account dependencies of several resources through the concept of representative label. It is thus more efficient than a conventional approach. The column generation method is included in a Branch and Price scheme with two types of branching. One is based on arc selection, and the other on solving a VRPTW. We have implemented various accelerating methods which are specific to MTVRPTW. We give the results of our algorithm on Solomon instances.Results from exact methods were available in the literature for the MTVRPTW with time limit on the trips. We proposed a new and more efficient algorithm, based on our methods, to solve this variant of the problem.

O referencial da Teoria da Localização embasa o modelo matemático de otimização dinâmico desenvolvido a fim de se determinar os melhores locais dos frigoríficos-abatedouros exportadores no Brasil visando à minimização dos custos associados ao transporte, bem como os custos associados à instalação de novas unidades industriais de abate, resultando, assim, em aumento de competitividade para a cadeia. Este trabalho visa responder a três questões: (i) localizações das unidades industriais de abate; (ii) tamanho e número ótimos de cada unidade industrial de abate e (iii) fluxos mensais da matéria-prima necessários para atender a demanda dos frigoríficos-abatedouros exportadores, bem como os fluxos ofertados mensalmente por eles a fim de se satisfazer a demanda dos países importadores da carne bovina brasileira. Desse modo, foram simulados quatro cenários alternativos. Os dois primeiros disseram respeito sobre a determinação da localização dos frigoríficos-abatedouros exportadores e respectivos fluxos de produtos num contexto ideal, ou seja, o modelo determinou onde os mesmos deveriam ser instalados. Enquanto o primeiro cenário considerou na modelagem os dez principais estados exportadores da carne bovina desossada congelada brasileira, o segundo considerou os seis principais estados, excluindo, assim, os estados que fazem parte da Amazônia Legal. No primeiro cenário, dos dez estados considerados, em cinco deveriam ser instalados ao menos um frigoríficoabatedouro exportador, enquanto no segundo cenário dos seis estados considerados em três deveriam ser instalados ao menos um frigorífico-abatedouro exportador. Ambos os cenários indicaram São Paulo como estado candidato à instalação de maior número de frigoríficosabatedouros exportadores. Além disso, em ambos os cenários a decomposição dos custos logísticos revelou que a maior parte do custo total mínimo obtido nos processamentos dos modelos decorreu da instalação dos frigoríficos-abatedouros exportadores,76,3% do custo total mínimo obtido no cenário 1 e 79,4% do custo total mínimo obtido no cenário 2, seguidos pelo custo de transporte da carne bovina aos mercados externos (14,9% e 14,1%) e custo de transporte da carne bovina aos portos exportadores (5,7% e 3,6%). O custo de transporte da matéria-prima aos frigoríficos-abatedouros exportadores foi 1,9% e 1,2% do custo total mínimo obtido no cenário 1 e 2, respectivamente, ao passo que o custo de transporte da carne bovina aos mercados internos foi de 1,2% e 1,7% do respectivo custo total mínimo. O terceiro e quarto cenários disseram respeito sobre quais frigoríficos-abatedouros exportadores já instalados deveriam ser responsáveis pelo abastecimento dos mercados externos demandantes de carne bovina desossada congelada brasileira. Ambos consideraram na modelagem as localizações atuais dos frigoríficos abatedouros exportadores existentes nos seis principais estados exportadores do produto. No entanto, o último cenário refere-se a projeção de aumento de demanda externa futura por carne bovina. Nesses cenários, como não há custo de intalação dos frigoríficos-abatedouros exportadores a ser incorridos, a maior parcela dos custos logísticos decorreu da distribuição da carne bovina aos mercados externos. Os resultados do terceiro cenário revelaram que 12 frigoríficos-abatedouros exportadores seriam suficientes para atender plenamente os mercados externos, ao passo que o aumento da demanda externa futura exigirá 14 frigoríficos-abatedouros exportadores. / The theoretical framework of the Location Theory supports the dynamic optimization mathematical model developed in order to determine the potential sites for the installation of exporter slaughterhouses in Brazil, minimizing the costs associated with transportation and the costs associated with the installation of new slaughter industrial units, thereby increasing the competitiveness of the chain. The following three questions were addressed: (i) at what locations should slaughter industrial units be installed; (ii) what is the optimal-size and number of each slaughter industrial, and (iii) what are the flows of raw material required monthly to meet the exporter slaughterhouses demand and the monthly supplied amount by them in order to meet the importing countries demands? Thus, four alternative scenarios were simulated. The first two scenarios are related to determine the exporter slaughterhousess locations and the products flows in an ideal environment, i.e., the model determines where they should be installed. The difference between these scenarios is that the former considers in the modeling the Brazilian top ten exporter states of frozen boneless beef, while the second considers the six major states, excluding, thus, the states that belong to the Amazon region. In the first scenario, at least one exporter slaughterhouse should be installed in five out of ten states considered, while in the second scenario at least one exporter slaughterhouse should be installed in three out of six states considered. Both scenarios indicated that most of the exporter slaughterhouses should be installed in São Paulo. Moreover, in both scenarios the decomposition of logistics costs has shown that most of the minimum total cost obtained in the models processing was due to the installation of the exporter slaughterhouses, 76.3% of the minimum total cost obtained in the scenario 1 and 79, 4% of the minimum total cost obtained in the scenario 2, followed by the cost of transporting beef up to the foreign markets (14.9% and 14.1%) and by the cost of transporting beef up to the exporter ports (5.7% and 3 , 6%). The cost of transporting the raw material up to the exporter slaughterhouses was 1.9% and 1.2% of the minimum total cost obtained in scenario 1 and 2, respectively, while the cost of transporting beef up to the domestic markets was 1.2% and 1.7% of the minimum total cost, respectively. The third and fourth scenarios concerned about which exporter slaughterhouses already installed should be responsible for fulfilling the demands of the external markets for the Brazilian frozen boneless beef. Both scenarios considered in the modeling the actual locations of the existing exporter slaughterhouses in the six main exporter states of the product. However, the latter scenario considers an increase in the beef future demand of the external markets. Since there is no cost related to the installation of the exporter slaughterhouses to be incurred in these scenarios, the largest share of logistics costs was related to the distribution of beef up to the foreign markets. The results of the third scenario indicates that 12 exporter slaughterhouses would be enough to fully meet the demands of the foreign markets for frozen boneless beef, while the increase in the external demands will require 14 exporter slaughterhouses.

Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de mean-variance hedging e princípio da programação dinâmica. / The investor, that negotiate assets, is subject to economic risks of any negotiation because there is no certainty regarding the appreciation or depreciation of an asset. Here comes the futures market, where contracts can be negotiated in order to protect (hedge) the risk of excessive losses or gains, making the purchase or sale assets, fair for both sides. The goal of this work consist in study Lévy pure-jump process with finite activity, also known as compound Poisson process, and its applications. Discovered by the French mathematician Paul Pierre Lévy, the Lévy processes admits jumps in paths, which is often observed in financial markets. We will define a hedging strategy for a market model with compound Poisson process using mean-variance hedging and dynamic programming.

In this dissertation, certain problems of stochastic optimal control and relevant analysis of random vibrations are considered. Dynamic Programming approach is used to find an optimal control law for a linear single-degree-of-freedom system subjected to Gaussian white-noise excitation. To minimize a system's mean response energy, a bounded in magnitude control force is applied. This approach reduces the problem of finding the optimal control law to a problem of finding a solution to the Hamilton-Jacobi-Bellman (HJB) partial differential equation. A solution to this partial differential equation (PDE) is obtained by developed 'hybrid' solution method. The application of bounded in magnitude control law will always introduce a certain type of nonlinearity into the system's stochastic equation of motion. These systems may be analyzed by the Energy Balance method, which introduced and developed in this dissertation. Comparison of analytical results obtained by the Energy Balance method and by stochastic averaging method with numerical results is provided. The comparison of results indicates that the Energy Balance method is more accurate than the well-known stochastic averaging method.