[pt] A formação do portfólio de uma empresa de Petróleo envolve complexas decisões devido ao ambiente de incertezas e é de extrema importância na definição do futuro estratégico da empresa. Recentemente, a otimização de um portfólio de ativos de exploração e produção de petróleo vem sendo amplamente tratada na literatura, entretanto observa-se uma escassez de trabalhos que consideram a otimização do portfólio de refino. Este trabalho tem por objetivo propor um modelo de formação de portfólio para empresas do setor de óleo e gás, que possuem atividades tanto no segmento de exploração e produção (upstream) quanto no segmento de refino (downstream), levando em conta a integração entre ambos. Assim como nos modelos tradicionais, os preços do barril de petróleo e a produtividade dos campos serão tratadas como incertezas. O modelo proposto utilizará técnicas de programação estocástica com aversão a risco, medido pelo CVaR (Conditional Value-at-Risk). A fim de validar a metodologia proposta, um estudo de caso baseado em uma empresa de óleo e gás será apresentado. A aplicação numérica indicou que o modelo que otimiza o portfólio conjunto de upstream e downstream apresenta resultado da função objetivo até 28 por cento superior ao modelo usualmente tratado na literatura que trata apenas do portfólio de upstream. / [en] The portfolio allocation of an Oil and Gas company involves complex decisions within an uncertain environment and is extremely important in defining the firm s economical and financial future behavior. Recently, the portfolio selection problem for oil exploration and production (E&P) projects has been widely treated in the literature, however, few studies consider the optimization of the combined upstream and downstream portfolio. The purpose of this work is to propose a portfolio selection model for oil and gas companies, which operates both in exploration and production (upstream) and in refining (downstream), considering the integration between them. Crude oil prices and fields performance are the main uncertainties of the problem. The proposed model makes use of risk aversion stochastic programming techniques, measured by CVaR (conditional value at risk). To validate the proposed methodology a case study based on an Oil Company will be presented. The numerical application indicates that the model considering both upstream and downstream portfolio presents objective function results 28 percent higher than the model usually used in the literature that only optimizes the upstream portfolio.

In the modern era of IT, cloud computing is becoming the new standard. Companies have gone from owning their own data centers to procuring virtualized computational resources as a service. This technology opens up for elasticity and cost savings. Computational resources have gone from being a capital expenditure to an operational expenditure. Vendors, such as Google, Amazon, and Microsoft, offer these services globally with different provisioning alternatives. In this thesis, we focus on providing a cost optimization algorithm for Spotify on the Google Cloud Platform. To achieve this we  construct an algorithm that breaks up the problem in four different parts. Firstly, we generate trajectories of monthly active users. Secondly, we split these trajectories up in regions and redistribute monthly active users to better describe the actual Google Cloud Platform footprint. Thirdly we calculate usage per monthly active users quotas from a representative week of usage and use these to translate the redistributed monthly active users trajectories to usage. Lastly, we apply an optimization algorithm to these trajectories and obtain an objective value. These results are then evaluated using statistical methods to determine the reliability. The final model solves the problem to optimality and provides statistically reliable results. As a consequence, we can give recommendations to Spotify on how to minimize their cloud cost, while considering the uncertainty in demand.

Mnoho inženýrských úloh vede na optimalizační modely s~omezeními ve tvaru obyčejných (ODR) nebo parciálních (PDR) diferenciálních rovnic, přičemž jsou v praxi často některé parametry neurčité. V práci jsou uvažovány tři inženýrské problémy týkající se optimalizace vibrací a optimálního návrhu rozměrů nosníku. Neurčitost je v nich zahrnuta ve formě náhodného zatížení nebo náhodného Youngova modulu. Je zde ukázáno, že dvoustupňové stochastické programování nabízí slibný přístup k řešení úloh daného typu. Odpovídající matematické modely, zahrnující ODR nebo PDR omezení, neurčité parametry a více kritérií, vedou na (vícekriteriální) stochastické nelineární optimalizační modely. Dále je dokázáno, pro jaký typ úloh je nutné použít stochastické programování (EO reformulace), a kdy naopak stačí řešit jednodušší deterministickou úlohu (EV reformulace), což má v praxi význam z hlediska výpočetní náročnosti. Jsou navržena výpočetní schémata zahrnující diskretizační metody pro náhodné proměnné a ODR nebo PDR omezení. Matematické modely odvozené pomocí těchto aproximací jsou implementovány a řešeny v softwaru GAMS. Kvalita řešení je určena na základě intervalových odhadů "optimality gapu" spočtených pomocí metody Monte Carlo. Parametrická analýza vícekriteriálního modelu vede na výpočet "efficient frontier". Jsou studovány možnosti aproximace modelu zahrnujícího pravděpodobnostní členy související se spolehlivostí pomocí smíšeného celočíselného nelineárního programování a reformulace pomocí penalizační funkce. Dále je vzhledem k budoucím možnostem paralelních výpočtů rozsáhlých inženýrských úloh implementován a testován PHA algoritmus. Výsledky ukazují, že lze tento algoritmus použít, i když nejsou splněny matematické podmínky zaručující konvergenci. Na závěr je pro deterministickou verzi jedné z úloh porovnána metoda konečných diferencí s metodou konečných prvků za použití softwarů GAMS a ANSYS se zcela srovnatelnými výsledky.

[pt] O objetivo do planejamento da operação hidrotérmica de médio e longo prazo é definir as metas para geração de cada hidroelétrica e termelétrica, a fim de atender à carga ao menor custo esperado de operação e respeitando as restrições operacionais. Algoritmos de Programação Dinâmica Estocástica (PDE) e de Programação Dinâmica Dual Estocástica (PDDE) têm sido amplamente aplicados para determinar uma política operativa ideal o despacho hidrotérmico. Em ambas as abordagens a estocasticidade das afluências é comumente produzida por modelos periódicos autoregressivos de lag p - PAR(p), cuja estimativa dos parâmetros é baseada nos dados históricos disponíveis. Como os estimadores são funções de fenômenos aleatórios, além da incerteza sobre as vazões, também há incerteza sobre os parâmetros estatísticos, o que não é capturado no modelo PAR (p) padrão. A existência de incerteza nos parâmetros significa que há um risco de que a política da operação hidrotérmica planejada não será a ótima. O objetivo desta tese é apresentar uma metodologia para incorporar a incerteza dos parâmetros do modelo PAR (p) no problema de programação estocástica hidrotérmica. São apresentados estudos de caso ilustrando o impacto da incerteza dos parâmetros nos custos operativos do sistema e como uma política operativa que incorpore esta incerteza pode reduzir este impacto. / [en] The objective of the medium and long-term hydrothermal scheduling problem is to define operational target for each power plant in order to meet the load at the lowest expected cost and respecting the operational constraints. Stochastic Dynamic Programming (SDP) and Stochastic Dual Dynamic Programming (SDDP) algorithms have been widely applied to determine the optimal operating policy for the hydrothermal dispatch. In both approaches, the stochasticity of the inflows is usually produced by periodic auto-regressive models - PAR (p), whose parameters are estimated based on available historical data. As the estimators are a function of random phenomena, besides the inflows uncertainty there is statistical parameter uncertainty, which is not captured in the standard PAR (p) model. The existence of uncertainty in the parameters means that there is a risk that the hydrothermal operating policy will not be optimal. This thesis presents a methodology to incorporate the PAR(p) parameter uncertainty into stochastic hydrothermal scheduling and to assess the resulting impact on the computation of a hydro operations policy. Case studies are presented illustrating the impact of parameter uncertainty in the system operating costs and how an operating policy that incorporates this uncertainty can reduce this impact.

[pt] No planejamento da operação hidrotérmica brasileiro, assim como em outros países hidro dependentes, a Programação Dinâmica Dual Estocástica (PDDE) é utilizada para calcular uma política ótima avessa a risco que, muitas vezes, considera modelos autorregressivos para modelagem das afluências às hidrelétricas. Em aplicações práticas, estes modelos podem induzir a uma variabilidade indesejável de variáveis primais (geração térmica) e duais (custo marginal e preço spot), que são altamente sensíveis a mudanças nas condições iniciais das vazões. Neste trabalho, são propostas duas abordagens diferentes para estabilizar as soluções da PDDE no problema de planejamento da operação energética: a primeira abordagem visa regularizar variáveis primais considerando uma penalidade adicional sobre as mudanças no despacho térmico ao longo do tempo. A segunda abordagem reduz indiretamente a variabilidade da geração térmica e do custo marginal ao ignorar informações de afluências passadas na função de custo futuro e compensando-a com um aumento na aversão ao risco. Para fins de comparação, a qualidade solução foi avaliada com um conjunto de índices propostos que resumem cada aspecto importante de uma política de planejamento hidrotérmico. Em conclusão, mostramos que é possível obter soluções com boa qualidade em comparação com benchmarks atuais e com uma redução significativa variabilidade. / [en] In the hydrothermal energy operation planning of Brazil and other hydro-dependent countries, Stochastic Dual Dynamic Programming (SDDP) computes a risk-averse optimal policy that often considers river-inflow autoregressive models. In practical applications, these models induce an undesirable variability of primal (thermal generation) and dual (marginal cost and spot price) solutions, which are highly sensitive to changes in current inflow conditions. In this work, we propose two differing approaches to stabilize SDDP solutions to the energy operation planning problem: the first approach aims at regularizing primal variables by considering an additional penalty on thermal dispatch revisions over time. The second approach indirectly reduces thermal generation and marginal cost variability by disregarding past inflow information in the cost-to-go function and compensating it with an increase in risk aversion. For comparison purposes, we assess solution quality with a set of proposed indexes summarizing each important aspect of a hydrothermal operation planning policy. In conclusion, we show it is possible to obtain high- quality solutions in comparison to current benchmarks and with significantly reduced variability.

[pt] Minerar bitcoins é uma atividade incerta, e para realizá-la, os participantes competem em um processo chamado Proof-Of-Work. Cada participante pode passar meses ou até anos sem fluxos positivos de caixa, enquanto os custos se mantém. Isto pode afastá-los da tecnologia e a saída de membros afeta a própria rede, que não sobrevive sem a presença de mineradores. Este trabalho propõe estudar o compartilhamento de recompensas em estruturas já existentes na rede: mineradores se juntando em pools de mineração e dividindo receitas e custos, assim diminuindo a variabilidade e gerando fluxos positivos de caixa mais constantes. A receita e custos são modelados, e um modelo de programação estocástica é proposto para encontrar as alocações ótimas que garantem a permanência dos membros no pool. Este grupo de é caracterizado por uma coalizão, estudado através de Teoria dos Jogos. O comportamento dos jogadores também é de estudo neste trabalho, e uma medida monetária de risco, na forma de CVaR (Conditional Value at Risk) é usada para representar o perfil de risco do minerador e as consequências para as alocações ótimas. Embora não haja benefício estrito em fazer parte do pool para um único período de análise, há ganho financeiro quando se analisa em múltiplos períodos, e o tempo médio para se acertar um hash diminui quando os participantes se juntam em um pool. Um ganho na probabilidade de mineração ao fazer parte de um pool aumentaria a receita média da coalizão, trazendo ganhos financeiros mesmo em um único período de análise. Divisões intuitivas de recursos, como por poder computacional ou igualitária podem não garantir estabilidade do pool, principalmente considerando períodos longos de tempo. Tal estabilidade é possível em um futuro sem receitas fixas de mineração, se ocorrerem também mudanças nas receitas variáveis e custos. Três funções objetivo diferentes representando três idéias de partilha de recompensa são comparadas e uma metodologia é proposta para uso conjunto de pelo menos duas destas, com objetivo de aumentar a justiça na divisão das recompensas. / [en] Mining Bitcoins is an uncertain activity, and to perform it, players must compete in a process known as Proof-Of-Work. A miner may spend months or even years without positive cash flows on this process, while still incurring in the associated costs. This outcome has the possibility to drive them away from the technology, and the departure of members affects the network itself, as it cannot survive without the presence of miners. This work proposes to study the sharing of rewards in structures already presented in the network: miners joining forces and taking place in mining pools, sharing revenues and costs, thus having positive cash flows more often, reducing variability in gains. The revenues and costs are modeled, and a stochastic optimization model is proposed to find the optimal allocations that guarantee that all members stay within the pool. This group of miners is characterized by a coalition, studied through Game Theory. The behavior of the players is also subject of this study, and a monetary risk measure, by the form of CVaR (Conditional Value at Risk) is used to represent the miner s risk profile and consequences to the optimal allocations. While there is no strict benefit from being part of a pool for a single block, there is financial gain when looking at multi-period, and the average time to correctly guess a hash decreases when players join forces in a pool. A gain in mining probability by being in the pool would raise the average reward of the coalition and allow for financial benefit even in single period.We observe that intuitive sharing allocations such as through computational power and equally dividing rewards may not guarantee the stability of the pool, mainly when longer periods of time are considered. Said stability is possible in the future without fixed incomes, but with changes to the variable rewards and the costs of mining. Lastly, three different objective functions representing three ideas to share the rewards within the nucleolus are compared and a method is proposed to collectively use at least two of them, aiming increased fairness in the sharing of rewards.

Historically, electricity supply was heavily centralized and was provided by conventional thermal power plants such as coal-fired, gas, or nuclear power plants. The share of conventional power generation is being increasingly replaced by power generation from renewable sources. In Europe, the share of electricity generation from fossil fuels fell from 49% in 2011 to 37% in 2020, whereas the share from renewables increased from 22% to 38% during the same timeframe. Renewable generation is expected to rise by 10% annually to almost triple the current renewable capacity by 2030. The accelerating adoption of renewables changes the character of the electricity infrastructure from a centralized energy supply to a highly decentralized one, such that generation is moving closer to the point of demand. This change brings numerous challenges with it. This work focuses on challenges in operational planning of distributed energy resources from the perspective of so-called aggregators that are increasingly participating in energy markets. Aggregators combine different energy resources, i.e., electricity producers and consumers, and operate them as a distributed power plant. However, the planning of the energy resources is still coordinated collectively in a centralized manner by the aggregator. This work aims to develop a framework to schedule energy resources from the perspective of an aggregator to cover a large variety of technical assets and to simultaneously consider market interactions such as bid acceptance and rejection possibilities. The inevitable and accelerating proliferation of renewable energy resources brings with it -- as a consequence of its intermittency -- a growing need in control reserve and storage technologies. Hence, a focus is placed on control reserve, energy storage, and integrated scheduling and bidding, as well as their trade-offs, to answer the following research questions: 1) What is the current state of control reserve formulations and how can they be improved? Specifically regarding reserve under consideration of limitations with respect to the rate of change of power output, maximum power output, and energy capacity. 2) What are the effects of using different control reserve formulations? 3) Which trade-offs exist in the operation of storage plants in a market environment? 4) Is it possible to derive a rigorous, tractable mathematical model to simultaneously determine scheduling and bidding decisions? 5) Which trade-offs exist between scheduling and bidding decisions and what are their effects? 6) To what extent is it possible to solve energy resource scheduling models faster while retaining sufficiently high solution quality? / In der Vergangenheit war die Stromerzeugung stark zentralisiert und wurde durch konventionelle Kraftwerke wie Kohle-, Gas- oder Kernkraftwerke bereitgestellt. Der Anteil der konventionellen Stromerzeugung wird zunehmend durch die Stromerzeugung aus erneuerbaren Quellen ersetzt. In Europa sank der Anteil der Stromerzeugung aus fossilen Brennstoffen von 49% im Jahr 2011 auf 37% im Jahr 2020, während der Anteil der erneuerbaren Energien im gleichen Zeitraum von 22% auf 38% anstieg. Es wird erwartet, dass die Stromerzeugung aus erneuerbaren Energien jährlich um 10 % steigt und sich die derzeitige Kapazität bis 2030 fast verdreifacht. Die zunehmende Einführung erneuerbarer Energien verändert den Charakter der Elektrizitätsinfrastruktur von einer zentralisierten zu einer stark dezentralisierten Energieversorgung, so dass die Erzeugung näher an den Ort des Bedarfs rückt. Dieser Wandel bringt zahlreiche Herausforderungen mit sich. Diese Arbeit konzentriert sich auf die Herausforderungen bei der Betriebsplanung dezentraler Energieanlagen aus der Perspektive sogenannter Aggregatoren, die zunehmend an den Energiemärkten teilnehmen. Aggregatoren fassen verschiedene Energieanlagen, d.h. Stromerzeuger und -verbraucher, zusammen und betreiben sie als dezentrales Kraftwerk. Die Planung der Energieressourcen wird jedoch weiterhin zentral durch den Aggregator koordiniert. Diese Arbeit zielt darauf ab, ein Framework für die Planung von Energieressourcen aus der Sicht eines Aggregators zu entwickeln, um eine große Vielfalt an technischen Anlagen abzudecken und gleichzeitig Marktinteraktionen wie Gebotsannahme- und Ablehnungsmöglichkeiten zu berücksichtigen. Der unvermeidliche und zunehmende Ausbau von erneuerbaren Energieressourcen bringt -- als Folge ihrer Unstetigkeit -- einen wachsenden Bedarf an Regelleistung- und Speichertechnologien mit sich. Daher liegt der Schwerpunkt auf Regelleistung, Energiespeicherung und integrierter Anlagen- und Gebotsplanung sowie deren Trade-offs, um die folgenden Forschungsfragen zu beantworten: 1) Was ist der aktuelle Stand von Regelleistungsmodellen und wie können diese verbessert werden? Insbesondere im Hinblick auf Regelleistung unter Berücksichtigung von Einschränkungen hinsichtlich der Änderungsrate der Leistungsabgabe, der maximalen Leistungsabgabe und der Energiekapazität. 2) Welche Auswirkungen hat die Verwendung unterschiedlicher Regelleistungsmodelle? 3) Welche Zielkonflikte bestehen beim Betrieb von Speicheranlagen in einem Marktumfeld? 4) Ist es möglich, ein rigoroses, praktikables mathematisches Modell zur gleichzeitigen Bestimmung von Anlagen- und Gebotsplanung aufzustellen? 5) Welche Zielkonflikte bestehen zwischen Anlagen- und Gebotsplanung und welche Auswirkungen haben sie? 6) Inwieweit ist es möglich, Modelle zur Planung von Energieressourcen schneller zu lösen und dabei eine ausreichend hohe Lösungsqualität beizubehalten?

By issuing interest rate derivative contracts, market makers such as large banks are exposed to undesired risk. There are several methods for banks to hedge themselves against this type of risk; one such method is the stochastic programming model developed by Blomvall and Hagenbjörk (2022). The effectiveness of their model relies on accurate pricing of interest rate derivatives and risk factor analysis, both of which are derived from a term structure. Blomvall and Ndengo (2013) present a discretized multiple yield curve framework for term structure measurement that allows for price deviations. The model uses regularization to deal with noise inherent in market price observations, where the regularization counteracts oscillations in the term structure and retains the smoothness of the curve by penalizing the first and second-order derivatives. Consequently, the resulting model creates a trade-off between a smooth curve and market price deviations. Changes in policy rates adjusted by a country’s central bank significantly impact the financial market and its actors. In this thesis, the model developed by Blomvall and Ndengo (2013) was further extended to include these steps in conjunction with monetary policy meetings. Two models were developed to realize the steps in the risk-free curve. The first model introduced an additional deviation term to allow for a shift in the curve. In the second model, the weights in the regularization were adjusted to allow for rapid changes on days surrounding the closest monetary policy meeting. A statistical test was conducted to determine the performance of the two models. The test showed that the model with adjusted regularization outperformed the model with an additional deviation term as well as a benchmark model without steps. However, both step models managed to reduce in-sample pricing errors, while the model with an additional deviation term performed worse than the benchmark model for out-of-sample data, given the current parameter setting. Other parameter combinations would potentially result in different outcomes, but it remains conjectural.

De nos jours, atteindre un niveau élevé de satisfaction des employés à l’intérieur d’horaires efficients est une tâche importante et ardue à laquelle les compagnies font face. Dans ce travail, nous abordons une nouvelle variante du problème de création d’horaire de personnel face à une demande inconnue, en tenant compte de la satisfaction des employés via l’incertitude endogène qui découle de la combinaison des préférences des employés envers les horaires, et de ceux qu’ils reçoivent. Nous abordons ce problème dans le contexte de la création d’horaire d’employés remplaçants, un problème opérationnel de l’industrie du transport en commun qui n’a pas encore été étudié, bien qu’assez présent dans les compagnies nord-américaines. Pour faire face aux défis qu’amènent les deux sources d’incertitude, les absences des employés réguliers et des employés remplaçants, nous modélisons ce problème en un programme stochastique en nombres entiers à deux étapes avec recours mixte en nombres entiers. Les décisions de première étape consistent à trouver les journées de congé des employés remplaçants. Une fois que les absences inconnues des employés réguliers sont révélées, les décisions de deuxième étape consistent à planifier les tâches des employés remplaçants. Nous incorporons les préférences des employés remplaçants envers les journées de congé dans notre modèle pour observer à quel point la satisfaction de ces employés peut affecter leurs propres taux d’absence. Nous validons notre approche sur un an de données de la ville de Los Angeles. Notre travail est présentement en cours d’implémentation chez un fournisseur mondial de solutions logicielles pour les opérations de transport en commun. / Nowadays, reaching a high level of employee satisfaction in efficient schedules is an important and difficult task faced by companies. In this work, we tackle a new variant of the personnel scheduling problem under unknown demand by considering employee satisfaction via endogenous uncertainty depending on the combination of their preferred and received schedules. We address this problem in the context of reserve staff scheduling, an operational problem from the transit industry that has not yet been studied, although rather present in North American transit companies. To handle the challenges brought by the two uncertainty sources, regular employee and reserve employee absences, we formulate this problem as a two-stage stochastic integer program with mixed-integer recourse. The first-stage decisions consist in finding the days off of the reserve employees. After the unknown regular employee absences are revealed, the second-stage decisions are to schedule the reserve staff duties. We incorporate reserve employees’ preferences for days off into the model to examine how employee satisfaction may affect their own absence rates. We validate our approach on one year of data from the city of Los Angeles. Our work is currently being implemented in a world-leader software solutions provider for public transit operations.

[pt] A Petrobras, maior empresa de óleo e gás do Brasil e uma das maiores do mundo, possui mais de 94 porcento da sua produção proveniente de campos offshore. Na região Sudeste o transporte dos trabalhadores para as unidades marítimas de exploração e produção é realizado por modal aéreo, através de helicópteros afretados de médio a grande porte. Para atender ao grande número de voos, a Petrobras possui uma central de planejamento e programação de voos, cujo objetivo é construir escalas de atendimento eficientes, em relação ao uso de recursos e ao nível de serviço. Um dos desafios enfrentados é gerar, manualmente, programações dos voos em situações de ruptura do atendimento, como por exemplo quando ocorre interrupção de pousos e decolagens devido a condições meteorológicas adversas (exigindo que os voos sejam programados para horários posteriores aos previamente planejados). Nessa dissertação de mestrado, é proposta uma abordagem de programação estocástica para gerar a programação de voos offshore ótima do ponto de vista do nível de serviço, reduzindo os atrasos esperados nos voos. Considerando a característica combinatória dos problemas de agendamento, utilizou-se o método de Aproximação pela Média Amostral (SAA) para gerar os cenários do modelo de programação estocástica. Um modelo de Simulação de Eventos Discretos também foi desenvolvido para avaliar o nível de serviço das programações de voos geradas. Os resultados numéricos indicam que a abordagem estocástica pode reduzir atrasos imprevisíveis, que causam grande impacto nos passageiros e na cadeia de suprimentos. / [en] Petrobras, the largest oil and gas company in Brazil and one of the largest in the world, has more than 94 percent of its production from offshore fields. In the Southeast region, workers are transported to offshore exploration and production units by air, using medium size to large size chartered helicopters. To serve the large number of flights, Petrobras has a flight planning and scheduling center, with the objective of building efficient service scales, related to the use of resources and the level of service. One of the challenges faced is to generate, manually, flight schedules in situations of disruption of service, such as when there is an interruption of landings and takeoffs due to adverse weather conditions (requiring that flights be scheduled for times after those previously planned). In this master s thesis, a stochastic programming approach is proposed to generate the optimal offshore flight schedule from the service level point of view, reducing expected flight delays. Considering the combinatorial characteristic of scheduling problems, the Sample Average Approximation (SAA) method was used to generate the scenarios of the stochastic programming model. A Discrete Event Simulation model was also developed to evaluate the service level of the generated flight schedules. The numerical results indicate that the stochastic approach can reduce unpredictable delays, which have a major impact on passengers and the supply chain.