[pt] Em função da dependência dos regimes hidrológicos, a incerteza associada ao planejamento energético no Brasil exige a modelagem estocástica das Séries Temporais associadas de maneira adequada e coerente. Percebe-se, portanto, a importância dos modelos de geração de cenários hidrológicos com vistas à otimização, via Programação Dinâmica Dual Estocástica (PDDE), do desempenho das operações do sistema elétrico, com consequente aumento de benefícios e confiabilidade e, sobretudo, redução de custos. Esta modelagem estocástica tem sido realizada por um modelo Autorregressivo Peridódico, PAR(p), que ajusta um modelo autorregressivo de ordem p para cada um dos estágios das séries históricas que compõem as configurações do sistema. Este trabalho mostra que a estrutura utilizada no processo de simulação de séries sintéticas do modelo vigente no Setor Elétrico Brasileiro, via distribuição Lognormal, gera uma não linearidade na equação do modelo, o que pode ocasionar inconvenientes de não convexidade que inviabilizam o correto cálculo das Funções de Custo Futuro, poliedros convexos aproximados por funções lineares por partes. Haja vista o exposto e as características do modelo estocástico gerador da árvore de cenários e sua utilização em modelos de otimização, este trabalho apresenta uma nova metodologia alternativa para a construção dos cenários, de forma que os inconvenientes supracitados sejam eliminados. Isto posto, será apresentado uma nova abordagem geral para a construção das árvores, considerando os passos Forward e Backward, fundamentais no processo de otimização empregado pela técnica de PDDE. A estrutura de simulação estocástica desenvolvida conjugou a técnica de computação intensiva de Bootstrap e o método de simulação de Monte Carlo. Foram geradas árvores de cenários com horizonte temporal condizente com o planejamento de médio prazo do despacho hidrotérmico. As séries sintéticas foram comparadas às históricas por meio de uma bateria de testes estatísticos e a aderência das séries geradas foi atestada, provando a adequabilidade do modelo desenvolvido no que tange à parte estocástica do problema. Por fim, a árvore de cenários gerada foi aplicada na PDDE e várias variáveis de resposta foram analisadas, permitindo concluir que o modelo desenvolvido é perfeitamente capaz de reproduzir estruturas compatíveis com o modelo vigente, contudo sem causar a referida não linearidade na equação do PAR(p) e a possível não convexidade do problema de otimização associado ao planejamento de operação de médio/longo prazo. / [en] Due to the highly dependence on the hydrological regimes, the uncertainty associated with energy planning in Brazil requires stochastic modeling of associated time series appropriately and consistently. It is clear, therefore, the importance of models to generate hydrologic scenarios to be used in the optimization via Stochastic Dual Dynamic Programming (SDDP), which improves the performance of system operations, with consequent increase in benefits and reliability and, above all, cost reduction. This stochastic modeling is performed by the PAR(p), which sets an autoregressive model of order p for each of the stages of the historical series that make up the system settings. It was shown in this work that the structure used in the simulation process of synthetic series of the model prevailing in SEB via lognormal distribution generates a nonlinearity relationship in the model equation, which causes the inconvenience of nonconvexity in the calculation of Expected Cost-to-go Functions, convex polyhedral approximated by piecewise linear functions. Considering the above and the characteristics of the stochastic model that generates the scenarios tree and its use in the optimization algorithms, this study aims the development of an alternative methodology for the construction of scenarios, so that the aforementioned drawbacks were eliminated. It is proposed a new general approach for the construction of trees, considering the steps Forward and Backward, fundamental in the process of optimization technique employed by SDDP. The structure of stochastic simulation technique developed conjugates computationally intensive Bootstrap method and Monte Carlo simulation. Scenarios trees were generated consistent with the medium-term planning of hydrothermal dispatch. The synthetic series were compared to the historical data through a battery of statistical tests and the goodness fiting of the series generated was tested that confirmed the suitability of the developed model with respect to the stochastic problem. Finally, the paths of the trees were applied to the SDDP and response variables were analyzed, leading to the conclusion that the model was able to perfectly reproduce structures compatible with the current model, but without causing the aforementioned non-linearity of the PAR(p) equation and possible non convexity in the Expected Cost-to-go Functions.

Les maladies animales émergentes, les maladies zoonotiques et le développement du commerce international ont conduit à une augmentation des besoins en systèmes de surveillance en santé animale performants. Toutefois, le contexte économique actuel conduit à des restrictions budgétaires importantes, induisant une diminution des ressources allouées à la surveillance. Dans ce contexte, l’évaluation régulière des dispositifs de surveillance, sur lesquels sont fondées les décisions sanitaires, est indispensable afin de vérifier leur bon fonctionnement, la qualité des données collectées, et permettre leur amélioration.Notre travail a porté sur l’évaluation d’un dispositif de surveillance complexe, Sylvatub, le dispositif de surveillance de l’infection à Mycobacterium bovis dans la faune sauvage, constitué de plusieurs composantes de surveillance et ciblant plusieurs espèces sauvages. Nous avons appliqué quatre méthodes d’évaluation : (i) une méthode quantitative d’estimation de la sensibilité de la surveillance par arbres de scénarios, (ii) une méthode quantitative d’estimation des coûts de la surveillance, permettant le calcul d’un ratio coût-efficacité, (iii) une méthode semi-quantitative permettant l’étude du fonctionnement général du dispositif et (iv) une méthode qualitative permettant d’investiguer l’acceptabilité de la surveillance. Ces travaux ont permis d’évaluer le dispositif Sylvatub dans son contexte environnemental et économique, en intégrant des facteurs comportementaux et sociaux, et ont permis la formulation de recommandations pour l’évolution du dispositif et son amélioration.Ces travaux ont également permis de souligner les avantages méthodologiques et opérationnels de l’utilisation complémentaire de plusieurs méthodes pour l’évaluation de dispositifs de surveillance complexes et proposent des perspectives méthodologiques pour favoriser l’intégration des méthodes d’évaluation. L’évaluation du dispositif Sylvatub devra être poursuivie et complétée par celle du dispositif de surveillance en élevage bovin afin d’étudier les interconnexions entre les populations domestiques et sauvages dans ce système multi-hôtes particulier. / Emerging animal diseases, zoonotic diseases and the development of international trade have led to an increase in the need for efficient animal health surveillance systems. However, the current economic environment led to significant budget cuts, resulting in a reallocation of resources dedicated to surveillance. In this context, regular evaluation of surveillance systems, on which are based the health decisions, is essential to ensure their operation, the quality of the collected data and to allow their improvement.This study focused on the evaluation of a complex surveillance system, the Sylvatub network for the surveillance of Mycobacterium bovis infection in wildlife, which consists of several surveillance components focusing on several wild species. We have used four evaluation methods: (i) a quantitative method to estimate the surveillance sensitivity by scenario trees modelling, (ii) a quantitative method to estimate the surveillance costs, enabling the estimation of a cost-effectiveness ratio, (iii) a semi-quantitative method to estimate the global operation of the system, and (iv) a qualitative method to investigate the acceptability of the surveillance. This study allowed to assess the Sylvatub network in its environmental and economical context, with the integration of behavioral and social factors; and allowed the development of recommendations for the evolution of the surveillance system and its improvement.This study has highlighted the methodological and operational advantages of the complementary use of several methods for the evaluation of complex surveillance systems. It provides methodological perspectives to support the integration of evaluation methods. The assessment of the Sylvatub system should be deepened and complemented by the evaluation of the surveillance system in cattle to explore interconnections between domestic and wild populations in this particular multi-host system.

<p>The Swedish National Debt Office (SNDO) is the Swedish Government’s financial administration. It has several tasks and the main one is to manage the central government’s debt in a way that minimizes the cost with due regard to risk. The debt management problem is to choose currency composition and maturity profile - a problem made difficult because of the many stochastic factors involved. </p><p>The SNDO has created a simulation model to quantitatively analyze different aspects of this problem by evaluating a set of static strategies in a great number of simulated futures. This approach has a number of drawbacks, which might be handled by using a financial optimization approach based on Stochastic Programming. </p><p>The objective of this master’s thesis is thus to apply financial optimization on the Swedish government’s strategic debt management problem, using the SNDO’s simulation model to generate scenarios, and to evaluate this approach against a set of static strategies in fictitious future macroeconomic developments. </p><p>In this report we describe how the SNDO’s simulation model is used along with a clustering algorithm to form future scenarios, which are then used by an optimization model to find an optimal decision regarding the debt management problem. </p><p>Results of the evaluations show that our optimization approach is expected to have a lower average annual real cost, but with somewhat higher risk, than a set of static comparison strategies in a simulated future. These evaluation results are based on a risk preference set by ourselves, since the government has not expressed its risk preference quantitatively. We also conclude that financial optimization is applicable on the government debt management problem, although some work remains before the method can be incorporated into the strategic work of the SNDO.</p>

The Swedish National Debt Office (SNDO) is the Swedish Government’s financial administration. It has several tasks and the main one is to manage the central government’s debt in a way that minimizes the cost with due regard to risk. The debt management problem is to choose currency composition and maturity profile - a problem made difficult because of the many stochastic factors involved. The SNDO has created a simulation model to quantitatively analyze different aspects of this problem by evaluating a set of static strategies in a great number of simulated futures. This approach has a number of drawbacks, which might be handled by using a financial optimization approach based on Stochastic Programming. The objective of this master’s thesis is thus to apply financial optimization on the Swedish government’s strategic debt management problem, using the SNDO’s simulation model to generate scenarios, and to evaluate this approach against a set of static strategies in fictitious future macroeconomic developments. In this report we describe how the SNDO’s simulation model is used along with a clustering algorithm to form future scenarios, which are then used by an optimization model to find an optimal decision regarding the debt management problem. Results of the evaluations show that our optimization approach is expected to have a lower average annual real cost, but with somewhat higher risk, than a set of static comparison strategies in a simulated future. These evaluation results are based on a risk preference set by ourselves, since the government has not expressed its risk preference quantitatively. We also conclude that financial optimization is applicable on the government debt management problem, although some work remains before the method can be incorporated into the strategic work of the SNDO.

Diese Arbeit leistet Beiträge zu zwei Gebieten der mathematischen Programmierung: stochastische Optimierung und gemischt-ganzzahlige nichtlineare Optimierung (MINLP). Im ersten Teil erweitern wir quantitative Stetigkeitsresultate für zweistufige stochastische gemischt-ganzzahlige lineare Programme auf Situationen in denen Unsicherheit gleichzeitig in den Kosten und der rechten Seite auftritt, geben eine ausführliche Übersicht zu Dekompositionsverfahren für zwei- und mehrstufige stochastische lineare und gemischt-ganzzahlig lineare Programme, und diskutieren Erweiterungen und Kombinationen des Nested Benders Dekompositionsverfahrens und des Nested Column Generationsverfahrens für mehrstufige stochastische lineare Programme die es erlauben die Vorteile sogenannter rekombinierender Szenariobäume auszunutzen. Als eine Anwendung dieses Verfahrens betrachten wir die optimale Zeit- und Investitionsplanung für ein regionales Energiesystem unter Einbeziehung von Windenergie und Energiespeichern. Im zweiten Teil geben wir eine ausführliche Übersicht zum Stand der Technik bzgl. Algorithmen und Lösern für MINLPs und zeigen dass einige dieser Algorithmen innerhalb des constraint integer programming Softwaresystems SCIP angewendet werden können. Letzteres erlaubt uns die Verwendung schon existierender Technologien für gemischt-ganzzahlige linear Programme und constraint Programme für den linearen und diskreten Teil des Problems. Folglich konzentrieren wir uns hauptsächlich auf die Behandlung der konvexen und nichtkonvexen nichtlinearen Nebenbedingungen mittels Variablenschrankenpropagierung, äußerer Approximation und Reformulierung. In einer ausführlichen numerischen Studie untersuchen wir die Leistung unseres Ansatzes anhand von Anwendungen aus der Tagebauplanung und des Aufbaus eines Wasserverteilungssystems und mittels verschiedener Vergleichstests. Die Ergebnisse zeigen, dass SCIP ein konkurrenzfähiger Löser für MINLPs geworden ist. / This thesis contributes to two topics in mathematical programming: stochastic optimization and mixed-integer nonlinear programming (MINLP). In the first part, we extend quantitative continuity results for two-stage stochastic mixed-integer linear programs to include situations with simultaneous uncertainty in costs and right-hand side, give an extended review on decomposition algorithm for two- and multistage stochastic linear and mixed-integer linear programs, and discuss extensions and combinations of the Nested Benders Decomposition and Nested Column Generation methods for multistage stochastic linear programs to exploit the advantages of so-called recombining scenario trees. As an application of the latter, we consider the optimal scheduling and investment planning for a regional energy system including wind power and energy storages. In the second part, we give a comprehensive overview about the state-of-the-art in algorithms and solver technology for MINLPs and show that some of these algorithm can be applied within the constraint integer programming framework SCIP. The availability of the latter allows us to utilize the power of already existing mixed integer linear and constraint programming technologies to handle the linear and discrete parts of the problem. Thus, we focus mainly on the domain propagation, outer-approximation, and reformulation techniques to handle convex and nonconvex nonlinear constraints. In an extensive computational study, we investigate the performance of our approach on applications from open pit mine production scheduling and water distribution network design and on various benchmarks sets. The results show that SCIP has become a competitive solver for MINLPs.

本論文提出追蹤特定目標線的二階段混合整數非線性隨機規劃模型，以建立追蹤目標線的投資組合。藉由引進情境樹(scenario tree)，我們將此類二階段隨機規劃問題，轉換成為等價的非隨機規劃模型。在金融商品的價格波動及交互作用下，所建立的投資組合在經過一段時間後，其追蹤目標線的能力可能會日趨降低，所以本論文亦提出調整投資組合的規劃模型。為符合實務考量，本論文同時考慮交易成本、股票放空的限制，並且加入期貨進行避險。為了反應投資者的預期心理，也引進了選擇權及情境樹。最後，我們使用台灣股票市場、期貨交易市場及台指選擇權市場的資料進行實證研究，亦探討不同成長率設定之目標線與投資比例對於投資組合的影響。 / To construct a portfolio tracking specific target line, this thesis studies how to do it via two-stage stochastic mixed-integer nonlinear model. We introduce scenario tree to convert this stochastic model into an deterministic equivalent model. Under the volatility of price and the interaction of each financial derivatives, the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical model to rebalance the tracking portfolio. These models consider the transactions cost and the limitation of shorting a stock, and the tracking portfolio will include a futures as a hedge position. To reflect the expectation of investors, we introduce scenario tree and also include a options as a hedge position. Finally, an empirical study will be performed by the data from Taiwan stock market, the futures market and the options market to explore the performance of the proposed models. We will analyze how the different benchmarks settings and invest ratio will affect the value of the tracking portfolio.