Nos últimos anos, percebeu-se um avanço substancial das metodologias sistemáticas de seleção de ativos em portfólios financeiros, baseadas em técnicas de otimização. A maior pressão por desempenho sobre as gestoras de recursos e a evolução dos softwares e pacotes de otimização foram fatores que contribuíram para esse desenvolvimento. Dentre as técnicas mais reconhecidas utilizadas na gestão de portfólios está a de otimização robusta, cuja aplicação na solução de problemas com dados incertos iniciou-se na década de 1970 e, desde então, vem evoluindo em sofisticação. Partindo de uma extensão recente do método, propõe-se um novo modelo linear que resolve o problema de otimização de um portfólio para múltiplos estágios, com inovações no tratamento da incerteza das estimativas de dispersão dos retornos. Os resultados mostram que o método proposto desempenha muito bem em termos de rentabilidade e de métricas de risco-retorno em momentos de turbulência dos mercados. Por fim, demonstra-se empiricamente que o modelo alcança um desempenho ainda melhor em termos de rentabilidade com a adoção de um estimador eficiente para o valor esperado dos retornos e com a simultânea redução do nível de robustez do modelo. / It has been realized in the last years a remarkable development of the optimization techniques to solve the problem of financial portfolio selection. The pressure on asset management firms to maintain a more stable performance and the evolution of specialized software packages have enabled this positive trend. One of the most recognized approaches applied to the management of investments is the robust optimization, whose use on uncertain portfolio optimization problems has begun in the 1970s and has experienced a substantial growth since then. Building on a recent version of this framework, it is proposed a new linear model of the robust multistage portfolio optimization problem, thereby incorporating uncertainty about dispersion inputs in an innovative way. The results show that this method performs very well during high volatility periods in terms of the terminal wealth and the risk-return tradeoff. Finally, it can be demonstrated empirically that the proposed method outperforms when an efficient return estimator is incorporated to the optimization model and the robustness level is reduced simultaneously.

Les ports maritimes se confrontent à des exigences rigoureuses imposées par l'évolution de la taille de la flotte mondiale des porte-conteneurs et des zones de stockage qui arrivent à des niveaux de saturation élevés. Pour répondre à ces défis, plusieurs ports ont décidé de créer des terminaux multimodaux qui jouent le rôle de méga-hubs pour les terminaux maritimes, en vue de libérer les zones de stockage de ces terminaux, de développer la part du transport massifié de conteneurs et de réduire les émissions des gaz à effet de serre en utilisant des modes alternatifs à la route. Néanmoins, la gestion de ces nouveaux schémas logistiques est laborieuse. Cela s’explique par plusieurs facteurs, entre autres, la nature dynamique et distribuée de ces systèmes, la diversité des opérations et le manque des informations nécessaires au contrôle de flux. La finalité de cette thèse est de développer des approches capables de répondre aux besoins des opérateurs portuaires dans un terminal multimodal, avec prise en compte des différentes sources d’incertitudes. Deux problèmes d'optimisation sont principalement considérés dans cette thèse, à savoir : l'optimisation de tournées de navettes ferroviaires (The Rail Shuttle Routing Problem) et l'ordonnancement de grues de quai (The Quay Crane Scheduling Problem). En vue d'aborder la complexité et l’aspect incertain de ces problèmes, nous proposerons des modélisations mathématiques, ainsi que des approches de résolution basées sur l’optimisation par colonies de fourmis, l’optimisation robuste et le couplage Simulation-Optimisation. Les différents tests numériques effectués ont prouvé l’efficacité des algorithmes proposés et leur robustesse. / Today, seaports face increasingly stringent requirements imposed by the considerable growth of goods transited by sea. Indeed, the organization of the port sector has evolved rapidly and has caused several negative impacts, including pollution and congestion of terminals, which constitute today the major concerns of port operators. To address those challenges, several ports have decided to build multimodal terminals that act as mega-hubs for maritime terminals, in order to free the storage areas on the maritime terminals, to promote the use of consolidated container modes of transfer and to reduce greenhouse gas emissions by using alternative modes to the road. Nevertheless, the management of these new logistic systems is laborious. This is due to several factors, including the dynamic and distributed nature of these systems, the variety of operations, and the lack of information needed to control flow. The aim of this thesis is to develop approaches capable of meeting the needs of port operators in a multimodal terminal, taking into account the different sources of uncertainty. Two optimization problems are mainly considered in this thesis, namely : the Rail Shuttle Routing Problem(RSRP) and the Quay Crane Scheduling Problem(QCSP). To address the complexity and uncertainties of these problems, we propose new mathematical models, as well as some heuristics approaches based on ant colony optimization, robust optimization and Simulation-Optimization. The various numerical tests carried out proved the effectiveness and the robustness of the proposed algorithms.

Nos últimos anos, percebeu-se um avanço substancial das metodologias sistemáticas de seleção de ativos em portfólios financeiros, baseadas em técnicas de otimização. A maior pressão por desempenho sobre as gestoras de recursos e a evolução dos softwares e pacotes de otimização foram fatores que contribuíram para esse desenvolvimento. Dentre as técnicas mais reconhecidas utilizadas na gestão de portfólios está a de otimização robusta, cuja aplicação na solução de problemas com dados incertos iniciou-se na década de 1970 e, desde então, vem evoluindo em sofisticação. Partindo de uma extensão recente do método, propõe-se um novo modelo linear que resolve o problema de otimização de um portfólio para múltiplos estágios, com inovações no tratamento da incerteza das estimativas de dispersão dos retornos. Os resultados mostram que o método proposto desempenha muito bem em termos de rentabilidade e de métricas de risco-retorno em momentos de turbulência dos mercados. Por fim, demonstra-se empiricamente que o modelo alcança um desempenho ainda melhor em termos de rentabilidade com a adoção de um estimador eficiente para o valor esperado dos retornos e com a simultânea redução do nível de robustez do modelo. / It has been realized in the last years a remarkable development of the optimization techniques to solve the problem of financial portfolio selection. The pressure on asset management firms to maintain a more stable performance and the evolution of specialized software packages have enabled this positive trend. One of the most recognized approaches applied to the management of investments is the robust optimization, whose use on uncertain portfolio optimization problems has begun in the 1970s and has experienced a substantial growth since then. Building on a recent version of this framework, it is proposed a new linear model of the robust multistage portfolio optimization problem, thereby incorporating uncertainty about dispersion inputs in an innovative way. The results show that this method performs very well during high volatility periods in terms of the terminal wealth and the risk-return tradeoff. Finally, it can be demonstrated empirically that the proposed method outperforms when an efficient return estimator is incorporated to the optimization model and the robustness level is reduced simultaneously.

[pt] Black e Litterman propuseram um modelo de otimização de portfólio que combina visões do investidor sobre retornos esperados de ativos com o equilíbrio neutro de mercado. No entanto, especificar visões sobre uma carteira de investimentos é uma tarefa difícil, especialmente quando os investidores têm opiniões conflitantes sobre o mesmo ativo. Neste trabalho, é proposto uma nova formulação para otimização de carteiras, que é robusta diferentes à visões do investidor. A nossa abordagem foi testada em dados sintéticos e dados reais disponíveis em uma plataforma do Banco Central do Brasil. Esta plataforma consolida projeções macroeconômicas de mais de uma centena de analistas profissionais e disponibiliza para o mercado numa base semanal. Por fim, é comparado o desempenho desta formulação robusta com o modelo Black-Litterman tradicional frequentemente utilizado na indústria financeira. Os resultados mostram que a metodologia robusta pode providenciar melhor desempenho ajustado ao risco em comparação com o modelo orignial e são menos sensíveis às visões do investor. / [en] Black and Litterman proposed a portfolio optimization model that combines investor s views on future asset s returns with neutral market equilibrium. However, specifying portfolio views is a challenging task, specially when investors have conflicting opinions on the same asset. In this thesis, we suggest a new portfolio optimization formulation that is robust for investor s views. Our approach was tested on synthetic and real data available on a framework developed by Central Bank of Brazil. This online framework collects projections on main macroeconomics variables from more than a hundred professional forecasters and provides public online access on a weekly basis. The performance of this new robust formulation is compared with the traditional Black-Litterman model. The result show that our robust methodology can provide better risk adjusted performance compared to the orignial model and are less sensitive to incorrect inverstor views.

The thesis focuses on the analysis of various extensions of the classical multi-period single-item stochastic inventory problem. Specifically, we investigate two particular approaches of modeling risk in the context of inventory management: risk-averse models and robust formulations. We analyze the classical newsvendor problem utilizing a coherent risk measure as the objective function. Properties of coherent risk measures allow us to offer a unifying treatment of risk averse and min-max type formulations. We show that the structure of the optimal policy of the risk-averse model is similar to that of the classical expected value problem for both single and multi-period cases. The result carries over even when there is a fixed ordering cost. We expand our analysis to robust formulations of multi-period inventory problems. We consider both independent and dependent uncertainty sets and prove the optimality of base-stock policies for the general problem formulation. We focus on budget of uncertainty approach and develop a heuristic that can also be employed for a class of parametric dependency structures. We compare our proposed heuristic against alternative solution techniques.

This research focuses on fleet management in freight transportation systems. Effective management requires effective planning and control decisions. Plans are often generated using estimates of how the system will evolve in the future; during execution, control decisions need to be made to account for differences between actual realizations and estimates. The benefits of minimum cost plans can be negated by performing costly adjustments during the operational phase. A planning approach that permits effective control during execution is proposed in this dissertation. This approach is inspired by recent work in robust optimization, and is applied to (i) dynamic asset management and (ii) vehicle routing problems. In practice, the fleet management planning is usually decomposed in two parts; the problem of repositioning empty, and the problem of allocating units to customer demands. An alternative integrated dynamic model for asset management problems is proposed. A computational study provides evidence that operating costs and fleet sizes may be significantly reduced with the integrated approach. However, results also illustrate that not considering inherent demand uncertainty generates fragile plans with potential costly control decisions. A planning approach for the empty repositioning problem is proposed that incorporates demand and supply uncertainty using interval around nominal forecasted parameters. The intervals define the uncertainty space for which buffers need to be built into the plan in order to make it a robust plan. Computational evidence suggests that this approach is tractable. The traditional approach to address the Vehicle Routing Problem with Stochastic Demands (VRPSD) is through cost expectation minimization. Although this approach is useful for building routes with low expected cost, it does not directly consider the maximum potential cost that a vehicle might incur when traversing the tour. Our approach aims at minimizing the maximum cost. Computational experiments show that our robust optimization approach generates solutions with expected costs that compare favorably to those obtained with the traditional approach, but also that perform better in worst-case scenarios. We also show how the techniques developed for this problem can be used to address the VRPSD with duration constraints.

Traditional methods in engineering design involve producing solutions at a single level. However, in complex engineering design problems, such as concurrent product and materials design, various levels of model complexity are considered. A design process in which design problems are defined and analyzed at various levels of design complexity is referred to as multilevel design. One example of multilevel design is the design of a material, product, assembly, and system. Dividing a design problem into multiple levels increases the possibility for introducing and propagating uncertainty. Design solutions that perform predictably in the presence of uncertainty are robust designs. Robust design concepts that were originally developed for designs at a single level can be applied to a multilevel design process. The Inductive Design Exploration Method (IDEM) is an existing design method used to produce robust multilevel design solutions. In this thesis, the strategy presented in IDEM is incorporated into design templates in order to extend its overall usefulness. Design templates are generic, reusable, modules that provide the theoretical and computational framework for solving design problems. Information collected, stored, and analyzed from design templates is leveraged for a variety of design problems. In this thesis, the possibilities of a template-based approach to multilevel design are explored. Two example problems, which employ the developed multilevel robust design template, are considered. Multilevel design templates are created for the design of a cantilever beam and its associated material and the design of a blast resistant panel. The design templates developed for example problems can be extended to facilitate a generic, modular, template-based approach to multilevel robust design.

This dissertation is a collection of previously-published manuscript and conference papers. In this dissertation, we will deal with a stochastic unit commitment problem with cooling systems for gas generators, a robust unit commitment problem with demand response and uncertain wind generation, and a power grid vulnerability analysis with transmission line switching. The latter two problems correspond to our theoretical contributions in two-stage robust optimization, i.e., how to efficiently solve a two-stage robust optimization, and how to deal with mixed-integer recourse in robust optimization. Due to copyright issue, this dissertation does not include any methodology papers written by the author during his PhD study. Readers are referred to the author's website for a complete list of publications.

For opportunistic spectrum access and spectrum sharing in cognitive radio networks, one key problem is how to develop wireless access schemes for secondary users so that harmful interference to primary users can be avoided and quality-of-service (QoS) of secondary users can be guaranteed. In this research, dynamic wireless access protocols for secondary users are designed and optimized for both infrastructure-based and ad-hoc wireless networks. Under the infrastructure-based model, the secondary users are connected through a controller (i.e., an access point). In particular, the problem of wireless access for eHealth applications is considered. In a single service cell, an innovative wireless access scheme, called electromagnetic interference (EMI)-aware prioritized wireless access, is proposed to address the issues of EMI to the medical devices and QoS differentiation for different eHealth applications. Afterwards, the resource management problem for multiple service cells, specifically, in multiple spatial reuse time-division multiple access (STDMA) networks is addressed. The problem is formulated as a dual objective optimization problem that maximizes the spectrum utilization of secondary users and minimizes their power consumption subject to the EMI constraints for active and passive medical devices and minimum throughput guarantee for secondary users. Joint scheduling and power control algorithms based on greedy approaches are proposed to solve the problem with much less computational complexity. In an ad-hoc wireless network, the robust transmission scheduling and power control problem for collision-free spectrum sharing between secondary and primary users in STDMA wireless networks is investigated. Traditionally, the problem only considers the average link gains; therefore, QoS violation can occur due to improper power allocation with respect to instantaneous channel gain realization. To overcome this problem, a robust power control problem is formulated. A column generation based algorithm is proposed to solve the problem by considering only the potential subset of variables when solving the problem. To increase the scalability, a novel distributed two-stage algorithm based on the distributed column generation method is then proposed to obtain the near-optimal solution of the robust transmission schedules for vertical spectrum sharing in an ad-hoc wireless network.

For opportunistic spectrum access and spectrum sharing in cognitive radio networks, one key problem is how to develop wireless access schemes for secondary users so that harmful interference to primary users can be avoided and quality-of-service (QoS) of secondary users can be guaranteed. In this research, dynamic wireless access protocols for secondary users are designed and optimized for both infrastructure-based and ad-hoc wireless networks. Under the infrastructure-based model, the secondary users are connected through a controller (i.e., an access point). In particular, the problem of wireless access for eHealth applications is considered. In a single service cell, an innovative wireless access scheme, called electromagnetic interference (EMI)-aware prioritized wireless access, is proposed to address the issues of EMI to the medical devices and QoS differentiation for different eHealth applications. Afterwards, the resource management problem for multiple service cells, specifically, in multiple spatial reuse time-division multiple access (STDMA) networks is addressed. The problem is formulated as a dual objective optimization problem that maximizes the spectrum utilization of secondary users and minimizes their power consumption subject to the EMI constraints for active and passive medical devices and minimum throughput guarantee for secondary users. Joint scheduling and power control algorithms based on greedy approaches are proposed to solve the problem with much less computational complexity. In an ad-hoc wireless network, the robust transmission scheduling and power control problem for collision-free spectrum sharing between secondary and primary users in STDMA wireless networks is investigated. Traditionally, the problem only considers the average link gains; therefore, QoS violation can occur due to improper power allocation with respect to instantaneous channel gain realization. To overcome this problem, a robust power control problem is formulated. A column generation based algorithm is proposed to solve the problem by considering only the potential subset of variables when solving the problem. To increase the scalability, a novel distributed two-stage algorithm based on the distributed column generation method is then proposed to obtain the near-optimal solution of the robust transmission schedules for vertical spectrum sharing in an ad-hoc wireless network.