abstract: Resource allocation is one of the most challenging issues policy decision makers must address. The objective of this thesis is to explore the resource allocation from an economical perspective, i.e., how to purchase resources in order to satisfy customers' requests. In this thesis, we attend to answer the question: when and how to buy resources to fulfill customers' demands with minimum costs? The first topic studied in this thesis is resource allocation in cloud networks. Cloud computing heralded an era where resources (such as computation and storage) can be scaled up and down elastically and on demand. This flexibility is attractive for its cost effectiveness: the cloud resource price depends on the actual utilization over time. This thesis studies two critical problems in cloud networks, focusing on the economical aspects of the resource allocation in the cloud/virtual networks, and proposes six algorithms to address the resource allocation problems for different discount models. The first problem attends a scenario where the virtual network provider offers different contracts to the service provider. Four algorithms for resource contract migration are proposed under two pricing models: Pay-as-You-Come and Pay-as-You-Go. The second problem explores a scenario where a cloud provider offers k contracts each with a duration and a rate respectively and a customer buys these contracts in order to satisfy its resource demand. This work shows that this problem can be seen as a 2-dimensional generalization of the classic online parking permit problem, and present a k-competitive online algorithm and an optimal online algorithm. The second topic studied in this thesis is to explore how resource allocation and purchasing strategies work in our daily life. For example, is it worth buying a Yoga pass which costs USD 100 for ten entries, although it will expire at the end of this year? Decisions like these are part of our daily life, yet, not much is known today about good online strategies to buy discount vouchers with expiration dates. This work hence introduces a Discount Voucher Purchase Problem (DVPP). It aims to optimize the strategies for buying discount vouchers, i.e., coupons, vouchers, groupons which are valid only during a certain time period. The DVPP comes in three flavors: (1) Once Expire Lose Everything (OELE): Vouchers lose their entire value after expiration. (2) Once Expire Lose Discount (OELD): Vouchers lose their discount value after expiration. (3) Limited Purchasing Window (LPW): Vouchers have the property of OELE and can only be bought during a certain time window. This work explores online algorithms with a provable competitive ratio against a clairvoyant offline algorithm, even in the worst case. In particular, this work makes the following contributions: we present a 4-competitive algorithm for OELE, an 8-competitive algorithm for OELD, and a lower bound for LPW. We also present an optimal offline algorithm for OELE and LPW, and show it is a 2-approximation solution for OELD. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2015

abstract: The 2009-10 influenza and the 2014-15 Ebola pandemics brought once again urgency to an old question: What are the limits on prediction and what can be proposed that is useful in the face of an epidemic outbreak? This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy. Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are: I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions? II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles? Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2016

abstract: The majority of research in experimental design has, to date, been focused on designs when there is only one type of response variable under consideration. In a decision-making process, however, relying on only one objective or criterion can lead to oversimplified, sub-optimal decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical during the decision-making process in order to balance the tradeoffs of all potential solutions. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest does not have a clear answer, particularly when the response variables have different distributions. Responses with different distributions have different requirements of the design. Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work. The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016

abstract: Generalized Linear Models (GLMs) are widely used for modeling responses with non-normal error distributions. When the values of the covariates in such models are controllable, finding an optimal (or at least efficient) design could greatly facilitate the work of collecting and analyzing data. In fact, many theoretical results are obtained on a case-by-case basis, while in other situations, researchers also rely heavily on computational tools for design selection. Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem. / Dissertation/Thesis / Doctoral Dissertation Statistics 2018

The control of complex robotic platforms is a challenging task, especially in designs with high levels of kinematic redundancy. Novel variable impedance actuators (VIAs) have recently demonstrated that, by allowing the ability to simultaneously modulate the output torque and impedance, one can achieve energetically more efficient and safer behaviour. However, this adds further levels of actuation redundancy, making planning and control of such systems even more complicated. VIAs are designed with the ability to mechanically modulate impedance during movement. Recent work from our group, employing the optimal control (OC) formulation to generate impedance policies, has shown the potential benefit of VIAs in tasks requiring energy storage, natural dynamic exploitation and robustness against perturbation. These approaches were, however, restricted to systems with smooth, continuous dynamics, performing tasks over a predefined time horizon. When considering tasks involving multiple phases of movement, including switching dynamics with discrete state transitions (resulting from interactions with the environment), traditional approaches such as independent phase optimisation would result in a potentially suboptimal behaviour. Our work addresses these issues by extending the OC formulation to a multiphase scenario and incorporating temporal optimisation capabilities (for robotic systems with VIAs). Given a predefined switching sequence, the developed methodology computes the optimal torque and impedance profile, alongside the optimal switching times and total movement duration. The resultant solution minimises the control effort by exploiting the actuation redundancy and modulating the natural dynamics of the system to match those of the desired movement. We use a monopod hopper and a brachiation system in numerical simulations and a hardware implementation of the latter to demonstrate the effectiveness and robustness of our approach on a variety of dynamic tasks. The performance of model-based control relies on the accuracy of the dynamics model. This can deteriorate significantly due to elements that cannot be fully captured by analytic dynamics functions and/or due to changes in the dynamics. To circumvent these issues, we improve the performance of the developed framework by incorporating an adaptive learning algorithm. This performs continuous data-driven adjustments to the dynamics model while re-planning optimal policies that reflect this adaptation. The results presented show that the augmented approach is able to handle a range of model discrepancies, in both simulation and hardware experiments using the developed robotic brachiation system.

De nombreux retours de produits dus au recyclage et à la réutilisation des déchets se développent dans le but de préserver les ressources naturelles limitées de notre planète. Ces nouveaux flux interagissant avec les flux de production traditionnels, il est important de les piloter de façon à satisfaire au mieux les demandes des clients et minimiser l'encours dans la chaîne logistique. Nos travaux s'inscrivent dans cette démarche. Nous nous plaçons dans un contexte où la capacité de production est limitée et nous considérons un problème opérationnel de gestion des stocks et de la production intégrant des flux de retours. Nous modélisons trois problèmes de production et de stockage à temps continu, avec des capacités de production limitées, des délais aléatoires et des coûts linéaires. Le premier prenant en compte la probabilité qu'un produit puisse être réutilisé comme produit fini ou seulement comme produit semi-fini (par partie), le deuxième présentant un problème où la réutilisation d'un retour comme produit fini nécessite une étape de remise à neuf et le troisième modélisant un système où les clients préviennent à l'avance du renvoi potentiel de leurs produits. Outre la caractérisation des politiques optimales de gestion, une part importante de nos contributions réside dans l'évaluation des performances de différentes politiques heuristiques et l'étude de l'impact de la capacité de production sur celles-ci. Enfin, nous nous servons dans tout ce document d'outils permettant la caractérisation des politiques optimales. La dernière partie de ce document vise à développer ces outils et à permettre l'étude de l'effet des paramètres d'un système formulé en processus de décision Markovien sur la politique optimale de celui-ci. / Flows of returns due to recycling and reusing waste are developing in order to preserve the limited natural resources of our planet. These new flows interact with the traditional production flows. Therefore, in order to provide customers with the best service level and minimize the stock in the supply chain, the control of the return flows appears to be of highest importance. We address this problem by modeling a situation with a limited porduction capacity and we consider an operational production/inventory problem that incorporates flows of returns. We model three continuous-time production/inventory problems with limited produc- tion capacities, random lead times, and linear costs. In the first problem we take into account the probability that a product can be reused as a finished product or only as semi-finished product (by parts), in the second problem we include a step of remanufac- turing before reusing the returned product, and in the third problem we consider a system with product returns that are announced in advance by the customers. Apart from the caracterization of the optimal policies for these cases, the performance assessments of some heuristic policies and the study of the poduction capacity effect on these heuristic policies stand as main contributions. Throughout this work we have used existing tools to characterize optimal policies for different Markov decision processes. The last chapter aims to improve these tools and enable us to study the influence of several system parameters on its optimal policy.

Made available in DSpace on 2014-10-09T12:50:30Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:58:49Z (GMT). No. of bitstreams: 1 00045.pdf: 1150397 bytes, checksum: fd8a86947b37fabf9aa8ff7b1e99d2a9 (MD5) / Dissertacao (Mestrado) / IEA/D / Escola Politecnica, Universidade de Sao Paulo - POLI/USP

In this diploma thesis, selected techniques for construction of optimal portfo- lios are presented. Risk measures and other criteria (Markowitz approach, Value at risk, Conditional value at risk, Mean absolute deviation, Spectral risk measure and Kelly criterion) are defined in the first part. We derived analytical solution for some cases of optimization problems, in some other cases there exists numeri- cal solution only however. Advantages and disadvantages, theoretical properties and practical aspects of software implementation in Wolfram Mathematica are also mentioned. Simulation methods suitable for portfolio optimization are brie- fly presented with their motivation in the second part. Multivariate distributions: normal, t-distribution and skewed t-distribution are presented in the third part with connection to optimization of portfolio with assumption of multivariate dis- tribution of financial losses. Optimization methods are illustrated on real data in the fourth part of this thesis. Analytical methods are compared with numerical ones. 1

abstract: Accelerated life testing (ALT) is the process of subjecting a product to stress conditions (temperatures, voltage, pressure etc.) in excess of its normal operating levels to accelerate failures. Product failure typically results from multiple stresses acting on it simultaneously. Multi-stress factor ALTs are challenging as they increase the number of experiments due to the stress factor-level combinations resulting from the increased number of factors. Chapter 2 provides an approach for designing ALT plans with multiple stresses utilizing Latin hypercube designs that reduces the simulation cost without loss of statistical efficiency. A comparison to full grid and large-sample approximation methods illustrates the approach computational cost gain and flexibility in determining optimal stress settings with less assumptions and more intuitive unit allocations. Implicit in the design criteria of current ALT designs is the assumption that the form of the acceleration model is correct. This is unrealistic assumption in many real-world problems. Chapter 3 provides an approach for ALT optimum design for model discrimination. We utilize the Hellinger distance measure between predictive distributions. The optimal ALT plan at three stress levels was determined and its performance was compared to good compromise plan, best traditional plan and well-known 4:2:1 compromise test plans. In the case of linear versus quadratic ALT models, the proposed method increased the test plan's ability to distinguish among competing models and provided better guidance as to which model is appropriate for the experiment. Chapter 4 extends the approach of Chapter 3 to ALT sequential model discrimination. An initial experiment is conducted to provide maximum possible information with respect to model discrimination. The follow-on experiment is planned by leveraging the most current information to allow for Bayesian model comparison through posterior model probability ratios. Results showed that performance of plan is adversely impacted by the amount of censoring in the data, in the case of linear vs. quadratic model form at three levels of constant stress, sequential testing can improve model recovery rate by approximately 8% when data is complete, but no apparent advantage in adopting sequential testing was found in the case of right-censored data when censoring is in excess of a certain amount. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2014

Neste trabalho apresentamos uma nova classe de robos bipedes com pernas articuladas e um corpo central. O projeto de robo proposto faz uso de contrapesos em cada um de seus links, e apresenta propriedades que simplificam excepcionalmente as equações dinâmicas que regem seu movimento. Prova- mos que o sistema encontrado, sob certas hipóteses, é linearizavel por meio de uma realimentaçao não-linear de seus estados. Resolvemos o problema de otimização do tempo de percurso de uma trajetória predefinida para este robo, admitindo-se limitações em seus atuadores. Projetamos um sistema de controle inspirado no conceito de \"flatness\" a fim de rastrear esta política ótima de percurso da trajetória. Testamos a robustez deste sistema em simulações de alguns exemplos numéricos. / In this thesis we present a new class of biped robots with articulate legs and a torso. The proposed design is constructed by means of applying counter- balances to each link of the leg, and therefore it has some properties that simplifies dramatically the dynamics of the robot. We prove that the result- ing system, under certain assumptions, is exact linearizable by a nonlinear feedback. We describe the solution to the time-optimal tracking problem of a predefined trajectory for this robot, assuming that its actuators have torque limits. We designed a control system inspired on the concept of °flatness\"in order to track this reference optimal trajectory. We evaluated the robustness of such system during the simulations of some numerical examples.