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A incerteza é um elemento fundamental da realidade. Então, torna-se natural a busca por métodos que nos permitam representar o desconhecido em termos matemáticos. Esses problemas originam uma grande classe de programas probabilísticos reconhecidos como modelos de programação estocástica. Eles são mais realísticos que os modelos determinísticos, e tem por objetivo incorporar a incerteza em suas definições. Essa tese aborda os problemas probabilísticos da classe de problemas de multi-estágio com incerteza e com restrições probabilísticas e com restrições probabilísticas conjuntas. Inicialmente, nós propomos um modelo de administração de ativos e passivos multi-estágio estocástico para a indústria de fundos de pensão brasileira. Nosso modelo é formalizado em conformidade com a leis e políticas brasileiras. A seguir, dada a relevância dos dados de entrada para esses modelos de otimização, tornamos nossa atenção às diferentes técnicas de amostragem. Elas compõem o processo de discretização desses modelos estocásticos Nós verificamos como as diferentes metodologias de amostragem impactam a solução final e a alocação do portfólio, destacando boas opções para modelos de administração de ativos e passivos. Finalmente, nós propomos um “framework” para a geração de árvores de cenário e otimização de modelos com incerteza multi-estágio. Baseados na tranformação de Knuth, nós geramos a árvore de cenários considerando a representação filho-esqueda, irmão-direita o que torna a simulação mais eficiente em termos de tempo e de número de cenários. Nós também formalizamos uma reformulação do modelo de administração de ativos e passivos baseada na abordagem extensiva implícita para o modelo de otimização. Essa técnica é projetada pela definição de um processo de filtragem com “bundles”; e codifciada com o auxílio de uma linguagem de modelagem algébrica. A eficiência dessa metodologia é testada em um modelo de administração de ativos e passivos com incerteza com restrições probabilísticas conjuntas. Nosso framework torna possível encontrar a solução ótima para árvores com um número razoável de cenários. / Uncertainty is a key element of reality. Thus, it becomes natural that the search for methods allows us to represent the unknown in mathematical terms. These problems originate a large class of probabilistic programs recognized as stochastic programming models. They are more realistic than deterministic ones, and their aim is to incorporate uncertainty into their definitions. This dissertation approaches the probabilistic problem class of multistage stochastic problems with chance constraints and joint-chance constraints. Initially, we propose a multistage stochastic asset liability management (ALM) model for a Brazilian pension fund industry. Our model is formalized in compliance with the Brazilian laws and policies. Next, given the relevance of the input parameters for these optimization models, we turn our attention to different sampling models, which compose the discretization process of these stochastic models. We check how these different sampling methodologies impact on the final solution and the portfolio allocation, outlining good options for ALM models. Finally, we propose a framework for the scenario-tree generation and optimization of multistage stochastic programming problems. Relying on the Knuth transform, we generate the scenario trees, taking advantage of the left-child, right-sibling representation, which makes the simulation more efficient in terms of time and the number of scenarios. We also formalize an ALM model reformulation based on implicit extensive form for the optimization model. This technique is designed by the definition of a filtration process with bundles, and coded with the support of an algebraic modeling language. The efficiency of this methodology is tested in a multistage stochastic ALM model with joint-chance constraints. Our framework makes it possible to reach the optimal solution for trees with a reasonable number of scenarios.

The Applied Miniaturisation Laboratory (AML) has recently built a laser-induced fluorescent capillary electrophoresis (LIF-CE) genetic analysis instrument, called the Tricorder Tool Kit (TTK). By using a photodiode instead of photomultiplier tubes in the optical detection, the AML has lowered the cost and size compared to commercial LIF-CE products. However, maintaining an adequate signal-to-noise (SNR) and limit of detection (LOD) is a challenge. By implementing a multistage amplifier, we increased the bandwidth and voltage swing while maintaining the transimpedance gain compared to the previous design. We also developed signal processing algorithms for post-experiment processing of CE. Using wavelet transform, iterative polynomial baseline fitting, and Jansson's deconvolution, we improved the SNR, reduced baseline variations, and separated overlapping peaks in CE signals. By improving the electronics and signal processing, we lowered the LOD of the TTK, which is a step towards the realisation of inexpensive point-of-care molecular medical diagnosis instruments. / Computer, Microelectronic Devices, Circuits and Systems

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In this thesis, we study a series of closely related multi-stage stochastic programming models in production planning, from both a modeling and an algorithmic point of view. We first consider a very simple multi-stage stochastic lot-sizing problem, involving a single item with no fixed charge and capacity constraint. Although a multi-stage stochastic integer program, this problem can be shown to have a totally unimodular constraint matrix. We develop primal and dual algorithms by exploiting the problem structure. Both algorithms are strongly polynomial, and therefore much more efficient than the Simplex method. Next, motivated by applications in semiconductor tool planning, we develop a general capacity planning problem under uncertainty. Using a scenario tree to model the evolution of the uncertainties, we present a multi-stage stochastic integer programming formulation for the problem. In contrast to earlier two-stage approaches, the multi-stage model allows for revision of the capacity expansion plan as more information regarding the uncertainties is revealed. We provide analytical bounds for the value of multi-stage stochastic programming over the two-stage approach. By exploiting the special simple stochastic lot-sizing substructure inherent in the problem, we design an efficient approximation scheme and show that the proposed scheme is asymptotically optimal. We conduct a computational study with respect to a semiconductor-tool-planning problem. Numerical results indicate that even an approximate solution to the multi-stage model is far superior to any optimal solution to the two-stage model. These results show that the value of multi-stage stochastic programming for this class of problem is extremely high. Next, we extend the simple stochastic lot-sizing model to an infinite horizon problem to study the planning horizon of this problem. We show that an optimal solution of the infinite horizon problem can be approximated by optimal solutions of a series of finite horizon problems, which implies the existence of a planning horizon. We also provide a useful upper bound for the planning horizon.

The advancement in integrated circuit (IC) technology has resulted in scaling down of device sizes and supply voltages without proportionally scaling down the threshold voltage of the MOS transistor. This, coupled with the increasing demand for low power, portable, battery-operated electronic devices, like mobile phones, and laptops provides the impetus for further research towards achieving higher integration on chip and low power consumption. High gain, wide bandwidth amplifiers driving large capacitive loads serve as error amplifiers in low-voltage low drop out regulators in portable devices. This demands low power, low area, and frequency-compensated multistage amplifiers capable of driving large capacitive loads. The first part of the research proposes two power and area efficient frequency compensation schemes: Single Miller Capacitor Compensation (SMC) and Single Miller Capacitor Feedforward Compensation (SMFFC), for multistage amplifiers driving large capacitive loads. The designs have been implemented in a 0.5??m CMOS process. Experimental results show that the SMC and SMFFC amplifiers achieve gain-bandwidth products of 4.6MHz and 9MHz, respectively, when driving a load of 25Kδ/120pF. Each amplifier operates from a ??1V supply, dissipates less than 0.42mW of power and occupies less than 0.02mm2 of silicon area. The inception of the latest IEEE standard like IEEE 802.16 wireless metropolitan area network (WMAN) for 10 -66 GHz range demands wide band amplifiers operating at high frequencies to serve as front-end circuits (e.g. low noise amplifier) in such receiver architectures. Devices used in cascade (multistage amplifiers) can be used to increase the gain but it is achieved at an expense of bandwidth. Distributing the capacitance associated with the input and the output of the device over a ladder structure (which is periodic), rather than considering it to be lumped can achieve an extension of bandwidth without sacrificing gain. This concept which is also known as distributed amplification has been explored in the second part of the research. This work proposes certain guidelines for the design of distributed low noise amplifiers operating at very high frequencies. Noise analysis of the distributed amplifier with real transmission lines is introduced. The analysis for gain and noise figure is verified with simulation results from a 5-stage distributed amplifier implemented in a 0.18??m CMOS process.

We consider a hydrothermal scheduling problem with a mid-term horizon(HTSPM) modeled as a large-scale multistage stochastic program with stochastic monthly inflows of water to each hydro generator. In the HTSPM we seek an operating policy to minimize the sum of present and expected future costs, which include thermal generation costs and load curtailment costs. In addition to various simple bounds, problem constraints involve water balance, demand satisfaction and power interchanges. Sampling-based decomposition algorithms (SBDAs) have been used in the literature to solve HTSPM. SBDAs can be used to approximately solve problem instances with many time stages and with inflows that exhibit interstage dependence. Such dependence requires care in computing valid cuts for the decomposition algorithm. In order to help maintain tractability, we employ an aggregate reservoir representation (ARR). In an ARR all the hydro generators inside a specific region are grouped to effectively form one hydro plant with reservoir storage and generation capacity proportional to the parameters of the hydro plants used to form that aggregate reservoir. The ARR has been used in the literature with energy balance constraints, rather than water balance constraints, coupled with time series forecasts of energy inflows. Instead, we prefer as a model primitive to have the time series model forecast water inflows. This, in turn, requires that we extend existing methods to compute valid cuts for the decomposition method under the resulting form of interstage dependence. We form a sample average approximation of the original problem and then solve this problem by these special-purpose algorithms. And, we assess the quality of the resulting policy for operating the system. In our analysis, we compute a confidence interval on the optimality gap of a policy generated by solving an approximation on a sampled scenario tree. We present computational results on test problems with 24 monthly stages in which the inter-stage dependency of hydro inflows is modeled using a dynamic linear model. We further develop a parallel implementation of an SBDA. We apply SBDA to solve the HTSPM for the Brazilian power system that has 150 hydro generators, 151 thermal generators and 4 regions that each characterize an aggregate reservoir. We create and solve four different HTSPM instances where we change the input parameters with respect to generation capacity, transmission capacity and load in order to analyze the difference in the total expected cost. / text

Significant research has been initiated recently to devise control strategies that could predict and compensate manufacturing errors using so called explicit Stream-of-Variation(SoV) models that relate process parameters in a Multistage Manufacturing Process (MMP) with product quality. This doctoral dissertation addresses several important scientific and engineering problems that will significantly advance the model-based, active control of quality in MMPs. First, we will formally introduce and study the new concept of compensability in MMPs, analogous to the concept of controllability in the traditional control theory. The compensability in an MMP is introduced as the property denoting one’s ability to compensate the errors in quality characteristics of the workpiece, given the allocation and character of measurements and controllable tooling. The notions of “within-station” and “between-station” compensability are also introduced to describe the ability to compensate upstream product errors within a given operation or between arbitrarily selected operations, respectively. The previous research also failed to concurrently utilize the historical and on-line measurements of product key characteristics for active model-based quality control. This dissertation will explore the possibilities of merging the well-known Run-to-Run (RtR) quality control methods with the model-based feed-forward process control methods. The novel method is applied to the problem of control of multi-layer overlay errors in lithography processes in semiconductor manufacturing. In this work, we first devised a multi-layer overlay model to describe the introduction and flow of overlay errors from one layer to the next, which was then used to pursue a unified approach to RtR and feedforward compensation of overlay errors in the wafer. At last, we extended the existing methodologies by considering inaccurately indentified noise characteristics in the underlying error flow model. This is also a very common situation, since noise characteristics are rarely known with absolute accuracy. We formulated the uncertainty in process noise characteristics using Linear Fractional Transformation (LFT) representation and solved the problem by deriving a robust control law that guaranties the product quality even under the worst case scenario of parametric uncertainties. Theoretical results have been evaluated and demonstrated using a linear state-space model of an actual industrial process for automotive cylinder head machining. / text

Although the design of Multistage testing (MST) has received increasing attention, previous studies mostly focused on comparison of the psychometric properties of MST with CAT and paper-and-pencil (P&P) test. Few studies have systematically examined the number of items in the routing test, the number of subtests in a stage, or the number of stages in a test design to achieve accurate measurement in MST. Given that none of the studies have identified an ideal MST test design using polytomously-scored items, the current study conducted a simulation to investigate the optimal design for MST using generalized partial credit model (GPCM). Eight different test designs were examined on ability estimation across two routing test lengths (short and long) and two total test lengths (short and long). The item pool and generated item responses were based on items calibrated from a national test consisting of 273 partial credit items. Across all test designs, the maximum information routing method was employed and the maximum likelihood estimation was used for ability estimation. Ten samples of 1,000 simulees were used to assess each test design. The performance of each test design was evaluated in terms of the precision of ability estimates, item exposure rate, item pool utilization, and item overlap. The study found that all test designs produced very similar results. Although there were some variations among the eight test structures in the ability estimates, results indicate that the performance overall of these eight test structures in achieving measurement precision did not substantially deviate from one another with regard to total test length and routing test length. However, results from the present study suggest that routing test length does have a significant effect on the number of non-convergent cases in MST tests. Short routing tests tended to result in more non-convergent cases, and the presence of fewer stage tests yielded more of such cases than structures with more stages. Overall, unlike previous findings, the results of the present study indicate that the MST test structure is less likely to be a factor impacting ability estimation when polytomously-scored items are used, based on GPCM. / text

Electric energy constitutes one of the most crucial elements to almost every aspect of life of people. The modern electric power systems face several challenges such as efficiency, economics, sustainability, and reliability. Increase in electrical energy demand, distributed generations, integration of uncertain renewable energy resources, and demand side management are among the main underlying reasons of such growing complexity. Additionally, the elements of power systems are often vulnerable to failures because of many reasons, such as system limits, weak conditions, unexpected events, hidden failures, human errors, terrorist attacks, and natural disasters. One common factor complicating the operation of electrical power systems is the underlying uncertainties from the demands, supplies and failures of system components. Stochastic programming provides a mathematical framework for decision making under uncertainty. It enables a decision maker to incorporate some knowledge of the intrinsic uncertainty into the decision making process. In this dissertation, we focus on application of two-stage and multistage stochastic programming approaches to electric energy systems modeling and optimization. Particularly, we develop models and algorithms addressing the sustainability and reliability issues in power systems. First, we consider how to improve the reliability of power systems under severe failures or contingencies prone to cascading blackouts by so called islanding operations. We present a two-stage stochastic mixed-integer model to find optimal islanding operations as a powerful preventive action against cascading failures in case of extreme contingencies. Further, we study the properties of this problem and propose efficient solution methods to solve this problem for large-scale power systems. We present the numerical results showing the effectiveness of the model and investigate the performance of the solution methods. Next, we address the sustainability issue considering the integration of renewable energy resources into production planning of energy-intensive manufacturing industries. Recently, a growing number of manufacturing companies are considering renewable energies to meet their energy requirements to move towards green manufacturing as well as decreasing their energy costs. However, the intermittent nature of renewable energies imposes several difficulties in long term planning of how to efficiently exploit renewables. In this study, we propose a scheme for manufacturing companies to use onsite and grid renewable energies provided by their own investments and energy utilities as well as conventional grid energy to satisfy their energy requirements. We propose a multistage stochastic programming model and study an efficient solution method to solve this problem. We examine the proposed framework on a test case simulated based on a real-world semiconductor company. Moreover, we evaluate long-term profitability of such scheme via so called value of multistage stochastic programming.