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In this thesis we consider two research problems, namely, (i) language constructs for modelling stochastic programming (SP) problems and (ii) solution methods for processing instances of different classes of SP problems. We first describe a new design of an SP modelling system which provides greater extensibility and reuse. We implement this enhanced system and develop solver connections. We also investigate in detail the following important classes of SP problems: singlestage SP with risk constraints, two-stage linear and stochastic integer programming problems. We report improvements to solution methods for single-stage problems with second-order stochastic dominance constraints and two-stage SP problems. In both cases we use the level method as a regularisation mechanism. We also develop novel heuristic methods for stochastic integer programming based on variable neighbourhood search. We describe an algorithmic framework for implementing decomposition methods such as the L-shaped method within our SP solver system. Based on this framework we implement a number of established solution algorithms as well as a new regularisation method for stochastic linear programming. We compare the performance of these methods and their scale-up properties on an extensive set of benchmark problems. We also implement several solution methods for stochastic integer programming and report a computational study comparing their performance. The three solution methods, (a) processing of a single-stage problem with second-order stochastic dominance constraints, (b) regularisation by the level method for two-stage SP and (c) method for solving integer SP problems, are novel approaches and each of these makes a contribution to knowledge.

My main research topic is about developing new domain decomposition algorithms for the solution of systems of partial differential equations. This was mainly applied to fluid dynamics problems (as compressible Euler or Stokes equations) and electromagnetics (time-harmonic and time-domain first order system of Maxwell's equations). Since the solution of large linear systems is strongly related to the application of a discretization method, I was also interested in developing and analyzing the application of high order methods (such as Discontinuos Galerkin methods) to Maxwell's equations (sometimes in conjuction with time-discretization schemes in the case of time-domain problems). As an active member of NACHOS pro ject (besides my main afiliation as an assistant professor at University of Nice), I had the opportunity to develop certain directions in my research, by interacting with permanent et non-permanent members (Post-doctoral researchers) or participating to supervision of PhD Students. This is strongly refflected in a part of my scientific contributions so far. This memoir is composed of three parts: the first is about the application of Schwarz methods to fluid dynamics problems; the second about the high order methods for the Maxwell's equations and the last about the domain decomposition algorithms for wave propagation problems.

Decomposition methods based on the hierarchical partitioning of the state space of queueing network models offer powerful evaluation tools for the performance analysis of computer systems and communication networks. These methods being conventionally implemented capture the exact solution of separable queueing network models but their credibility differs when applied to general queueing networks. This thesis provides a universal information theoretic framework for the implementation of hierarchical decomposition schemes, based on the principle of minimum relative entropy given fully decomposable subset and aggregate utilization, mean queue length and flow-balance constraints. This principle is used, in conjuction with asymptotic connections to infinite capacity queues, to derive new closed form approximations for the conditional and marginal state probabilities of general queueing network models. The minimum relative entropy solutions are implemented iteratively at each decomposition level involving the generalized exponential (GE) distributional model in approximating the general service and asymptotic flow processes in the network. It is shown that the minimum relative entropy joint state probability, subject to mean queue length and flow-balance constraints, is identical to the exact product-form solution obtained as if the network was separable. An investigation into the effect of different couplings of the resource units on the relative accuracy of the approximation is carried out, based on an extensive experimentation. The credibility of the method is demonstrated with some illustrative examples involving first-come-first-served general queueing networks with single and multiple servers and favourable comparisons against exact solutions and other approximations are made.

abstract: Agricultural supply chains are complex systems which pose significant challenges beyond those of traditional supply chains. These challenges include: long lead times, stochastic yields, short shelf lives and a highly distributed supply base. This complexity makes coordination critical to prevent food waste and other inefficiencies. Yet, supply chains of fresh produce suffer from high levels of food waste; moreover, their high fragmentation places a great economic burden on small and medium sized farms. This research develops planning tools tailored to the production/consolidation level in the supply chain, taking the perspective of an agricultural cooperative—a business model which presents unique coordination challenges. These institutions are prone to internal conflict brought about by strategic behavior, internal competition and the distributed nature of production information, which members keep private. A mechanism is designed to coordinate agricultural production in a distributed manner with asymmetrically distributed information. Coordination is achieved by varying the prices of goods in an auction like format and allowing participants to choose their supply quantities; the auction terminates when production commitments match desired supply. In order to prevent participants from misrepresenting their information, strategic bidding is formulated from the farmer’s perspective as an optimization problem; thereafter, optimal bidding strategies are formulated to refine the structure of the coordination mechanism in order to minimize the negative impact of strategic bidding. The coordination mechanism is shown to be robust against strategic behavior and to provide solutions with a small optimality gap. Additional information and managerial insights are obtained from bidding data collected throughout the mechanism. It is shown that, through hierarchical clustering, farmers can be effectively classified according to their cost structures. Finally, considerations of stochastic yields as they pertain to coordination are addressed. Here, the farmer’s decision of how much to plant in order to meet contracted supply is modeled as a newsvendor with stochastic yields; furthermore, options contracts are made available to the farmer as tools for enhancing coordination. It is shown that the use of option contracts reduces the gap between expected harvest quantities and the contracted supply, thus facilitating coordination. / Dissertation/Thesis / Dissertation Appendices A-M / Doctoral Dissertation Industrial Engineering 2015

Os anos noventa no Brasil foram marcados pela simultânea queda do trabalho infantil e aumento da freqüência escolar. Este estudo se propôs a investigar as causas desses fenômenos. Mais especificamente, buscou-se testar a importância relativa de três hipóteses para a explicação conjunta dos movimentos, quais sejam: mudanças no background familiar, em particular, o aumento generalizado da escolaridade dos pais das crianças e adolescentes; a deterioração do mercado de trabalho infantil e mudanças em variáveis educacionais. Para tanto, foram utilizados dados oriundos da Pesquisa Mensal do Emprego (PME) do Instituto Brasileiro de Geografia e Estatística (IBGE), que se caracterizam por apresentar a estrutura de um painel rotativo. O desenho da pesquisa é tal que uma mesma família é entrevistada em dois anos consecutivos. Para modelar o problema de decisão das famílias no tocante à alocação do tempo das crianças entre a escola, o trabalho (ou ambos) e o lazer (não trabalho e não escola), foi utilizado o modelo Logit Multinomial. Através da aplicação de uma modificação da técnica de Oaxaca-Blinder, verificou-se que as mudanças na probabilidade de uma criança (ou adolescente) trabalhar ou freqüentar a escola (ou ainda não estudar e não trabalhar) estão mais associadas a mudanças nas variáveis explicativas (características observáveis) do que nos coeficientes estimados (características não observáveis). Além disso, o fenômeno parece estar mais associado a mudanças em variáveis educacionais, como o aumento da escolaridade dos professores do ensino público, e mudanças no background familiar. Ainda mais importantes, no entanto, parecem ser as mudanças na distribuição da alocação do tempo da criança na 1ª entrevista (primeiro ano). Argumentou-se que, ao se estar controlando pelo estado de aprovação/reprovação e distorção idade/série, o resultado poderia estar associado a políticas educacionais de combate à reprovação e evasão escolar (assumindo que a queda nas taxas de reprovação foi resultado de tais políticas). / During the 1990s, child employment declined and school attendance increased sharply in Brazil. The aim of this study is to investigate the causes of this phenomenon, more specifically, to test the relative importance of three hypotheses: changes in the family background, in particular, the generalized raise in parent\'s schooling; the deterioration of child labor market and changes in educational variables. The analysis exploits Brazil\'s Monthly Employment Survey (PME) from IBGE (Instituto Brasileiro de Geografia e Estatística). The PME has a longitudinal design that allows us to observe the same family during two consecutive years. To model the problem of time allocation decisions between school, work (or both) and leisure (none), we used the Multinomial Logit Model. Through an extension of Oaxaca-Blinder technique, we verified that the changes in the probability of a child to work or to attend school are more associated to changes in the explanatory variables (observable characteristics) than to changes in the estimated coefficients (non-observable characteristics). Besides, the phenomenon seems to be more associated to changes in educational variables, such as the raise of the average schooling of public school teachers, and changes in the family background. In addition, the change in the distribution of children\'s time allocation in the 1st interview (first year) seems to be even more important to explain the decline in child labor and the increase in school attendance in Brazil. As we are controlling throughout the fact that the child failed or was approved in advancing school and for age-grade distortion, we argue that this result could be associated to educational policies that try combating school drop-out (assuming that the decline in the repetition rates resulted form that kind of policies).

Abstract Several numerical methods and algorithms, for solving the mathematical model of a continuous casting process, are presented, and theoretically studied, in this work. The numerical algorithms can be divided in to three different groups: the Schwarz type overlapping methods, the nonoverlapping Splitting iterative methods, and the Predictor-Corrector type nonoverlapping methods. These algorithms are all so-called parallel algorithms i.e., they are highly suitable for parallel computers. Multiplicative, additive Schwarz alternating method and two asynchronous domain decomposition methods, which appear to be a two-stage Schwarz alternating algorithms, are theoretically and numerically studied. Unique solvability of the fully implicit and semi-implicit finite difference schemes as well as monotone dependence of the solution on the right-hand side are proved. Geometric rate of convergence for the iterative methods is investigated. Splitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied. Convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analyzed in the case when both operators are linear, self-adjoint and positive definite. Several new finite-difference schemes for a nonlinear convection-diffusion problem are constructed and numerically studied. These schemes are constructed on the basis of non-overlapping domain decomposition and predictor-corrector approach. Different non-overlapping decompositions of a domain, with cross-points and angles, schemes with grid refinement in time in some subdomains, are used. All proposed algorithms are extensively numerically tested and are founded stable and accurate under natural assumptions for time and space grid steps. The advantages and disadvantages of the numerical methods are clearly seen in the numerical examples. All of the algorithms presented are quite easy and straight forward, from an implementation point of view. The speedups show that splitting iterative method can be parallelized better than multiplicative or additive Schwarz alternating method. The numerical examples show that the multidecomposition method is a very effective numerical method for solving the continuous casting problem. The idea of dividing the subdomains to smaller subdomains seems to be very beneficial and profitable. The advantages of multidecomposition methods over other methods is obvious. Multidecomposition methods are extremely quick, while being just as accurate as other methods. The numerical results for one processor seem to be very promising.

Os anos noventa no Brasil foram marcados pela simultânea queda do trabalho infantil e aumento da freqüência escolar. Este estudo se propôs a investigar as causas desses fenômenos. Mais especificamente, buscou-se testar a importância relativa de três hipóteses para a explicação conjunta dos movimentos, quais sejam: mudanças no background familiar, em particular, o aumento generalizado da escolaridade dos pais das crianças e adolescentes; a deterioração do mercado de trabalho infantil e mudanças em variáveis educacionais. Para tanto, foram utilizados dados oriundos da Pesquisa Mensal do Emprego (PME) do Instituto Brasileiro de Geografia e Estatística (IBGE), que se caracterizam por apresentar a estrutura de um painel rotativo. O desenho da pesquisa é tal que uma mesma família é entrevistada em dois anos consecutivos. Para modelar o problema de decisão das famílias no tocante à alocação do tempo das crianças entre a escola, o trabalho (ou ambos) e o lazer (não trabalho e não escola), foi utilizado o modelo Logit Multinomial. Através da aplicação de uma modificação da técnica de Oaxaca-Blinder, verificou-se que as mudanças na probabilidade de uma criança (ou adolescente) trabalhar ou freqüentar a escola (ou ainda não estudar e não trabalhar) estão mais associadas a mudanças nas variáveis explicativas (características observáveis) do que nos coeficientes estimados (características não observáveis). Além disso, o fenômeno parece estar mais associado a mudanças em variáveis educacionais, como o aumento da escolaridade dos professores do ensino público, e mudanças no background familiar. Ainda mais importantes, no entanto, parecem ser as mudanças na distribuição da alocação do tempo da criança na 1ª entrevista (primeiro ano). Argumentou-se que, ao se estar controlando pelo estado de aprovação/reprovação e distorção idade/série, o resultado poderia estar associado a políticas educacionais de combate à reprovação e evasão escolar (assumindo que a queda nas taxas de reprovação foi resultado de tais políticas). / During the 1990s, child employment declined and school attendance increased sharply in Brazil. The aim of this study is to investigate the causes of this phenomenon, more specifically, to test the relative importance of three hypotheses: changes in the family background, in particular, the generalized raise in parent\'s schooling; the deterioration of child labor market and changes in educational variables. The analysis exploits Brazil\'s Monthly Employment Survey (PME) from IBGE (Instituto Brasileiro de Geografia e Estatística). The PME has a longitudinal design that allows us to observe the same family during two consecutive years. To model the problem of time allocation decisions between school, work (or both) and leisure (none), we used the Multinomial Logit Model. Through an extension of Oaxaca-Blinder technique, we verified that the changes in the probability of a child to work or to attend school are more associated to changes in the explanatory variables (observable characteristics) than to changes in the estimated coefficients (non-observable characteristics). Besides, the phenomenon seems to be more associated to changes in educational variables, such as the raise of the average schooling of public school teachers, and changes in the family background. In addition, the change in the distribution of children\'s time allocation in the 1st interview (first year) seems to be even more important to explain the decline in child labor and the increase in school attendance in Brazil. As we are controlling throughout the fact that the child failed or was approved in advancing school and for age-grade distortion, we argue that this result could be associated to educational policies that try combating school drop-out (assuming that the decline in the repetition rates resulted form that kind of policies).

Ces travaux de recherche ont pour objectif de contribuer au développement et à l'exploitation d'outils de vérification des problèmes de mécanique linéaires dans le cadre des méthodes de décomposition de domaine sans recouvrement. Les apports de cette thèse sont multiples : * Nous proposons d'améliorer la qualité des champs statiquement admissibles nécessaires à l'évaluation de l'estimateur par une nouvelle méthodologie de reconstruction des contraintes en séquentiel et par des optimisations du calcul de l'intereffort en cadre sous-structuré.* Nous démontrons des bornes inférieures et supérieures de l'erreur séparant l'erreur algébrique (due au solveur itératif) de l'erreur de discrétisation (due à la méthode des éléments finis) tant pour une mesure globale que pour une quantité d'intérêt. Cette séparation permet la définition d'un critère d'arrêt objectif pour le solveur itératif.* Nous exploitons les informations fournies par l'estimateur et les espaces de Krylov générés pour mettre en place une stratégie auto-adaptative de calcul consistant en une chaîne de résolution mettant à profit remaillage adaptatif et recyclage des directions de recherche. Nous mettons en application le pilotage du solveur par un objectif de précision sur des exemples mécaniques en deux dimensions. / This research work aims at contributing to the development of verification tools in linear mechanical problems within the framework of non-overlapping domain decomposition methods.* We propose to improve the quality of the statically admissible stress field required for the computation of the error estimator thanks to a new methodology of stress reconstruction in sequential context and thanks to optimizations of the computations of nodal reactions in substructured context.* We prove guaranteed upper and lower bounds of the error that separates the algebraic error (due to the iterative solver) from the discretization error (due to the finite element method) for both global error measure mentand goal-oriented error estimation. It enables the definition of a new stopping criterion for the iterative solver which avoids over-resolution.* We benefit the information provided by the error estimator and the Krylov subspaces built during the resolution to set an auto-adaptive strategy. This strategy consists in sequel of resolutions and takes advantage of adaptive remeshing and recycling of search directions .We apply the steering of the iterative solver by objective of precision on two-dimensional mechanical examples.

Decomposition methods based on the hierarchical partitioning of the state space of queueing network models offer powerful evaluation tools for the performance analysis of computer systems and communication networks. These methods being conventionally implemented capture the exact solution of separable queueing network models but their credibility differs when applied to general queueing networks. This thesis provides a universal information theoretic framework for the implementation of hierarchical decomposition schemes, based on the principle of minimum relative entropy given fully decomposable subset and aggregate utilization, mean queue length and flow-balance constraints. This principle is used, in conjuction with asymptotic connections to infinite capacity queues, to derive new closed form approximations for the conditional and marginal state probabilities of general queueing network models. The minimum relative entropy solutions are implemented iteratively at each decomposition level involving the generalized exponential (GE) distributional model in approximating the general service and asymptotic flow processes in the network. It is shown that the minimum relative entropy joint state probability, subject to mean queue length and flow-balance constraints, is identical to the exact product-form solution obtained as if the network was separable. An investigation into the effect of different couplings of the resource units on the relative accuracy of the approximation is carried out, based on an extensive experimentation. The credibility of the method is demonstrated with some illustrative examples involving first-come-first-served general queueing networks with single and multiple servers and favourable comparisons against exact solutions and other approximations are made.