This dissertation, which consists of four parts, is to (i) present a mixed integer programming model for the strategic design of an assembly system in the international business environment established by the North American Free Trade Agreement (NAFTA) with the focus on modeling the material flow network with assembly operations, (ii) compare different decomposition schemes and acceleration techniques to devise an effective branch-and-price solution approach, (iii) introduce a generalization of Dantzig-Wolf Decomposition (DWD), and (iv) propose a combination of dual-ascent and primal drop heuristics. The model deals with a broad set of design issues (bill-of-materials restrictions, international financial considerations, and material flows through the entire supply chain) using effective modeling devices. The first part especially focuses on modeling material flows in such an assembly system. The second part is to study several schemes for applying DWD to the productionassembly- distribution system design problem (PADSDP). Each scheme exploits selected embedded structures. The research objective is to enhance the rate of DWD convergence in application to PADSDP through formulating a rationale for decomposition by analyzing potential schemes, adopting acceleration techniques, and assessing the impacts of schemes and techniques computationally. Test results provide insights that may be relevant to other applications of DWD. The third part proposes a generalization of column generation, reformulating the master problem with fewer variables at the expense of adding more constraints; the subproblem structure does not change. It shows both analytically and computationally that the reformulation promotes faster convergence to an optimal solution in application to a linear program and to the relaxation of an integer program at each node in the branchand- bound tree. Further, it shows that this reformulation subsumes and generalizes prior approaches that have been shown to improve the rate of convergence in special cases. The last part proposes two dual-ascent algorithms and uses each in combination with a primal drop heuristic to solve the uncapacitated PADSDP, which is formulated as a mixed integer program. Computational results indicate that one combined heuristic finds solutions within 0.15% of optimality in most cases and within reasonable time, an efficacy suiting it well for actual large-scale applications.

Techn. Hochsch., Diss., 2002--Aachen.

Les applications récentes telles que les bases de données forestières impliquent des observations de données spatiales associées à l'observation de nombreuses covariables spatiales. Nous considérons dans cette thèse le problème de l'estimation d'une forme paramétrique de la fonction d'intensité dans un tel contexte. Cette thèse développe les procédures de sélection des variables et donne des garanties quant à leur validité. En particulier, nous proposons deux approches différentes pour la sélection de variables : les méthodes de type lasso et les procédures de type Sélecteur de Dantzig. Pour les méthodes envisageant les techniques de type lasso, nous dérivons les propriétés asymptotiques des estimations obtenues par les fontions d'estimation dérivées par les vraisemblances de la Poisson et de la régression logistique pénalisées par une grande classe de pénalités. Nous prouvons que les estimations obtenues par de ces procédures satisfont la consistance, sparsité et la normalité asymptotique. Pour la partie sélecteur de Dantzig, nous développons une version modifiée du sélecteur de Dantzig, que nous appelons le sélecteur Dantzig linéaire adaptatif (ALDS), pour obtenir les estimations d'intensité. Plus précisément, les estimations ALDS sont définies comme la solution à un problème d'optimisation qui minimise la somme des coefficients des estimations soumises à une approximation linéaire du vecteur score comme une contrainte. Nous constatons que les estimations obtenues par de ces méthodes ont des propriétés asymptotiques semblables à celles proposées précédemment à l'aide de méthode régularisation du lasso adaptatif. Nous étudions les aspects computationnels des méthodes développées en utilisant les procédures de type lasso et de type Sélector Dantzig. Nous établissons des liens entre l'estimation de l'intensité des processus ponctuels spatiaux et les modèles linéaires généralisés (GLM), donc nous n'avons qu'à traiter les procédures de la sélection des variables pour les GLM. Ainsi, des procédures de calcul plus faciles sont implémentées et un algorithme informatique rapide est proposé. Des études de simulation sont menées pour évaluer les performances des échantillons finis des estimations de chacune des deux approches proposées. Enfin, nos méthodes sont appliquées pour modéliser les emplacements spatiaux, une espèce d'arbre dans la forêt observée avec un grand nombre de facteurs environnementaux. / Recent applications such as forestry datasets involve the observations of spatial point pattern data combined with the observation of many spatial covariates. We consider in this thesis the problem of estimating a parametric form of the intensity function in such a context. This thesis develops feature selection procedures and gives some guarantees on their validity. In particular, we propose two different feature selection approaches: the lasso-type methods and the Dantzig selector-type procedures. For the methods considering lasso-type techniques, we derive asymptotic properties of the estimates obtained from estimating functions derived from Poisson and logistic regression likelihoods penalized by a large class of penalties. We prove that the estimates obtained from such procedures satisfy consistency, sparsity, and asymptotic normality. For the Dantzig selector part, we develop a modified version of the Dantzig selector, which we call the adaptive linearized Dantzig selector (ALDS), to obtain the intensity estimates. More precisely, the ALDS estimates are defined as the solution to an optimization problem which minimizes the sum of coefficients of the estimates subject to linear approximation of the score vector as a constraint. We find that the estimates obtained from such methods have asymptotic properties similar to the ones proposed previously using an adaptive lasso regularization term. We investigate the computational aspects of the methods developped using either lasso-type procedures or the Dantzig selector-type approaches. We make links between spatial point processes intensity estimation and generalized linear models (GLMs), so we only have to deal with feature selection procedures for GLMs. Thus, easier computational procedures are implemented and computationally fast algorithm are proposed. Simulation experiments are conducted to highlight the finite sample performances of the estimates from each of two proposed approaches. Finally, our methods are applied to model the spatial locations a species of tree in the forest observed with a large number of environmental factors.

Dans ce document, nous étudions deux problèmes de sectorisation et proposons plusieurs méthodes de résolution exactes basées sur la décomposition de Dantzig-Wolfe et la génération de colonnes. Nous proposons deux modélisations en fonction de la manière d’appréhender l’objectif du problème qui consiste à obtenir des secteurs compacts. Pour chacune des modélisations, nous comparons des approches de résolution exactes basées sur des formulations compactes ou sur des formulations étendues obtenues par la décomposition de Dantzig-Wolfe. Le premier type de modèles proposé définit la fonction objectif à la manière d’un problème de p-median. Concernant les méthodes de résolution pour ce type de modèle, l’accent est mis sur l’accélération de la convergence de l’algorithme de génération de colonnes en mettant en place des techniques d’agrégation de contraintes afin de réduire la dégénérescence de l’algorithme du simplexe. Les expérimentations numériques montrent que la méthode d’agrégation de contraintes proposée permet effectivement de réduire le nombre d’itérations dégénérées. Cependant, elle ne suffit pas à accélérer l’algorithme de branch-and-price. Le choix d’utilisation de la formulation compacte ou de la formulation étendue dépend du type d’instances résolu. Le second type de modèles formule l’objectif d’une manière assez proche de celui des problèmes de p-centre. L’utilisation d’un tel objectif complexifie la résolution des sous-problèmes de génération de colonnes. L’accent est donc mis sur la conception d’algorithmes de branch-and-bound et de programmation dynamique pour les résoudre efficacement. Les expériences montrent que l’algorithme de branch-and-price surpasse les approches de résolution utilisant une formulation compacte du problème. / In this document, we study two districting problems and propose several exact methods, based on Dantzig-Wolfe decomposition and column generation, to solve them. For each model, we compare exact approaches based either on compact formulations or on extended formulations obtained using Dantzig-Wolfe decomposition. The first type of model that we propose defines the objective function in a p-median problem fashion. Regarding the methods used to solve that kind of model, we emphasize accelerating the convergence of the column generation algorithm by designing constraint aggregation techniques in order to reduce the degeneracy in the simplex algorithm. Numerical experiments show that this constraint aggregation method indeed reduces the proportion of degenerated iterations. However, it is not enough to speed up the branch-and-price algorithm. Choosing to tackle the problem through either a compact formulation or an extended formulation depends on the structure of the instances to solve. The second type of model formulates the objective function in a way quite similar to that of p-centre problems. Using such an objective function induces complex column generation subproblems. We focus on designing branch-and-bound and dynamic programming algorithms in order to solve them efficiently. Experiments show that the branch-and-price approach surpasses any proposed method based on compact formulations of the problem.

The goal of this thesis is to demonstrate practical application of sparse data representation in the processing of sparse signals. For solving several example problems - denoising, dequantization, and sparse signal decomposition - convex optimization was used. The solutions were implemented in the Matlab environment. For each of the problems, there are two solutions - one for one-dimensional, and one for two-dimensional signal.

O problema de dimensionamento de lotes com restrições de capacidade (CLSP) consiste em determinar um plano de produção que satisfaça a demanda requerida, respeitando as limitações de capacidade, com o menor custo possível, ou seja, minimizando os custos de produção, estocagem e preparação de máquina. Encontrar uma solução factível para o CLSP, considerando tempo de preparação de máquina, é NP-completo. Nesta dissertação, para a resolução do CLSP, utiliza-se a decomposição de Dantzig-Wolfe e o procedimento de geração de colunas, encontrando bons limitantes inferiores. Duas diferentes estratégias de decomposição são exploradas, decomposição por itens e períodos. Para a obtenção de uma solução inteira para o problema (limitante superior) foram exploradas heurísticas lagrangianas, onde a solução inicial para as heurísticas provém da geração de colunas. Os limitantes obtidos podem ser utilizados em métodos exatos, como por exemplo, em algoritmos do tipo branch-and-price. Experimentos computacionais, baseados em exemplares gerados aleatoriamente, foram realizados e os resultados analisados, as variações dos parâmetros das instâncias foram sugeridas na literatura / The Capacitated Lot Sizing Problem (CLSP) consists in determining a production plan such that all demands are met and the total costs of production, inventory and setup are minimized. Since the problem to find a feasible solution to the CLSP with setup times is NP-complete, large problem instances have been solved by heuristic methods. In this dissertation, we are particularly concerned in using the methodology of Dantzig-Wolfe decomposition and column generation to generate good bounds to the CLSP with setup times and costs. Here, we analyse two types of decomposition which are based on items and time periods (lower bound) and some lagrangian-based heuristics (upper bound). Numerical results based on randomly generated intances suggest that highquality lower bounds are obtained by column generation algorithms, such as well as upper bounds by heuristics. These bounds are useful in exact solution methods, such as branch-and-price algorithms

O problema de dimensionamento de lotes com restrições de capacidade (CLSP) consiste em determinar um plano de produção que satisfaça a demanda requerida, respeitando as limitações de capacidade, com o menor custo possível, ou seja, minimizando os custos de produção, estocagem e preparação de máquina. Encontrar uma solução factível para o CLSP, considerando tempo de preparação de máquina, é NP-completo. Nesta dissertação, para a resolução do CLSP, utiliza-se a decomposição de Dantzig-Wolfe e o procedimento de geração de colunas, encontrando bons limitantes inferiores. Duas diferentes estratégias de decomposição são exploradas, decomposição por itens e períodos. Para a obtenção de uma solução inteira para o problema (limitante superior) foram exploradas heurísticas lagrangianas, onde a solução inicial para as heurísticas provém da geração de colunas. Os limitantes obtidos podem ser utilizados em métodos exatos, como por exemplo, em algoritmos do tipo branch-and-price. Experimentos computacionais, baseados em exemplares gerados aleatoriamente, foram realizados e os resultados analisados, as variações dos parâmetros das instâncias foram sugeridas na literatura / The Capacitated Lot Sizing Problem (CLSP) consists in determining a production plan such that all demands are met and the total costs of production, inventory and setup are minimized. Since the problem to find a feasible solution to the CLSP with setup times is NP-complete, large problem instances have been solved by heuristic methods. In this dissertation, we are particularly concerned in using the methodology of Dantzig-Wolfe decomposition and column generation to generate good bounds to the CLSP with setup times and costs. Here, we analyse two types of decomposition which are based on items and time periods (lower bound) and some lagrangian-based heuristics (upper bound). Numerical results based on randomly generated intances suggest that highquality lower bounds are obtained by column generation algorithms, such as well as upper bounds by heuristics. These bounds are useful in exact solution methods, such as branch-and-price algorithms

abstract: No-confounding designs (NC) in 16 runs for 6, 7, and 8 factors are non-regular fractional factorial designs that have been suggested as attractive alternatives to the regular minimum aberration resolution IV designs because they do not completely confound any two-factor interactions with each other. These designs allow for potential estimation of main effects and a few two-factor interactions without the need for follow-up experimentation. Analysis methods for non-regular designs is an area of ongoing research, because standard variable selection techniques such as stepwise regression may not always be the best approach. The current work investigates the use of the Dantzig selector for analyzing no-confounding designs. Through a series of examples it shows that this technique is very effective for identifying the set of active factors in no-confounding designs when there are three of four active main effects and up to two active two-factor interactions. To evaluate the performance of Dantzig selector, a simulation study was conducted and the results based on the percentage of type II errors are analyzed. Also, another alternative for 6 factor NC design, called the Alternate No-confounding design in six factors is introduced in this study. The performance of this Alternate NC design in 6 factors is then evaluated by using Dantzig selector as an analysis method. Lastly, a section is dedicated to comparing the performance of NC-6 and Alternate NC-6 designs. / Dissertation/Thesis / Masters Thesis Industrial Engineering 2014

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Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-09-26T19:15:52Z No. of bitstreams: 1 DissCDAC.pdf: 10114021 bytes, checksum: b3e4f52846924539caadab8587fe2250 (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-26T18:36:20Z (GMT) No. of bitstreams: 1 DissCDAC.pdf: 10114021 bytes, checksum: b3e4f52846924539caadab8587fe2250 (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-26T18:36:39Z (GMT) No. of bitstreams: 1 DissCDAC.pdf: 10114021 bytes, checksum: b3e4f52846924539caadab8587fe2250 (MD5) / Made available in DSpace on 2018-01-26T18:42:45Z (GMT). No. of bitstreams: 1 DissCDAC.pdf: 10114021 bytes, checksum: b3e4f52846924539caadab8587fe2250 (MD5) Previous issue date: 2017-03-10 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / This work aims at treating the Dynamic Vehicle Allocation Problem (DVAP) in the context of the Brazilian Freight Transportation system. The problem consists of allocating empty vehicles to different terminals so as to attend the demand of freight transport during a predetermined planning horizon while maximizing the profit from these services. These type of decisions arise in customized freight transport services and in between-terminals operations of consolidation freight services. Given the size of the resulting models of real life problems confronted by third party logistics operators are large for using exact solution methods, heuristic methods have been used for giving good quality solution at the expense of optimality guarantee. In this context, the objective of this work is to contribute with solution methods that provide optimality guarantee or quality solution certificates for treating large-scale problems in reasonable computational times. The methods utilized are lagrangean relaxation, using subgradient optimization, and DantzigWolfe decomposition together with a lagrangian heuristic and factibilization method, respectively. Computational experiments are presented and analyzed for randomly generated instances and real-world instances from a brasilian freight operator. The latter method shows great potential for treating large-scale problems. / Este trabalho aborda o problema de Alocação Dinâmica de Veículos (PADV) no contexto de Transporte Rodoviário de Carga. O problema envolve alocar veículos de carga para atender a demanda de transporte de carga prevista entre terminais durante um horizonte de tempo multiperíodos e finito. O objetivo e maximizar o lucro gerado pelos serviços completados. Este tipo de decisões surge nos serviços de transporte de carga de lotação e na parcela de transporte de transferência dos serviços de transporte de carga consolidada. Dado que o tamanho dos problemas que enfrentam as transportadoras logísticas sÃo consideravelmente grandes parase resolver com métodos exatos em tempos computacionais aceitáveis, tem-se utilizado métodos heurísticos para dar boas soluções sem garantia de otimalidade mas em tempos toleráveis a estes problemas. Neste contexto, pretende-se contribuir com métodos de solução que proporcionem garantia de otimalidade e/ou boas soluções aproximadas, acompanhadas de certificados de otimalidade ou de qualidade de solução, para tratar problemas de porte em tempos razoáveis. Os métodos propostos estao baseados em relaxação lagrangiana, utilizando o método de otimização do subgradiente, e na decomposto de Dantzig Wolfe, utilizando a técnica de geração de colunas, além de heurísticas lagrangianas e de factibilização acopladas nestes métodos. Experimentos computacionais usando instâncias geradas aleatoriamente e baseados em dados reais de transportadoras brasileiras sao apresentados e analisados, para as duas abordagens, mostrando seus potenciais de aplicação pratica, principalmente para problemas de grande porte.