FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / Neste trabalho avaliamos mÃtodos heurÃsticos e exatos para o Problema de Particionamento de Conjuntos (PPC). Realizamos testes computacionais com heurÃsticas lagrangeanas baseadas em algoritmos gulosos, busca tabu e mÃtodo de otimizaÃÃo pelo subgradiente. Os resultados obtidos, comparados com os da literatura, comprovam a eficiÃncia de nossas heurÃsticas na obtenÃÃo de limites inferiores e superiores de boa qualidade, em tempo computacional razoÃvel, para instÃncias da literatura. Utilizamos um esquema de Branch and Bound para tentar resolver instÃncias do PPC ÃÂotimalidade e para comprovar a qualidade dos resultados alcanÃados por nossas heurÃsticas. / In this work we evaluate both exact and heuristic methods for the set partitioning problem (SPP). These heuristics are based on greedy algorithms, tabu search and subgradient optimization. Computational experiments performed on benchmark instances of the problem indicate that our heuristics are competitive with existing ones from the literature in obtaining both lower and upper bounds of good quality in reasonable execution time. We use a Branch and Bound algorithm that allows to prove optimality of solutions obtained by our heuristics for a large set of benchmark instances of the SPP. Thus, we show that our heuristics are efficient in obtaining feasible solutions of good quality for this problem.

Nos Estados republicanos modernos, o sistema de freios e contrapesos é um dos modelos institucionais responsável por assegurar o equilíbrio entre os Poderes e prevenir abusos por parte dos governantes. Dois questionamentos podem ser encontrados na literatura brasileira sobre o tema e fundamentam esta Dissertação: um geral sobre o suposto poder excessivo que o nosso sistema político confere ao Poder Executivo e outro, específico, de que nesse contexto, o veto teria um papel central na supremacia do presidente da república sobre o Congresso Nacional no âmbito do processo legislativo. Partindo dessas premissas, a pesquisa avalia se essas características estão condizentes com as expectativas e o desenho institucional proposto para o Estado brasileiro pela Assembleia Nacional Constituinte ANC de 1987. Com base nos anais da ANC e em referências históricas, conclui-se que, ao menos no tocante ao instituto do veto presidencial, o modelo de preponderância do Poder Executivo observado no processo legislativo decorreu de uma opção deliberada e reafirmada pela elite política em 1988, quando da promulgação da Constituição. / In modern republican states, the system of checks and balances is one of the institutional models responsible for ensuring the balance between powers and preventing abuses by rulers. Two issues can be found in the Brazilian academic literature on the matter that underlie this Dissertation: one concerning the alleged excessive power that our political system grant to the executive branch, and another one more specific that, in this context, the veto would have a main role in the supremacy of the President of the Republic over Congress in the legislative process. Beginning with these assumptions, this research evaluates whether these characteristics are consistent with the expectations and the institutional design proposed for the Brazilian State by the National Constituent Assembly (ANC) of 1987. Based on the ANC records and historical references, it concluded that, at least in regard to the presidential veto institute, the preponderance of the executive branch model observed in the legislative process derived from a deliberate and reaffirmed choice made by the political elite in 1988, at the promulgation of the Constitution.

Submitted by Miriam Lucas (miriam.lucas@unioeste.br) on 2018-02-22T16:42:27Z No. of bitstreams: 2 Miguel_Angel_Sanchez_Cuno_2016.pdf: 1159111 bytes, checksum: 5e8f5e6fcd310a19270e2164cb09c3e3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-02-22T16:42:27Z (GMT). No. of bitstreams: 2 Miguel_Angel_Sanchez_Cuno_2016.pdf: 1159111 bytes, checksum: 5e8f5e6fcd310a19270e2164cb09c3e3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-08-16 / Fundação Parque Tecnológico de Itaipu / This work presents the development of a Hybrid Algorithm to solve the problem of Planning the Expansion of Medium Voltage Overhead Networks. The Hybrid Algorithm uses two strategies to solve the problem. First uses a Constructive Heuristic Algorithm that tries to work with parameters instead of working with variables, with the objective of reducing the convergence time to the research process trying not to impair the quality of the solution. The second strategy is based in a Branch and Bound Algorithm, that uses the solution of the problem obtained as a starting point while the first strategy is running. Thus, this solution is used like incumbent in the second process. In this context the hybrid algorithm developed and implemented in this work, takes advantage of reducing the convergence time of the Constructive Heuristic Algorithm and the advantage of guarantee that the solution has the best quality, which are the solutions produced by algorithms type Branch and Bound. The Algorithm has been tested in three test systems, being established a plan to expand overhead medium voltage networks for each system. / Neste trabalho é apresentado um Algoritmo Híbrido para resolver o problema de Planejamento da Expansão de Redes Aéreas de Média Tensão. O Algoritmo Híbrido utiliza duas estratégias para resolver o problema. A primeira utiliza um Algoritmo Heurístico Construtivo que procura trabalhar com parâmetros ao invés de trabalhar com variáveis, com o objetivo de reduzir o tempo de convergência do processo de busca procurando não prejudicar a qualidade da solução. A segunda estratégia é baseada em um Algoritmo do tipo Branch and Bound, que utiliza a solução do problema obtida durante a execução da primeira estratégia como um ponto de partida. Assim, esta solução é usada como incumbente neste segundo processo. Neste contexto, o Algoritmo Híbrido desenvolvido e implementado neste trabalho, aproveita a vantagem de reduzir o tempo de convergência do Algoritmo Heurístico Construtivo e a vantagem de garantir que a solução seja a de melhor qualidade, que são as soluções produzidas por algoritmos do tipo Branch and Bound. O Algoritmo foi testado em três sistemas testes, sendo estabelecido um plano para a expansão de redes aéreas de média tensão para cada sistema

Linear optimization tools are used to solve many problems that arise in our day-to-day lives. The linear optimization models and methodologies help to find, for example, the best amount of ingredients in our food, the most suitable routes and timetables for the buses and trains we take, and the right way to invest our savings. We would cite many other situations that involves linear optimization, since a large number of companies around the world base their decisions in solutions which are provided by the linear optimization methodologies. In this thesis, we propose theoretical and computational developments to improve the performance of important linear optimization methods. Namely, we address simplex type methods, interior point methods, the column generation technique and the branch-and-price method. In simplex-type methods, we investigate a variant which exploits special features of problems which are formulated in the general form. We present a novel theoretical description of the method and propose how to efficiently implement this method in practice. Furthermore, we propose how to use the primal-dual interior point method to improve the column generation technique. This results in the primal-dual column generation method, which is more stable in practice and has a better overall performance in relation to other column generation strategies. The primal-dual interior point method also oers advantageous features which can be exploited in the context of the branch-and-price method. We show that these features improves the branching operation and the generation of columns and valid inequalities. For all the strategies which are proposed in this thesis, we present the results of computational experiments which involves publicly available, well-known instances from the literature. The results indicate that these strategies help to improve the performance of the linear optimization methodologies. In particular for a class of problems, namely the vehicle routing problem with time windows, the interior point branch-and-price method proposed in this study was up to 33 times faster than a state-of-the-art implementation available in the literature / Ferramentas de otimização linear são usadas para resolver diversos problemas do nosso dia-a- dia. Os modelos e as metodologias de otimização linear ajudam a obter, por exemplo, a melhor quantidade de ingredientes na nossa alimentação, os horários e as rotas de ônibus e trens que tomamos, e a maneira certa para investir nossas economias. Muitas outras situações que envolvem otimização linear poderiam ser aqui citadas, já que um grande número de empresas em todo o mundo baseia suas decisões em soluções obtidas pelos métodos de otimização linear. Nesta tese, são propostos desenvolvimentos teóricos e computacionais para melhorar o desempenho de métodos de otimização linear. Em particular, serão abordados métodos tipo simplex, métodos de pontos interiores, a técnica de geração de colunas e o método branch-and-price. Em métodos tipo simplex, é investigada uma variante que explora as características especiais de problemas formulados na forma geral. Uma nova descrição teórica do método é apresentada e, também, são propostas técnicas computacionais para a implementação eciente do método. Além disso, propõe-se como utilizar o método primal-dual de pontos interiores para melhorar a técnica de geração de colunas. Isto resulta no método primal-dual de geração de colunas, que é mais estável na prática e tem melhor desempenho geral em relação a outras estratégias de geração de colunas. O método primal-dual de pontos interiores também oferece características vantajosas que podem ser exploradas em conjunto com o método branch-and-price. De acordo com a investigação realizada, estas características melhoram a operação de ramificação e a geração de colunas e de desigualdades válidas. Para todas as estratégias propostas neste trabalho, são apresentados os resultados de experimentos computacionais envolvendo problemas de teste bem conhecidos e disponíveis publicamente. Os resultados indicam que as estratégias propostas ajudam a melhorar o desempenho das metodologias de otimização linear. Em particular para uma classe de problemas, o problema de roteamento de veículos com janelas de tempo, o método branch-and-price de pontos interiores proposto neste estudo foi até 33 vezes mais rápido que uma implementação estado-da-arte disponível na literatura

Die Tourenbildung beschäftigt sich mit der Konstruktion kostengünstiger Transportrouten zur Belieferung von Verbrauchern. Sie ist eine der weitreichensten Erfolgsgeschichten des Operations Research. Das starke Interesse an diesen Problemen durch Industrie und Forschung liegt zum einen am wirtschaftlichen Potenzial der Tourenbildung und -optimierung, zum anderen macht ihr Reichtum an Struktur sie zu einem faszinierenden Forschungsgebiet. In der vorliegenden Arbeit soll ein Überblick über einige, u. a. auch neuere mathematische Modell- und Lösungsansätze gegeben werden. Auf Grund der hohen Anzahl der Veröffentlichungen auf diesem Gebiet wird nicht zwingend ein Anspruch auf die vollständige Darlegung aller möglichen Problemstellungen im Zusammenhang mit dem TSP sowie dem VRP und deren Lösungsansätze erhoben. An den gegebenen Stellen wird statt dessen auf weiterführende Literatur verwiesen.

[pt] Os problemas de roteamento estão entre os problemas combinatórios mais difíceis de encontrar limites melhores do que os existentes ou de provar novas soluções ótimas. Nesta tese, são abordados o Capacitated Arc Routing Problem (CARP) e o Generalized Vehicle Routing Problem (GVRP). Em ambos os problemas, existe um conjunto de clientes os quais estão espalhados por um grafo dado, onde cada cliente possui uma demanda que deve ser atendida por exatamente um veículo de um conjunto de veículos idênticos. Os custos de travessia e o vértice de depósito são dados. O objetivo é encontrar rotas que coletam todas as demandas com custo mínimo, sem exceder a capacidade de nenhum veículo. No CARP, os clientes são um subconjunto de arestas, chamadas de arestas requireds, e para o GVRP, cada cliente é um subconjunto de vértices, chamado de grupo, onde cada grupo deve ser atendido visitando-se exatamente um vértice deste grupo. Além disto, vale notar que quando cada grupo possui apenas um vértice, o problema passa a ser o Capacitated Vehicle Routing Problem (CVRP). Primeiramente, são investigados métodos para melhorar os limites inferiores de instâncias de grande porte. É proposta a exploração da velocidade de uma heurística dual ascent para gerar cortes de capacidade. Em seguida, é apresentado um algoritmo de geração de colunas com um pricing eficiente para um tipo especial de rota não-elementar. O pricing proposto combina a técnica Decremental State-Space Relaxation (DSSR) com limites de complemento. Estas técnicas permitem o fortalecimento da regra de dominância entre as rotas, reduzindo drasticamente o número total de rótulos utilizados pela programação dinâmica. Finalmente, um algoritmo de branch-cut-and-price é criado o qual usa a geração de colunas e a separação de cortes previamente apresentadas. Além disto, este branch-cut-and-price é implementado usando strong branching e fixação por custo reduzido. Ao fim de cada parte, são apresentados resultados computacionais os quais avaliam a qualidade dos algoritmos propostos, os quais obtém novos limites inferiores para um grande número de instâncias do CARP e do GVRP. / [en] Routing problems stand among the hardest combinatorial problems to find high quality bounds or to prove new optimal solutions. In this thesis, we tackle the Capacitated Arc Routing Problem (CARP) and the Generalized Vehicle Routing Problem (GVRP). For both problems, there are a set of customers spread over a given graph, where each customer has a demand which must be serviced by exactly one vehicle from a set of identical vehicles. The traversal costs and a depot vertex are given. The objective is to find routes that collect all the demands, without exceeding the capacity of any vehicle, at minimum cost. For the CARP, the customers are a subset of edges, called the required edges, and for the GVRP, each customer is a subset of vertices, called clusters, where each cluster must be serviced by visiting exactly one vertex of it. Furthermore, it is noteworthy that when every cluster contains just a single vertex, the problem is the Capacitated Vehicle Routing Problem (CVRP). Firstly, we investigate methods to improve lower bounds for large scale instances. We propose to explore the speed of a new dual ascent heuristic to generate capacity cuts. The quality of the cuts found is next improved with a new exact separation which is used in the linear program resolution that follows the dual heuristic. Following, we present a column generation algorithm with an efficient pricing for a special kind of non-elementary routes. The proposed pricing algorithm combines Decremental State-Space Relaxation(DSSR) technique with completion bounds. These techniques allow the strengthening of the domination rule between routes, drastically reducing the total number of labels used during the dynamic programming. Finally, we devise a branch-cut-and-price algorithm which uses the previously presented column generation and cut separation. Moreover, this branch-cutand- price is implemented using strong branching and reduced cost fixing. At the end of each part, we present computational experiments which evaluate the quality of the proposed algorithms and show new best lower bounds for a large number of CARP and GVRP instances.

L’optimisation de la planification de la maintenance des équipements de production d’électricité est une question importante pour éviter des temps d’arrêt inutiles et des coûts opérationnels excessifs. Dans cette thèse, nous présentons une classification multidimensionnelle des études de Recherche Opérationnelle portant sur ce sujet. Le secteur des énergies renouvelables étant en pleine expansion, nous présentons et discutons ensuite d’un problème de maintenance de parcs éoliens terrestres. Le problème est traité sur un horizon à court terme et l’objectif est de construire un planning de maintenance qui maximise le revenu lié à production d’électricité des éoliennes tout en prenant en compte des prévisions de vent et en gérant l’affectation de techniciens. Nous présentons plusieurs modélisations du problème basées sur la programmation linéaire. Nous décrivons aussi une recherche à grands voisinages basée sur la programmation par contraintes.Cette méthode heuristique donne des résultats probants.Nous résolvons ensuite le problème avec une approche exacte basée sur une décomposition du problème. Dans cette méthode, nous construisons successivement des plannings de maintenance optimisés et rejetons, à l’aide de coupes spécifiques, ceux pour lesquels la disponibilité des techniciens est insuffisante. Les résultats suggèrent que cette méthode est la mieux adaptée pour ce problème. Enfin, pour prendre en compte l’incertitude inhérente à la prévision de vitesses de vent, nous proposons une approche robuste dans laquelle nous prenons des décisions garantissant la réalisabilité du planning de maintenance et le meilleur revenu pour les pires scénarios de vent. / Efficiently scheduling maintenance operations of generating units is key to prevent unnecessary downtime and excessive operational costs. In this work, we first present a multidimensional classification of the body of work dealing with the optimization of the maintenance scheduling in the operations research literature. Motivated by the recent emergence of the renewable energy sector as an Environmental priority to produce low-carbon power electricity, we introduce and discuss a challenging Maintenance scheduling problem rising in the onshore wind industry. Addressing the problem on a short-term horizon, the objective is to find a maintenance plan that maximizes the revenue generated by the electricity production of the turbines while taking into account wind predictions, multiple task execution modes, and technician-to-task assignment constraints. We start by presenting several integer linear Programming formulations of the problem. We then describe a constraint programming-based large neighborhood search which proves to be an efficient heuristic solution method. We then design an exact branch-and-check approach based on a decomposition of the problem. In this method, we successively build maintenance plans while discarding – using problem-specific cuts – those that cannot be performed by the technicians. The results suggest that this method is the best suited to the problem. To tackle the Inherent uncertainty on the wind speed, we also propose a robust approach in which we aim to take risk-averse decisions regarding the revenue associated with the maintenance plan and its feasibility.

Neste trabalho, estudamos o problema a recoloração convexa de grafos, denotado por RC. Dizemos que uma coloração dos vértices de um grafo G é convexa se, para cada cor tribuída d, os vértices de G com a cor d induzem um subgrafo conexo. No problema RC, é dado um grafo G e uma coloração de seus vértices, e o objetivo é recolorir o menor número possível de vértices de G tal que a coloração resultante seja convexa. A motivação para o estudo deste problema surgiu em contexto de árvores filogenéticas. Sabe-se que este problema é NP-difícil mesmo quando G é um caminho. Mostramos que o problema RC parametrizado pelo número de mudanças de cor é W[2]-difícil mesmo se a coloração inicial usa apenas duas cores. Além disso, provamos alguns resultados sobre a inaproximabilidade deste problema. Apresentamos uma formulação inteira para a versão com pesos do problema RC em grafos arbitrários, e então a especializamos para o caso de árvores. Estudamos a estrutura facial do politopo definido como a envoltória convexa dos pontos inteiros que satisfazem as restrições da formulação proposta, apresentamos várias classes de desigualdades que definem facetas e descrevemos os correspondentes algoritmos de separação. Implementamos um algoritmo branch-and-cut para o problema RC em árvores e mostramos os resultados computacionais obtidos com uma grande quantidade de instâncias que representam árvores filogenéticas reais. Os experimentos mostram que essa abordagem pode ser usada para resolver instâncias da ordem de 1500 vértices em 40 minutos, um desempenho muito superior ao alcançado por outros algoritmos propostos na literatura. / In this work we study the convex recoloring problem of graphs, denoted by CR. We say that a vertex coloring of a graph G is convex if, for each assigned color d, the vertices of G with color d induce a connected subgraph. In the CR problem, given a graph G and a coloring of its vertices, we want to find a recoloring that is convex and minimizes the number of recolored vertices. The motivation for investigating this problem has its roots in the study of phylogenetic trees. It is known that this problem is NP-hard even when G is a path. We show that the problem CR parameterized by the number of color changes is W[2]-hard even if the initial coloring uses only two colors. Moreover, we prove some inapproximation results for this problem. We also show an integer programming formulation for the weighted version of this problem on arbitrary graphs, and then specialize it for trees. We study the facial structure of the polytope defined as the convex hull of the integer points satisfying the restrictions of the proposed ILP formulation, present several classes of facet-defining inequalities and the corresponding separation algorithms. We also present a branch-and-cut algorithm that we have implemented for the special case of trees, and show the computational results obtained with a large number of instances. We considered instances which are real phylogenetic trees. The experiments show that this approach can be used to solve instances up to 1500 vertices in 40 minutes, comparing favorably to other approaches that have been proposed in the literature.

Les activités de transport et de gestion des stocks ont un impact important les unes sur les autres. Assurer un niveau de stock idéal peut demander des livraisons fréquentes, ce qui entraîne des coûts logistiques élevés. Pour optimiser les compromis entre les coûts de stock et de transport, des systèmes VMI (Vendor Managed Inventory) ont été développés pour gérer ensemble les opérations de stock et de transport. Pour un ensemble de clients ayant des demandes sur un horizon de temps, le problème de détermination des tournées et des quantités à livrer avec un coût minimum de gestion de stock et de transport est connu sous le nom de Inventory Routing Problem (IRP). Les systèmes à deux échelons ont également été étudiés pour améliorer le flux de véhicules dans les zones urbaines. étant donné que des nouvelles politiques de gestion sont apparues, dans le but de limiter le trafic des gros véhicules et leur vitesse dans les centres urbains, des Centres de Distribution (DC) sont mis en place pour coordonner les flux de marchandises à l'intérieur et à l'extérieur des zones urbaines. Les produits sont donc livrés aux clients par les fournisseurs via les DC.Nous proposons de combiner un système à deux échelons avec le IRP. Nous introduisons un Operational Two-Echelon Inventory Routing Problem (O-2E-IRP), ce qui est une nouvelle extension du IRP à notre connaissance. Dans le O-2E-IRP proposé, les clients doivent être servis par un fournisseur strictement via des DC et les tournées doivent être définis dans les deux échelons sur un horizon de temps donné. Trois politiques de réapprovisionnement et de configurations de routage différentes sont modélisées pour ce problème. Nous développons deux formulations mathématiques, ainsi qu'un algorithme Branch-and-Cut (B&C) combiné à une matheuristique pour résoudre le problème. De plus, nous analysons plusieurs inégalités valides disponibles pour le IRP et nous introduisons de nouvelles inégalités valides inhérentes au IRP à deux échelons. Des expériences de calcul approfondies ont été effectuées sur un ensemble d'instances générées de manière aléatoire. Les résultats obtenus montrent que les performances des méthodes sont liées à la politique de stock et à la configuration de routage.Dans le contexte d'un IRP à deux échelons, deux décisions tactiques importantes doivent être prises en plus des décisions de livraison de routage et de quantité de livraison: à partir de quel DC sera fourni chaque client et en utilisant quels véhicules ? Répondre à ces questions est extrêmement difficile car cela implique de pouvoir minimiser les coûts opérationnels d'un système de livraison VMI à deux échelons à long-terme et avec des demandes incertaines. Pour faire face à cela, nous présentons le Tactical Two-Echelon Inventory Routing Problem (T-2E-IRP) qui optimise les décisions en fonction d'un horizon à long-terme et en tenant compte des demandes stochastiques. Trois politiques de gestion des stocks sont modélisées et appliquées à un ou aux deux échelons. Nous développons une approche de simulation pour résoudre le T-2E-IRP sur un horizon de temps à long-terme. Nous proposons quatre formulations et deux algorithmes B&C pour définir l'affectation des clients et des véhicules aux DC en fonction d'un horizon de temps court. Ensuite, nous évaluons ces décisions d'affectation via un outil de simulation qui résout un sous-problème du T-2E-IRP, qui consiste en les décisions de livraisons du fournisseur aux DC et des DC aux clients, sur un horizon glissant. De nombreuses expériences sont effectuées pour un ensemble d'instances générées aléatoirement. L'impact de plusieurs paramètres utilisés pour déterminer l'affectation des clients et des véhicules aux DC sur le coût total est analysé. Basé sur des expériences, nous définissons la combinaison de paramètres qui fournit généralement les meilleurs résultats sur les instances générées. / Transport and inventory management activities have a great impact on each other. Ensuring an ideal inventory level can require frequent deliveries, leading to high logistics costs. To optimize the trade-offs between inventory and transportation costs, VMI (Vendor Managed Inventory) systems have been developed to manage inventory and transportation operations together. Given a set of customers with demands over a time horizon, the problem of determining routes and delivery quantities at a minimum inventory holding and transportation costs is known as Inventory Routing Problem (IRP). Two-echelon systems have also been studied to improve the freight vehicle flow inside urban areas. As new management policies have emerged, with the goal of limiting the traffic of large vehicles and their speed in urban centers, Distribution Centers (DC) are introduced to coordinate freight flows inside and outside the urban areas. Products are then delivered from the suppliers to the customers through the DC.We propose to combine a two-echelon system with the IRP. We introduce an Operational Two-Echelon Inventory Routing Problem (O-2E-IRP), which is a new extension of the IRP to the best of our knowledge. On the proposed O-2E-IRP, the customers must be served by a supplier strictly through DC and routes must be defined in both echelons over a given time horizon. Three different replenishment policies and routing configurations are modeled for this problem. We develop two mathematical formulations, and a Branch-and-Cut (B&C) algorithm combined with a matheuristic to solve the problem. In addition, we analyze several valid inequalities available for IRP, and we introduce new ones inherent to the IRP within two echelons. Extensive computational experiments have been carried out on a set of randomly generated instances. The obtained results show that the performance of the methods is related to the inventory policy and routing configuration.In the context of a two-echelon IRP, two important tactical decisions have to be taken in addition to route and quantity delivery decisions: from which DC will be supplied each customer and using which vehicles? Answering these questions is extremely difficult as it implies being able to minimize operational costs for a two-echelon VMI delivery system on long-term and with uncertain demands. In order to deal with this, we introduce the Tactical Two-Echelon Inventory Routing Problem (T-2E-IRP) that optimizes the decisions based on a long-term horizon and considering stochastic demands. Three inventory management policies are modeled and applied at one or both echelons. We develop a simulation approach to solve the T-2E-IRP on a long-term time horizon. We propose four formulations and two B&C algorithms to define the assignment of customers and vehicles to the DC based on a short time horizon. Then, we evaluate these assignment decisions through a simulation tool that solves a subproblem of the T-2E-IRP, which consists of the decisions of deliveries from the supplier to the DC and from the DC to the customers, on a rolling-horizon framework. Extensive computational experiments are performed for a set of randomly generated instances. The impact of several parameters used to determine the assignment of customers and vehicles to DC on the total cost is analyzed. Based on the experiments, we define the combination of parameters that generally provides the best results on the generated instances.

Étant donné un graphe G = (V U T, E), tel que V U T représente l'ensemble des sommets où T est un ensemble de terminaux, et une fonction poids w associée aux sommets non terminaux, le problème du séparateur de poids minimum consiste à partitionner V U T en k + 1 sous-ensembles {S, V1,..., Vk} tel qu'il n'y a aucune arête entre deux sous-ensembles différents Vi et Vj, chaque Vi contient exactement un terminal et le poids de S est minimum. Dans cette thèse, nous étudions le problème d'un point de vue polyèdral. Nous donnons deux formulations en nombres entiers pour le problème, et pour une de ces formulations, nous étudions le polyèdre associé. Nous présentons plusieurs inégalités valides, et décrivons des conditions de facette. En utilisant ces résultats, nous développons un algorithme de coupes et branchement pour le problème. Nous étudions également le polytope des séparateurs dans les graphes décomposables par sommets d'articulation. Si G est un graphe qui se décompose en G1 et G2, alors nous montrons que le polytope des séparateurs dans G peut être décrit à partir de deux systèmes linéaires liés à G1 et G2. Ceci donne lieu à une technique permettant de caractériser le polytope des séparateurs dans les graphes qui sont récursivement décomposables. Ensuite, nous étudions des formulations étendues pour le problème et proposons des algorithmes de génération de colonnes et branchement ainsi que des algorithmes de génération de colonnes, de coupes et branchement. Pour chaque formulation, nous présentons un algorithme de génération de colonnes, une procedure pour le calcul de la borne duale ainsi qu'une règle de branchement. De plus, nous présentons quatre variantes du problème du séparateur. Nous montrons que celles-ci sont NP-difficiles, et pour chacune d'elles nous donnons une formulation en nombres entiers et présentons certaines classes d'inégalités valides. / Given a graph G = (V U T, E) with V U T the set of vertices, where T is a set of terminals, and a weight function w, associated with the nonterminal nodes, the multi-terminal vertex separator problem consists in partitioning V U T into k + 1 subsets {S, V1,..., Vk} such that there is no edge between two different subsets Vi and Vj, each Vi contains exactly one terminal and the weight of S is minimum. In this thesis, we consider the problem from a polyhedral point of view. We give two integer programming formulations for the problem, for one of them, we investigate the related polyhedron. We describe some valid inequalities and characterize when these inequalities define facets. Using these results, we develop a Branch-and-Cut algorithm for the problem. We also study the multi-terminal vertex separator polytope in the graphs decomposable by one node cutsets. If G is a graph that decomposes into G1 and G2, we show that the multi-terminal vertex separator polytope in G can be described from two linear systems related to G1 and G2. This gives rise to a technique for characterizing the multi-terminal vertex separator polytope in the graphs that are recursively decomposable. Moreover, we propose three extended formulations for the problem and derive Branch-and-Price and Branch-and-Cut-and-Price algorithms. For each formulation we present a column generation scheme, the way to compute the dual bound, and the branching scheme. Finally, we discuss four variants of the multi-terminal vertex separator problem. We show that all these variants are NP-hard and for each one we give an integer programming formulation and present some class of valid inequalities.