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Transforming the aging electric grid to a smart grid is an active area of research in industry and the government. One of the main objectives of the smart grid is to improve the efficiency of power generation, transmission and distribution and also to improve the stability and the reliability of the grid. In order to achieve this, various processes involved in power generation, transmission, and distribution should be armed with advanced sensor technologies, computing, communication and networking capabilities to an unprecedented level. These high speed data transfer and computational abilities aid power system engineers to obtain wide area measurements, achieve better control of power system operations and improve the reliability of power supply and the efficiency of different power grid operations. In the process of making the grid smarter, problems existing in traditional grid applications can be identified and solutions have to be developed to fix the identified issues. In this dissertation, two problems that aid power system engineers to meet the above mentioned smart grid's objective are researched. One problem is related to the distribution-side smart grid and the other one is a part of the transmission-side smart grid. Advanced Metering Infrastructure (AMI) is one of the important distribution-side smart grid applications. AMI is a technology where smart meters are installed at customer site which gives the utilities the ability to monitor and collect information related to the amount of electricity, water, and gas consumed by the user. Many recent research studies suggested the use of 3G cellular CDMA2000 for AMI network as it provides an advanced and cost effective solution for smart grid communications. Taking into account both technical and non-technical factors such as extended lifetime, security, availability and control of the solution, Alliander, an electric utility in Netherlands deployed a private 3G CDMA2000 network for smart metering. Although 3G CDMA2000 satisfies the requirements of smart grid applications, an analysis on the use of the current state of the art 3G CDMA2000 for smart grid applications indicates that its usage results in high percentage of control overhead, high latency and high power consumption for data transfer. As a part of this dissertation, we proposed FLEX-MAC - a new Medium Access Control (MAC) protocol that reduces the latency and overhead in smart meter data collection when compared to 3G CDMA2000 MAC. As mentioned above the second problem studied in this dissertation is related to the transmission-side grid. Power grid transmission and sub-transmission lines are generally protected by distance relays. After a thorough analysis of U.S. historical blackouts, North American Electric Reliability Council (NERC) has concluded that the hidden failure induced tripping of distance relays is responsible for 70% of the U.S. blackouts. As a part of this dissertation, agent based distance relaying protection scheme is proposed to improve the robustness of distance relays to hidden failures and thus reduce the probability of blackouts. This dissertation has two major contributions. First, a hierarchically distributed non-intrusive Agent Aided Distance Relaying Protection Scheme (AADRPS) is proposed to improve the robustness of distance relays to hidden failures. The problem of adapting the proposed AADRPS to a larger power system network consisting of thousands of buses is modeled as an integer linear programming multiple facility location optimization problem. Distance relaying protection scheme is a real time system and has stringent timing requirements. Therefore, in order to verify if the proposed AADRPS meets the timing requirements or not and also to check for deadlocks, verification models based on UPPAAL real time model checker are provided in this dissertation. So, the entire framework consisting of AADRPS that aids in increasing the robustness of distance relays and reducing the possibility of blackouts, the multiple facility location optimization models and the UPPAAL real time model checker verification models form one of the major contributions of this dissertation. The second contribution is related to the MAC layer of AMI networks. In this dissertation, FLEX-MAC - a novel and flexible MAC protocol is proposed to reduce the overhead and latency in smart meter data collection. The novelty of the FLEX-MAC lies in its ability to change the mode of operation based on the type of the data being collected in a smart meter network. FLEX-MAC employs Frame and Channel Reserved (FCR) MAC or Frame Reserved and Random Channel (FRRC) MAC for scheduled data collection. Power outage data in an AMI network is considered as a random data . In a densely populated area, during an outage, a large number of smart meters attempt to report the outage, which significantly increases the Random Access CHannel (RACH) load. In order to reduce the RACH traffic during an outage, this dissertation proposes a Time Hierarchical Scheme (THS). Also, in order to minimize the total time to collect the power outage data, a Backward Recursive Dynamic Programming (BRDP) approach is proposed to adapt the transmission rate of smart meters reporting an outage. Both the Optimal Transmission Rate Adaption and Time Hierarchical Scheme form the basis of OTRA-THS MAC which is employed by FLEX-MAC for random data collection. Additionally, in this work, Markov chain models are presented for evaluating the performance of FCR and FRRC MACs in terms of average throughput and delay. Also, another Markov model is presented to find the mean time to absorption or mean time to collect power outage data of OTRA-TH MAC during an outage. / Ph. D.

Les décisions de localisation sont souvent soumises à des aspects dynamiques comme des changements dans la demande des clients. Pour y répondre, la solution consiste à considérer une flexibilité accrue concernant l’emplacement et la capacité des installations. Même lorsque la demande est prévisible, trouver le planning optimal pour le déploiement et l'ajustement dynamique des capacités reste un défi. Dans cette thèse, nous nous concentrons sur des problèmes de localisation avec périodes multiples, et permettant l'ajustement dynamique des capacités, en particulier ceux avec des structures de coûts complexes. Nous étudions ces problèmes sous différents points de vue de recherche opérationnelle, en présentant et en comparant plusieurs modèles de programmation linéaire en nombres entiers (PLNE), l'évaluation de leur utilisation dans la pratique et en développant des algorithmes de résolution efficaces. Cette thèse est divisée en quatre parties. Tout d’abord, nous présentons le contexte industriel à l’origine de nos travaux: une compagnie forestière qui a besoin de localiser des campements pour accueillir les travailleurs forestiers. Nous présentons un modèle PLNE permettant la construction de nouveaux campements, l’extension, le déplacement et la fermeture temporaire partielle des campements existants. Ce modèle utilise des contraintes de capacité particulières, ainsi qu’une structure de coût à économie d’échelle sur plusieurs niveaux. L'utilité du modèle est évaluée par deux études de cas. La deuxième partie introduit le problème dynamique de localisation avec des capacités modulaires généralisées. Le modèle généralise plusieurs problèmes dynamiques de localisation et fournit de meilleures bornes de la relaxation linéaire que leurs formulations spécialisées. Le modèle peut résoudre des problèmes de localisation où les coûts pour les changements de capacité sont définis pour toutes les paires de niveaux de capacité, comme c'est le cas dans le problème industriel mentionnée ci-dessus. Il est appliqué à trois cas particuliers: l'expansion et la réduction des capacités, la fermeture temporaire des installations, et la combinaison des deux. Nous démontrons des relations de dominance entre notre formulation et les modèles existants pour les cas particuliers. Des expériences de calcul sur un grand nombre d’instances générées aléatoirement jusqu’à 100 installations et 1000 clients, montrent que notre modèle peut obtenir des solutions optimales plus rapidement que les formulations spécialisées existantes. Compte tenu de la complexité des modèles précédents pour les grandes instances, la troisième partie de la thèse propose des heuristiques lagrangiennes. Basées sur les méthodes du sous-gradient et des faisceaux, elles trouvent des solutions de bonne qualité même pour les instances de grande taille comportant jusqu’à 250 installations et 1000 clients. Nous améliorons ensuite la qualité de la solution obtenue en résolvent un modèle PLNE restreint qui tire parti des informations recueillies lors de la résolution du dual lagrangien. Les résultats des calculs montrent que les heuristiques donnent rapidement des solutions de bonne qualité, même pour les instances où les solveurs génériques ne trouvent pas de solutions réalisables. Finalement, nous adaptons les heuristiques précédentes pour résoudre le problème industriel. Deux relaxations différentes sont proposées et comparées. Des extensions des concepts précédents sont présentées afin d'assurer une résolution fiable en un temps raisonnable. / Location decisions are frequently subject to dynamic aspects such as changes in customer demand. Often, flexibility regarding the geographic location of facilities, as well as their capacities, is the only solution to such issues. Even when demand can be forecast, finding the optimal schedule for the deployment and dynamic adjustment of capacities remains a challenge. In this thesis, we focus on multi-period facility location problems that allow for dynamic capacity adjustment, in particular those with complex cost structures. We investigate such problems from different Operations Research perspectives, presenting and comparing several mixed-integer programming (MIP) models, assessing their use in practice and developing efficient solution algorithms. The thesis is divided into four parts. We first motivate our research by an industrial application, in which a logging company needs to locate camps to host the workers involved in forestry operations. We present a MIP model that allows for the construction of additional camps, the expansion and relocation of existing ones, as well as partial closing and reopening of facilities. The model uses particular capacity constraints that involve integer rounding on the left hand side. Economies of scale are considered on several levels of the cost structure. The usefulness of the model is assessed by two case studies. The second part introduces the Dynamic Facility Location Problem with Generalized Modular Capacities (DFLPG). The model generalizes existing formulations for several dynamic facility location problems and provides stronger linear programming relaxations than the specialized formulations. The model can address facility location problems where the costs for capacity changes are defined for all pairs of capacity levels, as it is the case in the previously introduced industrial problem. It is applied to three special cases: capacity expansion and reduction, temporary facility closing and reopening, and the combination of both. We prove dominance relationships between our formulation and existing models for the special cases. Computational experiments on a large set of randomly generated instances with up to 100 facility locations and 1000 customers show that our model can obtain optimal solutions in shorter computing times than the existing specialized formulations. Given the complexity of such models for large instances, the third part of the thesis proposes efficient Lagrangian heuristics. Based on subgradient and bundle methods, good quality solutions are found even for large-scale instances with up to 250 facility locations and 1000 customers. To improve the final solution quality, a restricted model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian based heuristics provide highly reliable results, producing good quality solutions in short computing times even for instances where generic solvers do not find feasible solutions. Finally, we adapt the Lagrangian heuristics to solve the industrial application. Two different relaxations are proposed and compared. Extensions of the previous concepts are presented to ensure a reliable solution of the problem, providing high quality solutions in reasonable computing times.

Os consórcios são conhecidos pelo aumento da capacidade de realização que confere aos participantes, e maior eficiência no uso dos recursos disponíveis, o que auxiliaria os pequenos governos locais para solucionar a escassez de recursos. Este trabalho apresenta o estudo do sistema consorciado intermunicipal para destinação dos resíduos sólidos urbanos, para auxiliar os municípios de pequeno porte na solução da inadequada destinação do lixo, responsáveis por constantes impactos ambientais. Os estudos foram realizados através de análises de custos com enfoque logístico, no nível estratégico de localização de facilidades e roteirização e programação da frota. Os estudos foram possíveis, com o auxílio do software TransCAD, uma ferramenta de Sistema de Informações Geográficas. Através do TransCAD, foi realizado a localização dos aterros sanitários, obedecendo-se as restrições impostas, e a roteirização da frota de veículos, que levassem ao menor custo logístico. Para se chegar à situação de menor custo, diversas configurações foram consideradas, nas quais foram variados o número de aterros que atendem os municípios, e a presença ou não de estações de transferência de resíduos. O método desenvolvido promoveu a análise de custos da implantação e operação do sistema consorciado, que consiste desde a coleta de resí-duos, até a disposição final em aterros sanitários. Os resultados deste trabalho comprovaram quantitativamente que o consórcio é mais eficiente do que a solução isolada para cada município. / The consortium are known by the growth of the accomplishment capacity that grants to the participants, and larger efficiency in the use of the available resources, what would aid the small local governments to solve the lack of resources. This work presents the study of the intermunicipal consortium system for the destination of the urban solid waste, to aid the small cities to solve the inadequate destination of the waste, responsible for constant environmental damages. The studies were developed through the costs analysis with logistics focus, on the strategic level of facilities location and the vehicle routing. The studies were possible with the aid of the software TransCAD, a tool of Geographical Information System. Through the TransCAD, being obeyed the imposed restrictions, the location of the sanitary landfill was made, and vehicles routing, to take to the lowest logistics cost. To reach the situation of lowest cost, several configurations were considered, in which the number of sanitary landfill for the cities were varied, and the inclusion or not the solid waste transfer stations. The developed method promoted the cost analysis of the implantation and operation of the consortium system, from the waste collection, until the final disposition in sanitary landfills. The results of this work proved quantitatively that the consortium is more efficient than the isolated solution for each city.

Inom byggindustrin är det svårt att skapa standardiserade logistikprocesser eftersom det vid varje nytt bygge även skapas en ny organisation. Förutsättningarna skiljer sig även mellan olika byggen, vilket försvårar ett förbättringsarbete. Skanska Väg och Anläggning Norr fick under 2017 uppdraget att bygga om Vasaplan i centrala Umeå, och i september 2018 stod projektet klart. Ombyggnationen var i det stora hela ett mycket lyckat projekt, men efter färdigställandet av projektet har problem angående materialtillgång identifierats. Syftet med arbetet är att undersöka hur leveranser till en byggarbetsplats kan optimeras samt hurvida ett mellanlager kan underlätta hanteringen av leveranserna till byggarbetsplatsen. En jämförelse har gjorts där det har undersökts ifall det är mer lönsamt att använda sig av lagerhållning, eller endast av JIT-leveranser. Förhoppningen är att arbetet kan bidra till att Skanska i framtiden får ett mer standardiserat tillvägagångssätt vid planering av leveranser till byggarbetsplats av material som kräver liknande lagerhållning och transport som granithällar. För att lösa detta har två matematiska modeller använts; Anläggningslokaliseringsproblemet (ALP) samt en matematisk modell som optimerar placering av material på en lageryta. Två stycken produktionsflödesmodeller, JIT och EOQ, har även använts i beräkningarna. Resultatet från produktionsflödesmodellerna, JIT och EOQ, visar att JIT-leveranser med hjälp av en omlastningscentral alltid är den mest kostnadseffektiva lösningen då lageryta är en direkt kostnad för Skanska. I de fall lager inte är en direkt utgift för Skanska så rekommenderar den matematiska modellen för ALP en optimal användning av de lager som är tillgängliga. / For every new construction project, a new organisation is created. It is therefore a challenge for the construction industry to create standardized logistic processes. In addition, different construction projects have different traits, which results in further challenges for improvement efforts for the construction logistic processes. In 2017 Skanska Väg och Anläggning Norr did the reconstruction of Vasaplan in the central of Umeå, and in September 2018 the reconstruction project was done. The reconstruction was in its entirety a very successful project, however when the project was finished problems regarding material supply were identified. The aim of this paper is to analyze how deliveries to a construction site can be optimized and whether storage spaces can aid in the handling of deliveries to the construction site. A comparison has been made between storing material and using JIT-deliveries. The hope is to help Skanska in developing a more standardized approach when it comes to planning the deliveries of materials that has similar storage and transport conditions as the slabs of granite used. To solve this two mathematical models have been used; Facility location problem and a mathematical model that optimizes the placement of materials in a storage space. Two production flow models, JIT and EOQ, were also used when performing the calculations. The result from the production flow models, JIT and EOQ, show that JIT deliveries are always the most cost effective solution when storage space is a direct cost for Skanska, when used together with a logistics center. However, when storing is no extra expense for Skanska, the mathematical model for the Facility location problem suggests a optimal use of the storage spaces that are available.

Ser eficiente é um requisito para a sustentabilidade das empresas concessionárias de distribuição de energia elétrica no Brasil. A busca pela eficiência deve estar em harmonia com a melhoria contínua da qualidade, da segurança e da satisfação dos consumidores e das partes envolvidas. O desafio de atender múltiplos objetivos requer que as empresas do setor desenvolvam soluções inovadoras, com a mudança de processos, tecnologia, estrutura e a capacitação das pessoas. Desenvolver um modelo operacional eficiente e uma gestão rigorosa dos custos são fatores-chave para o sucesso das empresas, considerando o contexto regulatório de revisão tarifária que incentiva a melhoria do desempenho. O modelo operacional é definido a partir da organização logística dos recursos para atendimento da demanda de serviços, que define também os custos fixos e variáveis de pessoal (salário, horas extras, refeições), infraestrutura (manutenção de prédios, ferramentas e equipamentos) e deslocamentos (manutenção de veículos, combustível), por exemplo. A melhor alocação e o melhor dimensionamento de bases operacionais possibilitam a redução dos custos com deslocamento e infraestrutura, favorecendo o aproveitamento da força de trabalho em campo, a melhoria do atendimento dos clientes e da segurança dos colaboradores. Este trabalho apresenta uma metodologia de otimização de custos através da alocação de bases e equipes operacionais, com o modelamento matemático dos objetivos e restrições do negócio e a aplicação de algoritmo evolutivo para busca das melhores soluções, sendo uma aplicação de Pesquisa Operacional, no campo da Localização de Instalações, em distribuição de energia elétrica. O modelo de otimização desenvolvido possibilita a busca pelo ponto de equilíbrio ótimo que minimiza o custo total formado pelos custos de infraestrutura, frota (veículos e deslocamentos) e pessoal. O algoritmo evolutivo aplicado no modelo oferece soluções otimizadas pelo melhoramento de conjuntos de variáveis binárias com base em conceitos da evolução genética. O modelo de otimização fornece o detalhamento de toda a estrutura operacional e de custos para uma determinada solução do problema, utilizando premissas de produtividade e deslocamentos (velocidades e distâncias) para definir as abrangências de atuação das bases operacionais, recursos (equipes, pessoas, veículos) necessários para atendimento da demanda de serviços, e projetar todos os custos fixos e variáveis associados. A metodologia desenvolvida neste trabalho considera também a projeção de demanda futura para a aplicação no estudo de caso, que evidenciou a efetividade da metodologia como ferramenta para a melhoria da eficiência operacional em empresas de distribuição de energia elétrica. / Being efficient is a requirement for the sustainability of electricity distribution companies in Brazil. The quest for efficiency must be in harmony with the continuous improvement of quality, safety and satisfaction of customers and all stakeholders involved. The challenge of attending multi-objectives requires companies in the sector to develop innovative solutions with the change of processes, technology, structure and enabling their professionals to drive this. Developing an efficient operational model and a strict cost management are keys for companies to achieve success, considering the regulatory context of tariff reviewing that encourages performance improvement. The operational model is defined from the logistics organization of resources to meet the demand of services, which also defines fixed and variable costs with people/teams (payments, overtime, meals), infrastructure (maintenance of building, tools and equipments) and fleet (maintenance of vehicles and fuel costs), for example. The best allocation and the best design of operational facilities (or operational bases) will reduce infrastructure costs and truck rolls, releasing workforce to attend customers and reducing displacements risks. This work presents a cost optimization methodology through the allocation of operational bases and teams, with the mathematical modelling of business objectives, constraints and using Evolutionary Algorithm to find the best solution, as an application of Operations Research in the field of Facility Location in electricity distribution. The optimization model enables the search for the optimal balance point that minimizes the total cost formed by infrastructure, fleet and people. The Evolutionary Algorithm applied in the model offers optimized solutions through the improvement of sets of binary variables based on genetic evolution concepts. The optimization model also gives detailed information about the operational structure and costs for a given allocation solution, using productivity and displacements (speed, distances) information to define the service regions for each operational base and resources (people, vehicles) needed to attend the demand of services, defining all fixed and variable costs for this. The methodology presented in this paper also considers the future demand of services (forecast), used in a case study that showed the effectives of this methodology as a tool for the improvement of operational efficiency in electricity distribution companies.

Ser eficiente é um requisito para a sustentabilidade das empresas concessionárias de distribuição de energia elétrica no Brasil. A busca pela eficiência deve estar em harmonia com a melhoria contínua da qualidade, da segurança e da satisfação dos consumidores e das partes envolvidas. O desafio de atender múltiplos objetivos requer que as empresas do setor desenvolvam soluções inovadoras, com a mudança de processos, tecnologia, estrutura e a capacitação das pessoas. Desenvolver um modelo operacional eficiente e uma gestão rigorosa dos custos são fatores-chave para o sucesso das empresas, considerando o contexto regulatório de revisão tarifária que incentiva a melhoria do desempenho. O modelo operacional é definido a partir da organização logística dos recursos para atendimento da demanda de serviços, que define também os custos fixos e variáveis de pessoal (salário, horas extras, refeições), infraestrutura (manutenção de prédios, ferramentas e equipamentos) e deslocamentos (manutenção de veículos, combustível), por exemplo. A melhor alocação e o melhor dimensionamento de bases operacionais possibilitam a redução dos custos com deslocamento e infraestrutura, favorecendo o aproveitamento da força de trabalho em campo, a melhoria do atendimento dos clientes e da segurança dos colaboradores. Este trabalho apresenta uma metodologia de otimização de custos através da alocação de bases e equipes operacionais, com o modelamento matemático dos objetivos e restrições do negócio e a aplicação de algoritmo evolutivo para busca das melhores soluções, sendo uma aplicação de Pesquisa Operacional, no campo da Localização de Instalações, em distribuição de energia elétrica. O modelo de otimização desenvolvido possibilita a busca pelo ponto de equilíbrio ótimo que minimiza o custo total formado pelos custos de infraestrutura, frota (veículos e deslocamentos) e pessoal. O algoritmo evolutivo aplicado no modelo oferece soluções otimizadas pelo melhoramento de conjuntos de variáveis binárias com base em conceitos da evolução genética. O modelo de otimização fornece o detalhamento de toda a estrutura operacional e de custos para uma determinada solução do problema, utilizando premissas de produtividade e deslocamentos (velocidades e distâncias) para definir as abrangências de atuação das bases operacionais, recursos (equipes, pessoas, veículos) necessários para atendimento da demanda de serviços, e projetar todos os custos fixos e variáveis associados. A metodologia desenvolvida neste trabalho considera também a projeção de demanda futura para a aplicação no estudo de caso, que evidenciou a efetividade da metodologia como ferramenta para a melhoria da eficiência operacional em empresas de distribuição de energia elétrica. / Being efficient is a requirement for the sustainability of electricity distribution companies in Brazil. The quest for efficiency must be in harmony with the continuous improvement of quality, safety and satisfaction of customers and all stakeholders involved. The challenge of attending multi-objectives requires companies in the sector to develop innovative solutions with the change of processes, technology, structure and enabling their professionals to drive this. Developing an efficient operational model and a strict cost management are keys for companies to achieve success, considering the regulatory context of tariff reviewing that encourages performance improvement. The operational model is defined from the logistics organization of resources to meet the demand of services, which also defines fixed and variable costs with people/teams (payments, overtime, meals), infrastructure (maintenance of building, tools and equipments) and fleet (maintenance of vehicles and fuel costs), for example. The best allocation and the best design of operational facilities (or operational bases) will reduce infrastructure costs and truck rolls, releasing workforce to attend customers and reducing displacements risks. This work presents a cost optimization methodology through the allocation of operational bases and teams, with the mathematical modelling of business objectives, constraints and using Evolutionary Algorithm to find the best solution, as an application of Operations Research in the field of Facility Location in electricity distribution. The optimization model enables the search for the optimal balance point that minimizes the total cost formed by infrastructure, fleet and people. The Evolutionary Algorithm applied in the model offers optimized solutions through the improvement of sets of binary variables based on genetic evolution concepts. The optimization model also gives detailed information about the operational structure and costs for a given allocation solution, using productivity and displacements (speed, distances) information to define the service regions for each operational base and resources (people, vehicles) needed to attend the demand of services, defining all fixed and variable costs for this. The methodology presented in this paper also considers the future demand of services (forecast), used in a case study that showed the effectives of this methodology as a tool for the improvement of operational efficiency in electricity distribution companies.

逆物流回收的複雜度遠比正向物流高，企業為專注核心價值多半將逆物流活動委外專業物流服務供應商。對第三方逆物流業者而言，選擇適當的回收處理中心位址為其重要核心能力之一，而現今研究對於選址模式中之回收不確定性，大多以歷史資料作為參數，無根據區域特性不同而有所分別。故本研究希望探討在零售商提供資訊的情境下，結合消費者問卷建構廢棄產品的使用年限機率、並以二元迴歸邏輯分析建構回收機率以此預測區域回收數量，透過資訊分享以建立更好的回收處理中心選址設置模式，使第三方逆物流業者可按照此模式選擇最適當的回收點位置與回收處理量安排用以求得利潤最大化。 / Since reverse logistics is much more complex than forward logistics, third-party logistics providers are often the prior choice for firms to obtain their core value when a reverse logistic activity is needed. For third-party logistics providers, the location is one of their crucial core values; while most of them can only rely on historical data to assume the best location, due to the uncertainty of recycling in present studies.Therefore, this paper tries to construct the probability of products’ used-years by combining the retailers’ information with consumer-oriented questionnaires. Binary logistic regression is the methodology used to analyze and predict recycling probability. By information-sharing the third-party logistics providers will be able to construct a better selecting model for the best facility location, which will reach the most suitable recycling quantity to maximize their profits.

This thesis addresses two planning problems motivated by the operations of PSOD air transportation: scheduled maintenance planning, and base location and fleet allocation. In the first part of the thesis, we study tactical planning for scheduled maintenance which determines the daily maintenance capacities for two operating conditions: a growth phase and the steady state. We model tactical maintenance capacity planning during the growth phase as an integer program and develop an optimization-based local search to solve the problem. Tactical planning of steady state maintenance capacity concerns a special case for which we determine the optimal and the long run capacities with a pseudo-polynomial time algorithm. In the second part of the thesis, we address operational planning for scheduled maintenance which is concerned with assigning itineraries to jets and determining the specific jets to be scheduled for maintenance on a daily basis given a certain maintenance capacity. We present a solution methodology that employs a look-ahead approach to consider the impact of our current decisions on the future and decomposes the problem exploiting the differences between jets with respect to the proximity to their next maintenance. We further develop an integrated framework in order to capture the interaction between operational level maintenance decisions and flight scheduling. In the third and final part of the thesis, we present the tactical level base location and fleet allocation problem. As PSOD air transportation experiences changes in travel demand and fleet size, decisions regarding where to open new bases and how to allocate the number of jets among the bases are made. We first present a solution approach in which high level information about flight scheduling is used in a traditional facility location problem. We next develop a model that works directly with transportation requests and integrates a simplified version of flight scheduling with the base location and fleet allocation decisions in order to capture more detail.

In this dissertation, we introduce new families of valid inequalities for general linear mixed integer programs (MIPs) and second-order conic MIPs (SOCMIPs) and establish several theoretical properties and computational effectiveness of these inequalities. First we introduce the mixed n-step mixed integer rounding (MIR) inequalities for a generalization of the mixing set which we refer to as the n-mixing set. The n-mixing set is a multi-constraint mixed integer set in which each constraint has n integer variables and a single continuous variable. We then show that mixed n-step MIR can generate multi-row valid inequalities for general MIPs and special structure MIPs, namely, multi- module capacitated lot-sizing and facility location problems. We also present the results of our computational experiments with the mixed n-step MIR inequalities on small MIPLIB instances and randomly generated multi-module lot-sizing instances which show that these inequalities are quite effective. Next, we introduce the n-step conic MIR inequalities for the so-called polyhedral second-order conic (PSOC) mixed integer sets. PSOC sets arise in the polyhedral reformulation of SOCMIPs. We first introduce the n-step conic MIR inequality for a PSOC set with n integer variables and prove that all the 1-step to n-step conic MIR inequalities are facet-defining for the convex hull of this set. We also provide necessary and sufficient conditions for the PSOC form of this inequality to be valid. Then, we use the aforementioned n-step conic MIR facet to derive the n-step conic MIR inequality for a general PSOC set and provide conditions for it to be facet-defining. We further show that the n-step conic MIR inequality for a general PSOC set strictly dominates the n-step MIR inequalities written for the two linear constraints that define the PSOC set. We also prove that the n-step MIR inequality for a linear mixed integer constraint is a special case of the n-step conic MIR inequality. Finally, we conduct a polyhedral study of the triplet formulation for the single row facility layout problem (SRFLP). For any number of departments n, we prove that the dimension of the triplet polytope (convex hull of solutions to the triplet formulation) is n(n - 1)(n - 2)/3. We then prove that several valid inequalities presented in Amaral (2009) for this polytope are facet-defining. These results provide theoretical support for the fact that the linear program solved over these valid inequalities gives the optimal solution for all instances studied by Amaral (2009).