This dissertation studies two important models in the field of the distributed generation technologies to provide resiliency to the electric power distribution system. In the first part of the dissertation, we study the impact of assessing a Combined Cooling Heating Power system (CCHP) on the optimization and management of an on-site energy system under stochastic settings. These mathematical models propose a scalable stochastic decision model for large-scale microgrid operation formulated as a two-stage stochastic linear programming model. The model is solved enhanced algorithm strategies for Benders decomposition are introduced to find an optimal solution for larger instances efficiently. Some observations are made with different capacities of the power grid, dynamic pricing mechanisms with various levels of uncertainty, and sizes of power generation units. In the second part of the dissertation, we study a mathematical model that designs a Microgrid (MG) that integrates conventional fuel based generating (FBG) units, renewable sources of energy, distributed energy storage (DES) units, and electricity demand response. Curtailment of renewable resources generation during the MG operation affects the long-term revenues expected and increases the greenhouses emission. Considering the variability of renewable resources, researchers should pay more attention to scalable stochastic models for MG for multiple nodes. This study bridges the research gap by developing a scalable chance-constrained two-stage stochastic program to ensure that a significant portion of the renewable resource power output at each operating hour will be utilized. Finally, some managerial insights are drawn into the operation performance of the Combined Cooling Heating Power and a Microgrid.

Yes / This paper presents a robust framework for active and reactive power management in distribution networks using electric vehicles (EVs). The method simultaneously minimizes the energy cost and the voltage deviation subject to network and EVs constraints. The uncertainties related to active and reactive loads, required energy to charge EV batteries, charge rate of batteries and charger capacity of EVs are modeled using deterministic uncertainty sets. Firstly, based on duality theory, the max min form of the model is converted to a max form. Secondly, Benders decomposition is employed to solve the problem. The effectiveness of the proposed method is demonstrated with a 33-bus distribution network.

Avec la forte croissance du e-commerce et l'augmentation continue de la population des villes impliquant des niveaux de congestion plus élevés, les réseaux de distribution doivent déployer des échelons supplémentaires pour offrir un ajustement dynamique aux besoins des entreprises au cours du temps et faire face aux aléas affectant l’activité de distribution. Dans ce contexte, les praticiens s'intéressent aux réseaux de distribution à deux échelons. Dans cette thèse, nous commençons par présenter une revue complète des problèmes de design des réseaux de distribution et souligner des caractéristiques essentielles de modélisation. Ces aspects impliquent la structure à deux échelons, l’aspect multi-période, l’incertitude et les méthodes de résolution. Notre objectif est donc, d’élaborer un cadre complet pour le design d’un réseau de distribution efficace à deux échelons, sous incertitude et multi-périodicité, dans lequel les produits sont acheminés depuis les plateformes de stockage (WP) vers les plateformes de distribution (DP) avant d'être transportés vers les clients. Ce cadre est caractérisé par une hiérarchie temporelle entre le niveau de design impliquant des décisions relatives à la localisation des plateformes et à la capacité allouée aux DPs sur une échelle de temps annuelle, et le niveau opérationnel concernant des décisions journalières de transport. % sur une base journalière.Dans une première étude, nous introduisons le cadre complet pour le problème de design de réseaux de distribution à deux échelons avec une demande incertaine, une demande et un coût variables dans le temps. Le problème est formulé comme un programme stochastique à plusieurs étapes. Il implique au niveau stratégique des décisions de localisation des DPs ainsi que des décisions d'affectation des capacités aux DPs sur plusieurs périodes de design, et au niveau opérationnel des décisions de transport sous forme d'arcs origine-destination. Ensuite, nous proposons deux modèles alternatifs basés sur la programmation stochastique à deux étapes avec recours, et les résolvons par une approche de décomposition de Benders intégrée à une technique d’approximation moyenne d’échantillon (SAA). Par la suite, nous nous intéressons à la livraison du dernier kilomètre dans un contexte urbain où les décisions de transport dans le deuxième échelon sont caractérisées par des tournées de véhicules. Un problème multi-période stochastique de localisation-routage à deux échelons avec capacité (2E-SM-CLRP) est défini, dans lequel les décisions de localisation concernent les WPs et les DPs. Le modèle est un programme stochastique à deux étapes avec recours en nombre entier. Nous développons un algorithme de décomposition de Benders. Les décisions de localisation et de capacité sont déterminées par la solution du problème maître de Benders. Le sous-problème résultant est un problème multi-dépôt de tournées de véhicule avec des dépôts et véhicules capacitaires qui est résolu par un algorithme de branch-cut-and-price.Enfin, nous étudions le cadre à plusieurs étapes proposé pour le problème stochastique multi-période de design de réseaux de distribution à deux échelons et évaluons sa tractabilité. Pour ceci, nous développons une heuristique à horizon glissant qui permet d’obtenir des bornes de bonne qualité et des solutions de design pour le modèle à plusieurs étapes. / With the high growth of e-commerce and the continuous increase in cities population contrasted with the rising levels of congestion, distribution schemes need to deploy additional echelons to offer more dynamic adjustment to the requirement of the business over time and to cope with all the random factors. In this context, a two-echelon distribution network is nowadays investigated by the practitioners.In this thesis, we first present a global survey on distribution network design problems and point out many critical modeling features, namely the two-echelon structure, the multi-period setting, the uncertainty and solution approaches. The aim, here, is to propose a comprehensive framework for the design of an efficient two-echelon distribution network under multi-period and stochastic settings in which products are directed from warehouse platforms (WPs) to distribution platforms (DPs) before being transported to customers. A temporal hierarchy characterizes the design level dealing with facility-location and capacity decisions over a set of design periods, while the operational level involves transportation decisions on a daily basis.Then, we introduce the comprehensive framework for the two-echelon distribution network design problem under uncertain demand, and time-varying demand and cost, formulated as a multi-stage stochastic program. This work looks at a generic case for the deployment of a retailer's distribution network. Thus, the problem involves, at the strategic level, decisions on the number and location of DPs along the set of design periods as well as decisions on the capacity assignment to calibrate DP throughput capacity. The operational decisions related to transportation are modeled as origin-destination arcs. Subsequently, we propose alternative modeling approaches based on two-stage stochastic programming with recourse, and solve the resulting models using a Benders decomposition approach integrated with a sample average approximation (SAA) technique.Next, we are interested in the last-mile delivery in an urban context where transportation decisions involved in the second echelon are addressed through multi-drop routes. A two-echelon stochastic multi-period capacitated location-routing problem (2E-SM-CLRP) is defined in which facility-location decisions concern both WPs and DPs. We model the problem using a two-stage stochastic program with integer recourse. To solve the 2E-SM-CLRP, we develop a Benders decomposition algorithm. The location and capacity decisions are fixed from the solution of the Benders master problem. The resulting subproblem is a capacitated vehicle-routing problem with capacitated multi-depot (CVRP-CMD) and is solved using a branch-cut-and-price algorithm.Finally, we focus on the multi-stage framework proposed for the stochastic multi-period two-echelon distribution network design problem and evaluate its tractability. A scenario tree is built to handle the set of scenarios representing demand uncertainty. We present a compact formulation and develop a rolling horizon heuristic to produce design solutions for the multi-stage model. It provides good quality bounds in a reasonable computational times.

The aim in this thesis is to develop efficient enumeration algorithms to solve certain strongly NP-hard scheduling problems. These algorithms were developed using a combination of ideas from Integer Programming, Constraint Programming and Scheduling Theory. In order to combine different techniques in one algorithm, decomposition methods are applied. The main idea on which the first part of our results is based is to separate the optimality and feasibility components of the problem and let different methods tackle these components. Then IP is ``responsible' for optimization, whereas specific combinatorial algorithms tackle the feasibility aspect. Branch-and-cut and branch-and-price algorithms based on this idea are proposed to solve the single-machine and multi-machine variants of the scheduling problem to minimize the sum of the weights of late jobs. Experimental research shows that the algorithms proposed outperform other algorithms available in the literature. Also, it is shown that these algorithms can be used, after some modification, to solve the problem of minimizing the maximum tardiness on unrelated machines. The second part of the thesis deals with the one-machine scheduling problem to minimize the weighted total tardiness. To tackle this problem, the idea of a partition of the time horizon into intervals is used. A particularity of this approach is that we exploit the structure of the problem to partition the time horizon. This particularity allowed us to propose two new Mixed Integer Programming formulations for the problem. The first one is a compact formulation and can be used to solve the problem using a standard MIP solver. The second formulation can be used to derive lower bounds on the value of the optimal solution of the problem. These lower bounds are of a good quality, and they can be obtained relatively fast.

This dissertation focuses on extending solution methods in the area of stochastic optimization. Attention is focused to three specific problems in the field. First, a solution method for mixed integer programs subject to chance constraints is discussed. This class of problems serves as an effective modeling framework for a wide variety of applied problems. Unfortunately, chance constrained mixed integer programs tend to be very challenging to solve. Thus, the aim of this work is to address some of these challenges by exploiting the structure of the deterministic reformulation for the problem. Second, a stochastic program for integrating renewable energy sources into traditional energy systems is developed. As the global push for higher utilization of such green resources increases, such models will prove invaluable to energy system designers. Finally, a process for transforming clinical medical data into a model to assist decision making during the treatment planning phase for palliative chemotherapy is outlined. This work will likely provide decision support tools for oncologists. Moreover, given the new requirements for the usage electronic medical records, such techniques will have applicability to other treatment planning applications in the future.

Hub and Spoke systems, is a important research area in localization theory. This occur, because of these systems are very used in logistics problems, e.g., telecommunication networks and transport of passenger and load.To serve the demand of each pair source destination, basically, the Hub and Spoke system replaces direct connections between the pairs for a hubs network. These hubs group the traffic sharing the transportation medium. To get the best hubs configuration is necessary efficient methods, because this problem, hubs allocation, is a NP-problem. In this work was developed an parallel implementation of the Benders Decomposition method for the uncapacitated multiple allocation hub location problem. In our implementation we use the Skorin- Kapov model. The parallel implementation of Benders Decomposition for hub and spoke problem is not known in literature. The results show that the parallel approach is applicable and more efficient that nonparallel one. The experiments reveals that the parallel algorithm had a time execution 70% minor when compared with the nonparallel one. / Sistemas do tipo eixo raio, tornaram-se uma importante área de pesquisa da teoria de localização nas últimas décadas. Esse destaque deve-se em grande parte ao sucesso de sua utilização em sistemas logísticos, tanto de transporte de passageiros quanto de cargas, e em redes de telecomunicações. Ao invés de servir cada par origem destino de demanda com uma conexão direta, sistemas do tipo eixo raio substituem essas conexões diretas por uma rede de concentradores. Esses concentradores permitem que o tráfego seja agrupado e transportado através de um meio de transporte compartilhado, para ser então entregue aos respectivos destinos. Sendo um problema NP, é necessário o uso de métodos eficientes para sua resolução. Neste trabalho, é desenvolvida uma implementação em paralelo do método de Decomposição de Benders para o problema de localização de concentradores de alocação múltipla não capacitados. A implementação em paralelo do método de Decomposição de Benders para o problema eixo raio não é conhecido na literatura, entretanto os bons resultados obtidos pelo algoritmo paralelo desenvolvido revelam que a abordagem paralela é aplicável e mais eficiente. Nos experimentos realizados, o algoritmo paralelo apresentou um tempo de resposta até 70% menor que o tempo de resposta do algoritmo seqüencial.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2018-11-06T17:02:42Z No. of bitstreams: 1 marcelodesouzaaleixo.pdf: 2786878 bytes, checksum: dfbd57d9b8be2153917fe637209df9f0 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-11-23T13:19:16Z (GMT) No. of bitstreams: 1 marcelodesouzaaleixo.pdf: 2786878 bytes, checksum: dfbd57d9b8be2153917fe637209df9f0 (MD5) / Made available in DSpace on 2018-11-23T13:19:16Z (GMT). No. of bitstreams: 1 marcelodesouzaaleixo.pdf: 2786878 bytes, checksum: dfbd57d9b8be2153917fe637209df9f0 (MD5) Previous issue date: 2018-06-29 / Este trabalho apresenta uma metodologia para cálculo da reserva girante do sistema elétrico de potência. A proposta inclui a curva de capabilidade dos geradores bem como cenários de carga e de geração eólica bem como falhas no sistema de geração e transmissão. O fluxo de potência ótimo é utilizado para determinar as condições iniciais do sistema, caso base. A partir daí o problema é resolvido de forma interativa entre dois estágios em umaestruturamestreeescravo: Oproblemamestreutilizaprogramaçãolinearinteirapara determinar o número mínimo de unidades de geração disponíveis (ligadas); O problema escravo verifica se o número de unidades ligadas é suficiente para operação do sistema. Este problema corresponde ao Fluxo de Potência Ótimo com o objetivo de obter o mínimo corte de carga para cada condição operativa. O corte de Benders é produzido para cada cenário, altenativamente, será investigado a utilização da média dos cortes de Benders. O processo termina quando não ocorrer corte de carga. A metodologia é testada utilizando um sistema teste de 4 barras como exemplo tutorial e também aplicada nos sistemas IEEE 14, 39 e 118 barras. / This work presents a methodology for calculating the spinning reserve of the electric power system. The proposal includes the capability curve of the generators as well as errors of prediction of load, wind generation, failures in the system of generation and transmission. The optimal power flow is used to determine the initial conditions of the system, base case. From this point the problem is solved interactively between two stages in a master and slave structure: The first uses integer linear programming to determine the minimum number of available (turn on) generation units; The second corresponds to the Optimum Power Flow with the purpose of obtaining the minimum load shedding for each operative condition. The cut of Benders is produced for each scenario, alternatively, the use of the average of cuts will be investigated. The process ends when there is no load shedding. The methodology is tested using a 4-bar test system as a tutorial example and also applied in IEEE systems 14, 39 and 118 bars.

In this dissertation, we address three different combinatorial optimization problems (COPs), each of which has specific real-life applications. Owning to their specific nature, these problems are different from those discussed in the literature. For each of these problems, we present a mathematical programming formulation, analyze the problem to determine its useful, inherent structural properties, and develop an efficient methodology for its solution by exploiting these properties. The first problem that we address is the course timetabling problem encountered at Virginia Tech. The course timetabling problem for a university is a difficult problem and has been studied by many researchers over the years. As a result, a plethora of models and approaches have been reported in the literature. However, most of these studies have focused on applications pertaining to course scheduling for a single or at most few departments of a university. The sheer size of the university-wide timetabling problem that we address, involving thousands of courses to be scheduled in hundreds of classrooms in each semester, makes it a challenging problem. We employ an appropriate decomposition technique that relies on some inherent structural properties of the problem both during the modeling and algorithmic development phases. We show the superiority of the schedules generated by our methodology over those that are currently being used. Also, our methodology requires only a reasonable amount of computational time in solving this large-size problem. A facility layout problem involving arbitrary-shaped departments is the second problem that we investigate in this dissertation. We designate this problem as the arbitrary-shaped facility layout problem (ASFLP). The ASFLP deals with arranging a given set of departments (facilities, workstations, machines) within the confines of a given floor space, in order to optimize a desired metric, which invariably relates to the material handling cost. The topic of facility planning has been addressed rather extensively in the literature. However, a major limitation of most of the work reported in the literature is that they assume the shape of a department to be a rectangle (or even a square). The approach that relies on approximating an arbitrary-shaped department by a rectangle might result in an unattractive solution. The key research questions for the ASFLP are: (1) how to accurately model the arbitrary-shaped departments, and (2) how to effectively and efficiently determine the desired layout. We present a mixed-integer programming model that maintains the arbitrary shapes of the departments. We use a meta-heuristic to solve the large-size instances of the ASFLP in a reasonable amount of time. The third problem that we investigate is a supply chain scheduling problem. This problem involves two stages of a supply chain, specifically, a manufacturer and one or more customers. The key issue is to achieve an appropriate coordination between the production and distribution functions of the manufacturer so as to minimize the sum of the shipping and job tardiness costs. We, first, address a single customer problem, and then, extend our analysis to the case of multiple customers. For the single-customer problem, we present a polynomial-time algorithm to solve it to optimality. For the multiple-customer problem, we prove that this problem is NP-hard and solve it by appropriately decomposing it into subproblems, one of which is solvable in polynomial time. We propose a branch-and-bound-based methodology for this problem that exploits its structural properties. Results of an extensive computational experimentation are presented that show the following: (1) our algorithms are efficient to use and effective to implement; and (2) significant benefits accrue as a result of integrating the production and distribution functions. / Ph. D.

This dissertation develops mathematical models to efficiently manage the inland waterway port operations while minimizing the overall supply chain cost. In the first part, a capacitated, multi-commodity, multi-period mixed-integer linear programming model is proposed capturing diversified inland waterway transportation network related properties. We developed an accelerated Benders decomposition algorithm to solve this challenging NP-hard problem. The next study develops a two-stage stochastic mixed-integer nonlinear programming model to manage congestion in an inland waterway transportation network under stochastic commodity supply and water-level fluctuation scenarios. The model also jointly optimizes trip-wise towboat and barge assignment decisions and different supply chain decisions (e.g., inventory management, transportation decisions) in such a way that the overall system cost can be minimized. We develop a parallelized hybrid decomposition algorithm, combining Constraint Generation algorithm, Sample Average Approximation (SAA), and an enhanced variant of the L-shaped algorithm, to effectively solve our proposed optimization model in a timely fashion. While the first two parts develop models from the supply chain network design viewpoint, the next two parts propose mathematical models to emphasize the port and waterway transportation related operations. Two two-stage, stochastic, mixed-integer linear programming (MILP) models are proposed under stochastic commodity supply and water level fluctuations scenarios. The last one puts the specific focus in modeling perishable inventories. To solve the third model we propose to develop a highly customized parallelized hybrid decomposition algorithm that combines SAA with an enhanced Progressive Hedging and Nested Decomposition algorithm. Similarly, to solve the last mathematical model we propose a hybrid decomposition algorithm combining the enhanced Benders decomposition algorithm and SAA to solve the large size of test instances of this complex, NP-hard problem. Both proposed approaches are highly efficient in solving the real-life test instances of the model to desired quality within a reasonable time frame. All the four developed models are validated a real-life case study focusing on the inland waterway transportation network along the Mississippi River. A number of managerial insights are drawn for different key input parameters that impact port operations. These insights will essentially help decisions makers to effectively and efficiently manage an inland waterway-based transportation network.

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