We define an order cutoff for a retailer as a time in the day such that orders sent to the depot before this point will be delivered by tomorrow, and orders submitted after will be delivered by the day after tomorrow. The later a retailer’s cutoff, the sooner it receives its orders which helps it to maintain ideal inventory levels. Generally, not all retailers in a supply chain can have the latest cutoff since transportation takes a significant amount of time. This thesis tries to assign optimal order cutoffs to retailers. We call this an order cutoff assignment problem and we solve it using three different mathematical programming approaches. The approaches are exhaustive route generation and selection, a series of mixed integer programs, and branch-and-price. 60 sample problems were solved and results showed that branch-and-price is often the most effective method.

This dissertation considers daily operations management for a fleet of trucks providing container pickup and delivery service to a port. Truck congestion at access points for ports may lead to serious inefficiencies in drayage operations, and the resultant cost impact to the intermodal supply chain can be significant. Recognizing that port congestion is likely to continue to be a major problem for drayage operations given the growing volume of international containerized trade, this research seeks to develop optimization approaches for maximizing the productivity of drayage firms operating at congested seaports. Specifically, this dissertation addresses two daily drayage routing and scheduling problems. In the first half of this dissertation, we study the problem of managing a fleet of trucks providing container pickup and delivery service to a port facility that experiences different access wait times depending on the time of day. For this research, we assume that the wait time can be estimated by a deterministic function. We develop a time-constrained routing and scheduling model for the problem that incorporates the time-dependent congestion delay function. The model objective is to find routes and schedules for drayage vehicles with minimum total travel time, including the waiting time at the entry to the port due to congestion. We consider both exact and heuristic solution approaches for this difficult optimization problem. Finally, we use the framework to develop an understanding of the potential impact of congestion delays on drayage operations, and the value of planning with accurate delay information. In the second half of this dissertation, we study methods for managing a drayage fleet serving a port with an appointment-based access control system. Responding to growing access congestion and its resultant impacts, many U.S. port terminals have implemented appointment systems, but little is known about the impact of such systems on drayage productivity. To address this knowledge gap, we develop a drayage operations optimization approach based on a column generation integer programming heuristic that explicitly models a time-slot port access control system. The approach determines pickup and delivery sequences with minimum transportation cost. We use the framework to develop an understanding of the potential efficiency impacts of access appointment systems on drayage operations. Findings indicate that the set of feasible drayage tasks and the fleet size required to complete them can be quite sensitive to small changes in time-slot access capacities at the port.

Home healthcare has been a growing sector of the economy over the last three decades with roughly 23,000 companies now doing business in the U.S. producing over $56 billion in combined annual revenue. As a highly fragmented market, profitability of individual companies depends on effective management and efficient operations. This dissertation aims at reducing costs and improving productivity for home healthcare companies. The first part of the research involves the development of a new formulation for the therapist routing and scheduling problem as a mixed integer program. Given the time horizon, a set of therapists and a group of geographically dispersed patients, the objective of the model is to minimize the total cost of providing service by assigning patients to therapists while satisfying a host of constraints concerning time windows, labor regulations and contractual agreements. This problem is NP-hard and proved to be beyond the capability of commercial solvers like CPLEX. To obtain good solutions quickly, three approaches have been developed that include two heuristics and a decomposition algorithm. The first approach is a parallel GRASP that assigns patients to multiple routes in a series of rounds. During the first round, the procedure optimizes the patient distribution among the available therapists, thus trying to reach a local optimum with respect to the combined cost of the routes. Computational results show that the parallel GRASP can reduce costs by 14.54% on average for real datasets, and works efficiently on randomly generated datasets. The second approach is a sequential GRASP that constructs one route at a time. When building a route, the procedure tracks the amount of time used by the therapists each day, giving it tight control over the treatment time distribution within a route. Computational results show that the sequential GRASP provides a cost savings of 18.09% on average for the same real datasets, but gets much better solutions with significantly less CPU for the same randomly generated datasets. The third approach is a branch and price algorithm, which is designed to find exact optima within an acceptable amount of time. By decomposing the full problem by therapist, we obtain a series of constrained shortest path problems, which, by comparison are relatively easy to solve. Computational results show that, this approach is not efficient here because: 1) convergence of Dantzig-Wolfe decomposition is not fast enough; and 2) subproblem is strongly NP-hard and cannot be solved efficiently. The last part of this research studies a simpler case in which all patients have fixed appointment times. The model takes the form of a large-scale mixed-integer program, and has different computational complexity when different features are considered. With the piece-wise linear cost structure, the problem is strongly NP-hard and not solvable with CPLEX for instances of realistic size. Subsequently, a rolling horizon algorithm, two relaxed mixed-integer models and a branch-and-price algorithm were developed. Computational results show that, both the rolling horizon algorithm and two relaxed mixed-integer models can solve the problem efficiently; the branch-and-price algorithm, however, is not practical again because the convergence of Dantzig-Wolfe decomposition is slow even when stabilization techniques are applied. / text

With recent and continuing advances in bioinformatics, the volume of sequence data has increased tremendously. Along with this increase, there is a growing need to develop efficient algorithms to process such data in order to make useful and important discoveries. Careful analysis of genomic data will benefit science and society in numerous ways, including the understanding of protein sequence functions, early detection of diseases, and finding evolutionary relationships that exist among various organisms. Most sequence analysis problems arising from computational genomics and evolutionary biology fall into the class of NP-complete problems. Advances in exact and approximate algorithms to address these problems are critical. In this thesis, we investigate a novel graph theoretical model that deals with fundamental evolutionary problems. The model allows incorporation of the evolutionary operations ``insertion', ``deletion', and ``substitution', and various parameters such as relative distances and weights. By varying appropriate parameters and weights within the model, several important combinatorial problems can be represented, including the weighted supersequence, weighted superstring, and weighted longest common sequence problems. Consequently, our model provides a general computational framework for solving a wide variety of important and difficult biological sequencing problems, including the multiple sequence alignment problem, and the problem of finding an evolutionary ancestor of multiple sequences. In this thesis, we develop large scale combinatorial optimization techniques to solve our graph theoretical model. In particular, we formulate the problem as two distinct but related models: constrained network flow problem and weighted node packing problem. The integer programming models are solved in a branch and bound setting using simultaneous column and row generation. The methodology developed will also be useful to solve large scale integer programming problems arising in other areas such as transportation and logistics.

Au cours de ces dernières décennies,au fur et à mesure de l’augmentation du trafic, l’espace aérien a été divisé en secteurs de plus en plus petits afin d’éviter la saturation de ces derniers. Ce principe de sectorisation présente une limite dans la mesure où l’on doit ménager un temps suffisant au contrôleur pour gérer son trafic et donc générer des secteurs dont la taille permet de satisfaire cette contrainte. De plus, le contrôleur ne connaît que le trafic lié à son secteur et lorsqu’un avion passe d’un secteur à un autre,il s’opère un dialogue entre les contrôleurs et les pilotes qui induit une charge de travail supplémentaire(coordination).Au cours d’une journée de trafic ordinaire,la charge de contrôle fluctue dans le temps en fonction des demandes de trafic entre les diverses paires origine-destination. Dans le système opérationnel actuel, le nombre de contrôleurs varie en fonction des fluctuations de trafic. La nuit par exemple, le nombre d’équipes de contrôle est réduit car il y a beaucoup moins de trafic.Les secteurs sont alors regroupés en groupe de trois à quatre avant attribution à une équipe de contrôleurs. Il est donc nécessaire d’optimiser la planification sur une journée du schéma de regroupement et de dégroupement des secteurs: resectorisation dynamique de l’espace aérien. Un des objectifs est de fournir des groupes de secteurs présentant un minimum de coordinations et équilibrés en terme de charge de contrôle afin que chaque équipe de contrôleurs travaille de la même façon. Les instants de commutation entre configurations de secteurs en fonction des fluctuations de trafic doivent être déterminés, et les distances entre configurations successives doivent être prises en compte afin d’éviter des changements brusques au sein d’un espace aérien donné. Le développement d’un algorithme efficace pour résoudre le problème dynamique résultant est d’autant plus important que le trafic aérien est amené évoluer de manière significative au cours des années qui viennent. / The current airspace configuration is highly structured, fixed and is less responsive to changes causing the overall system to lack the flexibility, adaptability, and responsibility needed to handle the increasing air traffic demands in the near future. The work presented in this thesis aims at improving the flexibility and adaptability of today's airspace management in Europe in a pretactical context. We focus on the development of a method to support a process of automatic generation of a sequence of sector configurations composed of predefined sectors. Airspace configurations should be dynamically adjusted to provide maximum efficiency and flexibility in response to demand fluctuations. We dynamically build configurations by combining existing elementary sectors. In this step, any sector combination which forms controllable airspace blocks is eligible and may be used during the day of operation. In this work, we developed efficient methods to solve DAC problem. We formulated and study the sectorization problem from an algorithmic point of view. We proposed methods based on a mathematical modeling and heuristic optimization techniques. We also introduced here an approach to evaluate the workload inside sectors.

abstract: Vehicles powered by electricity and alternative-fuels are becoming a more popular form of transportation since they have less of an environmental impact than standard gasoline vehicles. Unfortunately, their success is currently inhibited by the sparseness of locations where the vehicles can refuel as well as the fact that many of the vehicles have a range that is less than those powered by gasoline. These factors together create a "range anxiety" in drivers, which causes the drivers to worry about the utility of alternative-fuel and electric vehicles and makes them less likely to purchase these vehicles. For the new vehicle technologies to thrive it is critical that range anxiety is minimized and performance is increased as much as possible through proper routing and scheduling. In the case of long distance trips taken by individual vehicles, the routes must be chosen such that the vehicles take the shortest routes while not running out of fuel on the trip. When many vehicles are to be routed during the day, if the refueling stations have limited capacity then care must be taken to avoid having too many vehicles arrive at the stations at any time. If the vehicles that will need to be routed in the future are unknown then this problem is stochastic. For fleets of vehicles serving scheduled operations, switching to alternative-fuels requires ensuring the schedules do not cause the vehicles to run out of fuel. This is especially problematic since the locations where the vehicles may refuel are limited due to the technology being new. This dissertation covers three related optimization problems: routing a single electric or alternative-fuel vehicle on a long distance trip, routing many electric vehicles in a network where the stations have limited capacity and the arrivals into the system are stochastic, and scheduling fleets of electric or alternative-fuel vehicles with limited locations to refuel. Different algorithms are proposed to solve each of the three problems, of which some are exact and some are heuristic. The algorithms are tested on both random data and data relating to the State of Arizona. / Dissertation/Thesis / Ph.D. Industrial Engineering 2014

This study considers a vehicle routing problem with time windows, accessibility restrictions on customers and a fleet that is heterogeneous with regard to capacity, average speed and cost. A vehicle can perform multiple routes per day, all starting and ending at a single depot, and it is assigned to a single driver, whose total work hours are limited. The available fleet is divided into an owned fleet, for which a variable cost is incurred, and a chartered fleet, for which only a fixed cost is incurred for each vehicle used. A column generation algorithm embedded in a branch-and-bound framework is proposed. The column generation pricing subproblem required a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performing multiple routes per day and to address the need to determine the workdays start time within the planning horizon. To make the algorithm efficient, a constructive heuristic and a learning metaheuristic algorithm based on tabu search were also developed. Both were used on branch-and-bound tree nodes to generate a good initial solution to the linear restricted master problem; particularly, to find a good initial primal bound to the branch-and-bound tree. / Este estudo aborda um problema de roteirização de veículos com janelas de tempo, restrições de acessibilidade nos clientes e uma frota que é heterogênea em relação à capacidade de carga, velocidade média de deslocamento e custo. Um veículo pode percorrer múltiplas rotas por dia, todas começando e terminando em um mesmo depósito, e está designado a um único motorista, cujo total de horas trabalhadas no dia está limitado a um valor máximo. A frota disponível é dividida em uma frota própria, para a qual um custo variável é incorrido, e uma frota de freteiros, para a qual apenas um custo fixo é incorrido para cada veículo utilizado. Um algoritmo baseado em geração de colunas, integrado a um procedimento de branch-and-bound, é proposto neste estudo. O subproblema de precificação da geração de colunas requereu um algoritmo específico para o problema do caminho mínimo elementar com restrições sobre recursos capaz de lidar com a possibilidade de cada veículo percorrer múltiplas rotas por dia e capaz de lidar com a necessidade de determinar o instante de início do dia de trabalho do motorista dentro do horizonte de planejamento. Para tornar o algoritmo eficiente, uma heurística construtiva e uma heurística de melhoria baseada em busca tabu também foram desenvolvidos. Ambos são utilizados nos nós da árvore de branch-and-bound para gerar boas soluções iniciais para o problema mestre restrito da geração de colunas; particularmente, para encontrar um bom limitante primal inicial para a árvore de branch-and-bound.

O planejamento de rotações de culturas é um tema de interesse em ascensão por permitir uma redução significativa no uso de adubos industriais, agrotóxicos e outros produtos químicos no cultivo, permitindo a auto-sustentação e qualidade das terras cultivadas. Este trabalho centraliza em utilizar rotações para atender uma demanda periódica prédeterminada, respeitando as restrições relativas a aspectos ecológicos que auxiliam na estabilidade geral do solo para definir uma rotação de culturas factível. Modelos matemáticos que consideram um tamanho mínimo de lote a ser usado por uma rotação e métodos heurísticos, baseados em geração de colunas, são apresentados. Uma análise detalhada do comportamento dos métodos perante variações em diferentes parâmetros e critérios é realizada. A primeira heurística, denominada Algoritmo GC-BC, obteve resultados de melhor qualidade e de forma mais rápida que a segunda heurística, denominada Heurística Lote Fixo. Entretanto, combinando ambas heurísticas foi possível obter os resultados mais satisfatórios, ou seja, soluções que respeitam a condição de lote mínimo em um tempo computacional aceitável para um planejamento anual, cujos valores são próximos a um limitante superior. A ideia subjacente de gerar colunas adicionais para um problema mestre restrito produz soluções de qualidade, o que pode vir a ser aplicado em outras áreas de pesquisa que necessitam da geração de colunas para uma resolução em tempo computacional viável / The crop rotation planning is a rising topic for providing a significative reduction on the usage of industrial fertilizers, pesticides and other chemical, allowing the soil to selfsustain. This study focus on using rotations to meet a periodic and pre-defined demand while ecologic restrictions, that help sustain the soils stability, define a valid crop rotation. Mathematical models that consider a minimum size of a used lot associated with a given rotation and heuristic resolution methods, based on column generation, are presented. A detailed analysis of the methods behaviour before changes on parameters and criteria is performed. The first heuristic, called GC-BC Algorithm, achieved better and faster results compared to the second heuristic, called Fixed Lot Heuristic. However, combining both heuristics produced even better results, that is, solutions that respect the minimum lot sizing restrictions in good execution time for an annual planning. The idea behind of generating additional columns to the restricted master problem produces good quality solutions, which may be applicable in other research areas that require column generation for their resolution with a reasonable execution time

Nas últimas décadas, diversas propostas de técnicas e de processos visando aumentar a sustentabilidade da agricultura ganharam evidência. Tais propostas geram novos modelos de planejamento em que devem ser considerados aspectos técnicos e ecológicos de produção, bem como o acesso de pequenos agricultores familiares ao mercado consumidor. Neste tipo de planejamento da produção, a rotação de culturas desempenha um papel fundamental, pois contribui para a manutenção dos recursos produtivos, para a minimização do uso de recursos não-renováveis e para o controle biológico da população de herbívoros, patógenos e plantas espontâneas. Nesta tese abordamos dois problemas de Programação de Rotação de Culturas (PRC) focados na produção de base sustentável de hortaliças: o problema de PRC com restrições de Adjacências (PRC-A) e o problema de PRC com atendimento da Demanda (PRC-D). O planejamento da produção de hortaliças é complexo pois envolve, em geral, um grande número de culturas com limitações específicas quanto à época de plantio e com períodos de cultivo e produtividades muito variáveis. A programação de rotação de culturas para as áreas de plantio é formulada como um modelo de otimização 01 e, para os dois problemas, em cada programação considera se tanto aspectos técnicos (época de plantio e colheita etc.) quanto ecológicos (adubação verde, pousio etc.). No problema PRC-A o objetivo é a maximização da ocupação das áreas produtivas em que as restrições de plantio são estendidas às áreas adjacentes. Como a formulação matemática para o problema tem, em geral, um número muito grande de restrições e variáveis, com matriz de restrições esparsa e bloco-diagonal, o modelo é reformulado com a Decomposição DantzigWolfe, o que permitiu sua resolução por procedimentos baseados em geração de colunas, heurísticos e exatos. No problema PRC-D desejase suprir a demanda de um conjunto de hortaliças tendo-se disponível um conjunto de áreas heterogêneas. As culturas passíveis de plantio, bem como as suas produtividades, dependem da área considerada. O problema foi formulado como um modelo de otimização linear em que cada variável está associada a uma programação de rotação de culturas. O modelo contém potencialmente um número grande de programações de rotação e é resolvido por geração de colunas. Experimentos computacionais usando instâncias baseadas em dados reais confirmam a eficácia dos modelos e das metodologias propostos para os problemas / Over the last decades, various proposals for techniques and processes to increase agricultural sustainability have been put forward. These proposals bring new planning models in which technical and ecological production aspects must be considered, as well as the access of small farmers to the consumer market. In this type of agricultural production planning, crop rotation plays a fundamental role as it contributes to maintaining productive resources, to reducing the use of non-renewable resources, and to biologically controlling the population of herbivores, pathogens and spontaneous plants. In this thesis, two problems concerning the Crop Rotation Schedule (CRS) focusing on sustainable production vegetables are addressed: the problem of the CRS having Adjacent constraints (CRS-A) and the problem of the CRS under Demand constraints (CRS-D). Production planning of vegetables is complex as it generally involves a large number of crop species having specific limitations regarding the planting season and very varied production times and productivity. The crop rotation schedule problem is formulated as an optimization model 0-1, and for both problems, in each schedule technical (planting and harvesting season etc.) and ecological (green manure, fallow etc.) aspects are considered. Concerning the CRS-A problem, the aim is to maximize the occupation of cropping areas in which planting constraints are extended to adjacent areas. As the mathematical formulation for the problem generally has a large number of restrictions and variables and the structure of the constraint matrix of the problem is sparse and block-diagonal, the model has been reformulated using the Dantzig-Wolfe Decomposition strategy, which has enabled the use of a heuristic and exact procedures based on the column generation approach for its resolution. In the CRS-D problem, the aim is to meet the market demands for vegetables having a set of heterogeneous cropping areas available. The potential planting crops, as well as their productivity, depend on the considered cropping area. The problem is formulated as an optimization linear model in which each variable is associated to a crop rotation schedule. The model may include a large number of rotation schedules and is solved by the column generation approach. Computational experiments using instances based on real-world data confirm the efficiency of models and methodologies proposed for the problems

Major cyber attacks against the cyber networks of organizations has become a common phenomenon nowadays. Cyber attacks are carried out both through the spread of malware and also through multi-stage attacks known as hacking. A cyber network can be represented directly as a simple directed or undirected network (graph) of nodes and arcs. It can also be represented by a transformed network such as the attack graph which uses information about network topology, attacker profile, and existing vulnerabilities to represent all the potential attack paths from readily accesible vulnerabilities to valuable target nodes. Then, interdicting or hardening a subset of arcs in the network naturally maps into deploying security countermeasures on the associated devices or connections. In this dissertation, we develop network interdiction models and algorithms to optimally select a subset of arcs which upon interdiction minimizes the spread of infection or minimizes the loss from multi-stage attacks. In particular, we define four novel network connectivity-based metrics and develop interdiction models to optimize the metrics. Direct network representation of the physical cyber network is used as the underlying network in this case. Two of the interdiction models prove to be very effective arc removal methods for minimizing the spread of infection. We also develop multi-level network interdiction models that remove a subset of arcs to minimize the loss from multi-stage attacks. Our models capture the defenderattacker interaction in terms of stackelberg zero-sum games considering the attacker both as a complete rational and bounded rational agents. Our novel solution algorithms based on constraint and column generation and enhanced by heuristic methods efficiently solve the difficult multi-level mixed-integer programs with integer variables in all levels in reasonable times.