Pour les opérateurs, les réseaux FTTH représentent à la fois la solution de référence pour répondre à la demande croissante de trafic fixe, et un investissement considérable dû à leur mise en place. Le but de ces travaux est d'assurer le déploiement de réseaux de qualité à moindre coût. Nous commençons à présenter les différents aspects de la planification de ces réseaux qui en font un problème complexe. La littérature concernée est abordée afin d'exhiber les nouveaux défis que nous relevons. Puis nous élaborons des stratégies permettant de trouver la meilleure solution dans différents contextes. Plusieurs politiques de maintenance ou d'utilisation du génie civil sont ainsi explorées. Les problèmes rencontrés sont analysés à la lumière de divers outils d'optimisation (programmation entière, inégalités valides, programmation dynamique, approximations, complexités, inapproximabilité...) que nous utilisons et développons selon nos besoins. Les solutions proposées ont été testées et validées sur des instances réelles, et ont pour but d'être utilisées par Orange / For operators, FTTH networks are the most widespread solution to the increasing traffic demand. Their layout requires a huge investment. The aim of this work is to ensure a cost effective deployment of quality networks. We start by presenting aspects of this network design problem which make it a complex problem. The related literature is reviewed to highlight the novel issues that we solve. Then, we elaborate strategies to find the best solution in different contexts. Several policies regarding maintenance or civil engineering use will be investigated. The problems encountered are tackled using several combinatorial optimization tools (integer programming, valid inequalities, dynamic programming, approximations, complexity theory, inapproximability…) which will be developed according to our needs. The proposed solutions were tested and validated on real-life instances, and are meant to be implemented in a network planning tool from Orange

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Integer programs (IPs) are mathematical models that can provide an optimal solution to a variety of different problems. They have been used to reduce costs and optimize organizations. Additionally, IPs are NP-complete resulting in many IPs that cannot be solved. Cutting planes or valid inequalities have been used to decrease the time required to solve IPs. Lifting is a technique that strengthens existing valid inequalities. Lifting inequalities can result in facet defining inequalities, which are the theoretically strongest valid inequalities. Because of these properties, lifting procedures are used in software to reduce the time required to solve an IP. The thesis introduces a new algorithm for exact synchronized simultaneous uplifting over an arbitrary initial inequality for knapsack problems. Synchronized Simultaneous Lifting (SSL) is a pseudopolynomial time algorithm requiring O(nb+n[superscript]3) effort to solve. It exactly uplifts two sets simultaneously into an initial arbitrary valid inequality and creates multiple inequalities of a particular form. This previously undiscovered class of inequalities generated by SSL can be facet defining. A small computational study shows that SSL is quick to execute, requiring on average less than a quarter of a second. Additionally, applying SSL inequalities to a knapsack problem enabled commercial software to solve problems that it could not solve without them.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Integer programs (IP) are used in companies and organizations across the world to reach financial and time-related goals most often through optimal resource allocation and scheduling. Unfortunately, integer programs are computationally difficult to solve and in some cases the optimal solutions are unknown even with today’s advanced computing machines. Lifting is a technique that is often used to decrease the time required to solve an IP to optimality. Lifting begins with a valid inequality and strengthens it by changing the coefficients of variables in the inequality. Often times, this technique can result in facet defining inequalities, which are the theoretically strongest inequalities. This thesis introduces a new type of lifting called synchronized simultaneous lifting (SSL). SSL allows for multiple sets of simultaneously lifted variables to be simultaneously lifted which generates a new class of inequalities that previously would have required an oracle to be found. Additionally, this thesis describes an algorithm to perform synchronized simultaneous lifting for a binary knapsack inequality called the Synchronized Simultaneous Lifting Algorithm (SSLA). SSLA is a quadratic time algorithm that will exactly simultaneously lift two sets of simultaneously lifted variables. Short computational studies show SSLA can sometimes solve IPs to optimality that CPLEX, an advanced integer programming solver, alone cannot solve. Specifically, the SSL cuts allowed a 76 percent improvement over CPLEX alone.

The primary aim of this thesis is to develop effective solution techniques for large-scale maritime inventory routing problems that possess a core substructure common in many real-world applications. We use the term “large-scale” to refer to problems whose standard mixed-integer linear programming (MIP) formulations involve tens of thousands of binary decision variables and tens of thousands of constraints and require days to solve on a personal computer. Although a large body of literature already exists for problems combining vehicle routing and inventory control for road-based applications, relatively little work has been published in the realm of maritime logistics. A major contribution of this research is in the advancement of novel methods for tackling problems orders of magnitude larger than most of those considered in the literature. Coordinating the movement of massive vessels all around the globe to deliver large quantities of high value products is a challenging and important problem within the maritime transportation industry. After introducing a core maritime inventory routing model to aid decision-makers with their coordination efforts, we make three main contributions. First, we present a two-stage algorithm that exploits aggregation and decomposition to produce provably good solutions to complex instances with a 60-period (two-month) planning horizon. Not only is our solution approach different from previous methods discussed in the maritime transportation literature, but computational experience shows that our approach is promising. Second, building on the recent successes of approximate dynamic programming (ADP) for road-based applications, we present an ADP procedure to quickly generate good solutions to maritime inventory routing problems with a long planning horizon of up to 365 periods. For instances with many ports (customers) and many vessels, leading MIP solvers often require hours to produce good solutions even when the planning horizon is limited to 90 periods. Our approach requires minutes. Our algorithm operates by solving many small subproblems and, in so doing, collecting and learning information about how to produce better solutions. Our final research contribution is a polyhedral study of an optimization problem that was motivated by maritime inventory routing, but is applicable to a more general class of problems. Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in a distribution network so that they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) that we study captures a core structure encountered in many of these environments. We model the FCTPwB as a mixed-integer linear program and derive two classes of facets, both exponential in size, for the convex hull of solutions for the problem with a single consumer and show that they can be separated in polynomial time. Finally, a computational study demonstrates that these classes of facets are effective in reducing the integrality gap and solution time for more general instances of the FCTPwB.

Approved for public release, distribution is unlimited / We optimize long-term project schedules subject to annual budget constraints, where the duration and cost of each task may increase as the project progresses. Initially, tasks are scheduled without regard to budgets and the project completion time is minimized. Treating the task durations as random variables, we then use simulation to describe the distribution of the project completion time. Next, we minimize the completion time under budget constraints with fixed task durations, where budget violations are tolerated albeit with penalties. Annual reviews are then introduced, which allow underway tasks to be delayed or monthly budgets to be increased. We obtain estimates of the completion time of the project and its final cost under each of these scenarios. The U.S. Army Future Combat Systems (FCS) is used for illustration. FCS is a suite of information technologies, sensors, and command systems with an estimated acquisition cost of over $90 billion. The U.S. General Accounting Office found that FCS is at risk of substantial cost overrun and delay. We analyze three schedule plans for FCS to identify which can be expected to deliver the earliest completion time and the least cost. / Major, Australian Army

In this dissertation, we leverage predictive and prescriptive analytics to develop decision support systems to promote the use of renewable energy in society. Since electricity from renewable energy sources is still relatively expensive, there are variety of financial incentive programs available in different regions. Our research focuses on financial incentive programs and tackles two main problem: 1) how to optimally design and control hybrid renewable energy systems for residential and commercial buildings given the capacity based and performance based incentives, and 2) how to develop a model-based system for policy makers for designing optimal financial incentive programs to promote investment in net zero energy (NZE) buildings. In order to customize optimal investment and operational plans for buildings, we developed a mixed integer program (MIP). The optimization model considers the load profile and specifications of the buildings, local weather data, technology specifications and pricing, electricity tariff, and most importantly, the available financial incentives to assess the financial viability of investment in renewable energy. It is shown how the MIP model can be used in developing customized incentive policy designs and controls for renewable energy system.

In this thesis, we propose novel optimization and spatial queueing models that expand the currently existing methods by allowing multiple servers to be located at the same station and multiple servers to be dispatched to a single call. In particular, a mixed integer linear programming (MILP) model is introduced that determines how to locate and dispatch ambulances such that the coverage level is maximized. The model allows multiple servers to be located at the same station and balances the workload among them while maintaining contiguous first priority response districts. We also propose an extension to the approximate Hypercube queueing model by allowing multi-server dispatches. Computational results suggest that both models are effective in optimizing and analyzing the emergency systems. We also introduce the M[G]/M/s/s queueing model as an extension to the M/M/s/s model which allows for multiple servers to be assigned to a single customer.

Les travaux de cette thèse sont les fruits de collaboration depuis 2008 entre l’ICL et le Centre Ingénierie et Santé (CIS) de l'Ecole des Mines de Saint Etienne. CIS et ICL sont tous deux membres de l'Institut Fédératif de Recherche en Science, Ingénierie et Santé (IFRESIS) et participent tous deux aux travaux du Cancéropôle Lyon Auvergne Rhône-Alpes (CLARA) dont Franck Chauvin animait l'axe IV sur Epidémiologie, SHS, Information du Patient et Organisation des Soins. Cette thèse a été initiée avec la volonté de développer une recherche originale sur l'optimisation de la production de soins en cancérologie.Nous nous intéressons à différentes problématiques de la gestion de soins des patients dans un hôpital de jour en cancérologie. Nous visons à équilibrer au mieux les besoins journaliers en lits tout en prenant en compte l'adhérence aux protocoles de soins, les contraintes des oncologues et les aléas des flux de patients. Pour un hôpital de jour en oncologie, nous avons identifié et étudié les décisions suivantes : I. Le planning médical une fois par an afin de déterminer les périodes de travail des oncologues dans une semaine. Nous avons proposé une formulation originale sous forme d'un modèle de programmation linéaire en nombres mixtes (MIP) et une approche en 3-étapes. II. L’affectation des nouveaux patients qui détermine le jour de la chimiothérapie pour chaque patient entrant. Nous avons présenté trois stratégies de planification et nous avons décrit un algorithme de simulation pour évaluer ces stratégies de planification. Les stratégies de planification proposées exploitent les informations contenues dans les protocoles de soins des patients et utilisent l’optimisation Monte Carlo III. La planification des rendez-vous. Nous avons présenté deux méthodes pour la résolution de ce problème : une approche basée sur la relaxation Lagrangienne et une heuristique basée sur une optimisation par recherche localeIV. La planification des jours fériés : permet de remédier au problème des semaines comportant des jours fériés. Nous avons développé un modèle en programmation linéaire en nombres mixtes permettant de répartir rapidement la charge du jour férié sur les jours en amont et en aval sans trop dégradé l’efficacité du traitement, ni surcharger le travail de l’HDJ. / This research is performed in close collaboration with the cancer center ICL. The « Institut de Cancérologie de la Loire » (Loire Cancer Institute), a.k.a. ICL, is a French public comprehensive cancer center providing oncology.This thesis addresses the problem of determining the work schedule, called medical planning, of oncologists for chemotherapy of oncology patients at ambulatory care units. A mixed integer programming (MIP) model is proposed for medical planning in order to best balance bed capacity requirements under capacity constraints of key resources such as beds and oncologists. The most salient feature of the MIP model is the explicit modeling of specific features of chemotherapy such as treatment protocols. The medical planning problem is proved to be NP-complete. A three-stage approach is proposed for determining good medical planning in reasonable computational time.

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Todd Easton / Integer Programming is used to solve numerous optimization problems. This class of mathematical models aims to maximize or minimize a cost function restricted to some constraints and the solution must be integer. One class of widely studied Integer Program (IP) is the Multiple Knapsack Problem (MKP). Unfortunately, both IPs and MKPs are NP-hard, potentially requiring an exponential time to solve these problems. Utilization of cutting planes is one common method to improve the solution time of IPs. A cutting plane is a valid inequality that cuts off a portion of the linear relaxation space. This thesis presents a new class of cutting planes referred to as merged knapsack cover inequalities (MKCI). These valid inequalities combine information from a cover inequality with a knapsack constraint to generate stronger inequalities. Merged knapsack cover inequalities are generated by the Merging Knapsack Cover Algorithm (MKCA), which runs in linear time. These inequalities may be improved by the Exact Improvement Through Dynamic Programming Algorithm (EITDPA) in order to make them stronger inequalities. Theoretical results have demonstrated that this new class of cutting planes may cut off some space of the linear relaxation region. A computational study was performed to determine whether implementation of merged knapsack cover inequalities is computationally effective. Results demonstrated that MKCIs decrease solution time an average of 8% and decrease the number of ticks in CPLEX, a commercial IP solver, approximately 4% when implemented in appropriate instances.

O Serviço de Gerenciamento de Fluxo de Tráfego Aéreo (ATFM) estabelece um controle de fluxo seguro, ordenado e eficiente de acordo com a capacidade da infraestrutura e dos serviços de controle. O Gerenciamento ´e realizado com o auxílio de sistemas automatizados. Tais sistemas implementam programas que ajustam a demanda de voos à capacidade do espaço aéreo. Algoritmos simples podem sugerir medidas ATFM para solucionar a saturação em um conjunto restrito de elementos regulados (aeródromos, regiões do espaço aéreo, fixos ou aerovias). A natureza interconectada dos elementos regulados, que compõem o fluxo de tráfego aéreo, demanda uma abordagem mais abrangente para atingir o uso ótimo desses recursos, uma vez que outros problemas podem surgir quando a otimização local é aplicada a um elemento sem levar em conta seus elementos relacionados. Nem sempre há a necessidade do planejamento estratégico ser um ótimo global, uma vez que cenários viáveis e sub-ótimos encontrados com menor custo computacional podem representar soluções satisfatórias. O aumento da demanda do tráfego aéreo, no entanto, tem fomentado a aplicação de programas de geração de medidas ATFM mais complexos. Esta pesquisa implementou um programa de otimização global para a geração de medidas ATFM em cenários de larga escala do mundo real. O problema ´e modelado como um problema de programa¸c~ao inteira e o modelo adotado ´e abrangente, pois prevê atraso em solo, em voo, alteração de velocidade e rerroteamento. O programa é capaz de balancear o fluxo atendendo restrições de capacidade dos aeródromos e dos setores. Além disso, foi desenvolvida uma interface de visualização e edição de dados para os cenários estudados. Dados de voos no espaço aéreo brasileiro foram processados e utilizados para testar a solução implementada e mostraram a viabilidade do método. A utilização de um programa de otimização que leva em conta mais restrições potencialmente irá contribuir com o aumento de eficiência no uso da infraestrutura e do espaço aéreo de forma segura. / The Air Traffic Flow Management Service (ATFM) establishes a secure, orderly and efficient flow control according to the capacity of the infrastructure and control services. The Management is performed with the aid of automated systems. Such systems implement programs that adjust the flight demand to the airspace capacity. Simple algorithms might suggest ATFM measures to resolve saturation in a restricted set of regulated elements (aerodromes, airspace regions, fixes or airways). The interconnected nature of the regulated elements that make up the air traffic flow requires a more comprehensive approach to achieve optimum use of these resources, since other problems can arise when local optimization is applied to an element without regard to its related elements. There is not always a need for strategic planning to be a global optimum, since feasible and sub-optimal scenarios encountered at lower computational cost might represent satisfactory solutions. The increase in air traffic demand, however, has encouraged the application of programs to generate more complex ATFM measures. This research implemented a global optimization program for the generation of ATFM measures in large-scale real-world scenarios. The problem is modeled as an integer programming problem and the adopted model is comprehensive, since it provides ground and airborne delays, change of speed and re-routing. The program is able to balance the flow by meeting capacity constraints of the aerodromes and sectors. In addition, a visualization and data editing interface was developed for the studied scenarios. Flight data in Brazilian airspace were processed and used to test the implemented solution and the viability of the method was shown. The use of an optimization program that takes into account more constraints will potentially contribute to increase the efficiency in use of infrastructure and airspace in a secure manner.