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.

Les calculs numériques ont été effectués à l'aide du logiciel SAGE. / En 1993, Conway et Schneeberger fournirent un critère simple permettant de déterminer si une forme quadratique donnée représente tous les entiers positifs ; le théorème des 15. Dans ce mémoire, nous nous intéressons à un problème analogue, soit la recherche d’un critère similaire permettant de détecter si une forme quadratique en trois variables représente tous les entiers impairs. On débute donc par une introduction générale à la théorie des formes quadratiques, notamment en deux variables, puis on expose différents points de vue sous lesquels on peut les considérer. On décrit ensuite le théorème des 15 et ses généralisations, en soulignant les techniques utilisées dans la preuve de Bhargava. Enfin, on démontre deux théorèmes qui fournissent des critères permettant de déterminer si une forme quadratique ternaire représente tous les entiers impairs. / In 1993, Conway and Schneeberger gave a simple criterion allowing one to determine whether a given quadratic form represents all positive integers ; the 15-theorem. In this thesis, we investigate an analogous problem, that is the search for a similar criterion allowing one to detect if a quadratic form in three variables represents all odd integers. We start with a general introduction to the theory of quadratic forms, namely in two variables, then, we expose different points of view under which quadratic forms can be considered. We then describe the 15-theorem and its generalizations, with a particular emphasis on the techniques used in Bhargava’s proof of the theorem. Finally, we give a proof of two theorems which provide a criteria to determine whether a ternary quadratic form represents all odd integers.

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.

Autonomous coordination among multiple aerial vehicles to ensure a collision free airspace is a critical aspect of today’s airspace. With the rise of Unmanned Aerial Vehicles (UAVs) in the military and commercial sectors, obstacle avoidance in a densely populated airspace is necessary. This thesis investigates finding optimal or near-optimal trajectories in real-time for aircraft in complex airspaces containing a large number of obstacles. The solution for the trajectories is described as a linear program subject to mixed integer constraints, known as a Mixed Integer Linear Program (MILP). The resulting MILP problem is solved in real time using a well-known, public domain MILP solver. In addition, an Exhaustive, Breadth-First Search algorithm was implemented and is used for comparison in terms of execution time and flight path optimality. The Exhaustive Search algorithm is comprised of a multi-branch tree structure that iterates through all possible flight paths from source to target. The MILP solution was implemented in both PC based and embedded system environments. The embedded system environment was implemented on an onboard processor to develop trajectories for each individual aircraft in real time.

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.

Title: Models of integer-valued time series with random coefficients Author: Petra Burdejová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Zuzana Prášková, CSc. Abstract: In the presented thesis, a generalized integer-valued autoregres- sive process of the order p (GINAR(p)) is considered first. The main aim is taken to introduction of random coefficient integer-valued autoregressive process (RCINAR(p)). We use a thinning operator in order to define the processes. The main characteristics of GINAR(p) and RCINAR(p) are obtained. Condi- tions for stationarity and ergodicity are stated. Three methods of estimation (Yule-Walker, Conditional least squares, Generalized method of moments) are given and compared in simulation with respect to the mean squared error (MSE). At the end, RCINAR(3) model is applied to a real dataset representing a number of earthquakes per year. Keywords: thinning operator, random coefficients, integer-valued time se- ries, GINAR, RCINAR

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.

Actuellement, les fabricants sont soumis à une pression économique importante et à une concurrence internationale accrue due à la globalisation des marchés. Pour réussir, les fabricants doivent être capables de répondre rapidement aux changements de la demande en adaptant leurs systèmes de production. Cette adaptation aux changements peut être réalisée à travers multiples reconfigurations du système de production.Les travaux présentés dans ce mémoire portent sur l'élaboration des méthodes de recherche opérationnelle permettant d'accompagner le décideur lors de la reconfiguration d'une ligne de transfert ou d'assemblage. Ce problème apparaît lorsqu'un nouveau produit doit être fabriqué par une ligne existante ou lorsqu'il y a eu des changements dans les caractéristiques du produit. Par conséquent, il devient nécessaire de modifier la configuration du système de production tout en minimisant les coûts induits. Ces coûts sont évalués différemment pour les systèmes automatisésou manuels. Dans le premier cas, qui correspond au cas des lignes de transfert, pour limiter les investissements, il est souhaitable de réutiliser au maximum les équipements existants à condition que les contraintes techniques et technologiques soient respectées. Dans le cas des lignes manuelles qui sont représentées dans notre étude par les lignes d'assemblage, l'objectif est de minimiser les coûts liés à l'apprentissage des opérateurs causés par la réaffectation de leurs tâches.Les méthodes de résolution exactes basées sur la modélisation mathématique et la programmation linéaire en nombre mixtes ainsi qu'une méthode de type goal programming sont développées dans ce travail pour argumenter la prise de décisions lors de la reconfiguration des lignes de production. Les méthodes proposées ont été testées avec succès sur des échantillons de problèmes proches des cas industriels et ont montré leur efficacité. / Global competition causes fluctuations in product demand and requires more frequent modifications of product characteristics. As a consequence, the production systems have to be frequently adapted to new production requirements.This work develops new combinatorial optimization methods for supporting decision makers at the reconfiguration stage considered for transfer and assembly lines. If new products have to be manufactured at the line or existing products are modified, then the line has to be reconfigured in order to meet new production requirements. In highly automated lines, as the transfer lines, the reconfiguration problem is focused on the readjustment of the equipment. To reduce the investment costs, the decision makers aim to reuse the available equipment as much as possible. The existence of compatibility constraints between new operations to be performed and existing facilities makes the reconfiguration problem hard and combinatorial.In manual assembly lines also studied in this thesis, the reconfiguration problem mostly concerns the reassignment of tasks to workers ant the minimization of the cost of retraining operators.The developed methods are based on the mathematical modelling and mixed integer programming, a goal programming approach is designed as well. These methods were successfully tested on a dataset of problem instances close to real industrial problems. The obtained results show the effectiveness and the efficiency of the solution methods proposed.

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.

[pt] O aumento da produção de petróleo brasileiro e o consequente aumento na demanda por transporte marítimo levaram a PETROBRAS a buscar ferramentas para aumentar a eficiência de seu transporte marítimo. Neste sentido, a atividade de programação de navios busca alocar os navios a um conjunto de cargas definido a priori, respeitando as restrições comerciais e operacionais, a fim de transportá-las com o menor custo possível. Com o intuito de auxiliar o programador nesta atividade, esta dissertação propõe um sistema de suporte à decisão (SSD) baseado em otimização para a programação de navios. O SSD proposto foi desenhado especificamente para a atividade de longo curso de navios de petróleo da PETROBRAS, sendo este gerado a partir da adaptação de modelos disponíveis na literatura acadêmica. Os testes comparativos realizados com o protótipo do SSD na atividade de longo curso de navios de petróleo mostraram que a ferramenta tem um significativo potencial de redução de custo. O SSD proposto se apresentou como uma opção viável para auxiliar a programação de navios da companhia na busca pela redução de custos de transporte marítimo. / [en] The increasing production of Brazilian oil and the consequent increase in the demand for shipping, led PETROBRAS to seek tools to increase the efficiency of its shipping. In this sense, the activity of ship scheduling seeks to assign vessels to a set of cargos, respecting business and operational restrictions in order to transport them with the lowest possible cost. To assist the ship scheduling planner in this activity, this dissertation proposes an optimization based decision support system (DSS) for ship scheduling. The proposed DSS was designed specifically for the long-term tanker scheduling activity at PETROBRAS and it was implemented based on models available in the academic literature. The comparative tests using the DSS prototype proposed in this dissertation showed that it has a potential for significant cost reduction. The proposed DSS was considered a viable tool to assist the ship scheduling planners in reducing shipping costs.