The thesis is based on using dynamical systems theories and techniques to study the qualitative dynamics of herpes simplex virus type 2 (HSV-2), a sexually-transmitted disease of major public health significance. A deterministic model for the interaction of the virus with the immune system in the body of an infected individual (in vivo) is designed first of all. It is shown, using Lyapunov function and LaSalle's Invariance Principle, that the virus-free equilibrium of the model is globally-asymptotically stable whenever a certain biological threshold, known as the reproduction number, is less than unity. Furthermore, the model has at least one virus-present equilibrium when the threshold quantity exceeds unity. Using persistence theory, it is shown that the virus will always be present in vivo whenever the reproduction threshold exceeds unity. The analyses (theoretical and numerical) of this model show that a future HSV-2 vaccine that enhances cell-mediated immune response will be effective in curtailling HSV-2 burden in vivo. A new single-group model for the spread of HSV-2 in a homogenously-mixed sexually-active population is also designed. The disease-free equilibrium of the model is globally-asymptotically stable when its associated reproduction number is less than unity. The model has a unique endemic equilibrium, which is shown to be globally-stable for a special case, when the reproduction number exceeds unity. The model is extended to incorporate an imperfect vaccine with some therapeutic benefits. Using centre manifold theory, it is shown that the resulting vaccination model undergoes a vaccine-induced backward bifurcation (the epidemiological importance of the phenomenon of backward bifurcation is that the classical requirement of having the reproduction threshold less than unity is, although necessary, no longer sufficient for disease elimination. In such a case, disease elimination depends upon the initial sizes of the sub-populations of the model). Furthermore, it is shown that the use of such an imperfect vaccine could lead to a positive or detrimental population-level impact (depending on the sign of a certain threshold quantity). The model is extended to incorporate the effect of variability in HSV-2 susceptibility due to gender differences. The resulting two-group (sex-structured) model is shown to have essentially the same qualitative dynamics as the single-group model. Furthermore, it is shown that adding periodicity to the corresponding autonomous two-group model does not alter the dynamics of the autonomous two-group model (with respect to the elimination of the disease). The model is used to evaluate the impact of various anti-HSV control strategies. Finally, the two-group model is further extended to address the effect of risk structure (i.e., risk of acquiring or transmitting HSV-2). Unlike the two-group model described above, it is shown that the risk-structured model undergoes backward bifurcation under certain conditions (the backward bifurcation property can be removed if the susceptible population is not stratified according to the risk of acquiring infection). Thus, one of the main findings of this thesis is that risk structure can induce the phenomenon of backward bifurcation in the transmission dynamics of HSV-2 in a population.

New survey data indicate that injection drug users (IDU) in Victoria, BC who share syringes do so with a single person. These partnerships pose an obvious health risk to IDU, as blood borne illnesses are transmitted through the sharing of injection equipment. Here we formulate an ordinary di erential equation (ODE) model of pair formation and separation. Susceptible-infectious (SI) disease dynamics are built into this model so as to describe the syringe-mediated transmission of human immune de ciency virus (HIV) and hepatitis C virus (HCV) among IDU. We utilize a novel parameter estimation approach, and t the distribution of partnership durations observed in Victoria. The basic reproduction number is derived, and its qualitative behavior explored with both analytical and numerical techniques.

Medical computer vision is a novel research discipline based on the application of computer vision methods to data sets acquired via medical imaging techniques. This work focuses on magnetic resonance imaging (MRI) data sets, particularly in studies of schizophrenia and multiple sclerosis. Research on these diseases is challenged by the lack of appropriate morphometric tools to accurately quantify lesion growth, assess the effectiveness of a drug treatment, or investigate anatomical information believed to be evidence of schizophrenia. Thus, most hypotheses involving these conditions remain unproven. This thesis contributes towards the development of such morphometric techniques. A framework combining several tools is established, allowing for compensation of bias fields, boundary detection by modelling partial volume effects (PVE), and a combined statistical and geometrical segmentation method. Most importantly, it also allows for the computation of confidence bounds in the location of the object being segmented by bounding PVE voxels. Bounds obtained in such fashion encompass a significant percentage of the volume of the object (typically 20-60%). A statistical model of the intensities contained in PVE voxels is used to provide insight into the contents of PVE voxels and further narrow confidence bounds. This not only permits a reduction by an order of magnitude in the width of the confidence intervals, but also establishes a statistical mechanism to obtain probability distributions on shape descriptors (e.g. volume), instead of just a raw magnitude or a set of confidence bounds. A challenging clinical study is performed using these tools: to investigate differences in asymmetry of the temporal horns in schizophrenia. This study is of high clinical relevance. The results show that our tools are sufficiently accurate for studies of this kind, thus providing clinicians, for the first time, with the means to corroborate unproven hypotheses or reliably assess patient evolution.

Electric Discharge Machining (EDM) is a process for eroding and removing material by transient action of electric sparks on electrically conductive materials immersed in a dielectric liquid and separated by a small gap. A spark-eroded surface is a surface with matt appearance and random distribution of overlapping craters. It is mechanically hard and stressed close to ultimate tensile strength of the material and sometimes covered with a network of micro cracks. The violent nature of the process leads a unique structure on the machined surface and generates residual stresses due mainly to the non-homogeneity of heat flow and metallurgical transformations. An extensive experimental study is presented to explore the surface and sub-surface characteristics together with the residual stresses induced by the process. Layer removal method is used to measure the residual stress profile in function of depth beneath. A finite element based model is proposed to determine residual stresses and compared with the experimental results. The residual stress pattern is found to be unchanged with respect to machining parameters. Thus, a unit amplitude shape function representing change in curvature with respect to removal depth is proposed. The proposed form is found as a special form of Gauss Distribution, which is the sum of two Gaussian peaks, with the same amplitude and pulse width but opposite center location that is represented by three constant coefficients. In each case, agreement with the proposed form is established with experimental results. Results have shown that these coefficients have a power functional dependency with respect to released energy.

Submitted by RUDOLPH DOS SANTOS GOMES PEREIRA null (rudolph_matematica@hotmail.com) on 2016-01-03T14:22:05Z No. of bitstreams: 1 Tese_Rudolph_v_final.pdf: 2383587 bytes, checksum: 45b8d198f894196679baa36bfb9a93d6 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-01-06T13:07:56Z (GMT) No. of bitstreams: 2 pereira_rsg_dr_prud_part.pdf: 896925 bytes, checksum: a46ee8a90a03226102b0ebde033afb19 (MD5) pereira_rsg_dr_prud_int.pdf: 2383587 bytes, checksum: 45b8d198f894196679baa36bfb9a93d6 (MD5) / Made available in DSpace on 2016-01-06T13:07:56Z (GMT). No. of bitstreams: 2 pereira_rsg_dr_prud_part.pdf: 896925 bytes, checksum: a46ee8a90a03226102b0ebde033afb19 (MD5) pereira_rsg_dr_prud_int.pdf: 2383587 bytes, checksum: 45b8d198f894196679baa36bfb9a93d6 (MD5) Previous issue date: 2015-12-11 / Os resultados apresentados pelo Sistema Nacional de Avaliação da Educação Básica, pelo Programa Internacional de Avaliação de Alunos e pelo Exame Nacional do Ensino Médio indicam que os alunos brasileiros possuem nível de proficiência baixo na disciplina de Matemática sendo capazes de realizar operações matemáticas básicas e a leitura e interpretação de gráficos simples. Esses indicadores apontam a necessidade de mudanças nos processos de ensino e de aprendizagem de Matemática na Educação Básica que podem iniciar com a atuação do professor, buscando alternativas para auxiliá-lo no ensino em sala de aula. Diante destas considerações, esta pesquisa visa investigar as contribuições da Educação a Distância, enquanto contexto formativo, em um curso de formação continuada de professores de Matemática, com atividades de Modelagem Matemática, para a manifestação e o desenvolvimento de conhecimentos e saberes da docência. No desenvolvimento da pesquisa foram adotadas as ações pautadas pelos referenciais teóricos da formação de professores, da alternativa pedagógica de Modelagem Matemática, bem como nas orientações da Educação a Distância. Os procedimentos metodológicos que nortearam a pesquisa foram pautados nos conceitos da pesquisa qualitativa. Na elaboração do curso consideramos as ferramentas ofertadas pela EaD para a comunicação entre os cursistas e o pesquisador, disponibilização de material e realização de atividades. A implementação e o desenvolvimento do curso de formação continuada de professores de Matemática em serviço na Educação Básica, ocorreu por meio do ambiente virtual de aprendizagem Moodle. O curso foi realizado na modalidade a distância, na forma semipresencial, com duração de cem horas, dividido em três módulos nos quais foram realizadas atividades de modelagem, e contou com a participação de seis cursistas. A coleta dos dados foi realizada pelas ferramentas de chat, fórum, diários e tarefas (memoriais reflexivos) onde eram registradas as expressões e reflexões dos cursistas durante o período de realização do curso de formação continuada. Para análise dos dados coletados, optamos pela Análise Textual Discursiva, que permitiu a interpretação e a compreensão dos registros efetuados pelos cursistas. Assim, a partir da análise textual discursiva realizada nos dados considerados nesta tese, foi possível evidenciar que a Educação a Distância, entendida como um contexto possível para a formação continuada de professores, favoreceu a manifestação e o desenvolvimento de conhecimentos e saberes da docência, por parte dos cursistas que participaram da pesquisa, permitindo, entre outras coisas, o desenvolvimento da autonomia desses docentes mediante às atividades propostas no curso realizado, levando-os a buscar soluções para as dificuldades pessoais encontradas pelos mesmos. / The results presented by the National Basic Education Evaluation System, by the International Program of Students Assessment, and by the High School National Exam indicate that Brazilian students have a low proficiency level in mathematics: they are able to perform basic mathematical operations and the reading and interpretation of simple graphs. These markers point to the need for changes in the Maths teaching and learning processes in the Basic Education which can be started with the teacher’s action, searching for alternatives to help him/her in the classroom activities. Taking that into consideration, this research aims at investigating the contributions given by Distance Learning, as a training context, in a Maths teacher continuing training course, with Mathematical Modeling activities, for the manifestation and development of knowledge and teaching knowledge. For the development of this research, the theoretical framework adopted was the one based on teacher training in the pedagogical alternative of the Mathematical Modeling, as well as the guidelines of the Distance Learning. The methodological procedures that guided the research were based on the concepts of qualitative research. In the course planning, tools offered by the Distance Learning process were considered for the communication between course takers and the researcher, material availability and activities performance. The implementation and development of the Continuing Training of Maths Teachers course at service in the Basic Education took place in the virtual learning environment known as Moodle. The course was offered in the distance mode, semi-distance learning, lasting a hundred hours, split in three modules in which modeling activities were performed. Six course takers took part in the project. The data collection was done by the following tools: chat, forum, daily logs and tasks (reflective memorials) where expressions and reflections by the course takers were registered during the length of the continuing training course. The Discursive Textual Analysis was adopted for the collected data analysis, which allowed for the interpretation and comprehension of the registrations made by the course takers. Hence, from the discursive textual analysis performed in the data considered in this doctoral dissertation, it was possible to conclude that distance learning, understood as a possible context for continuing teacher training, boosted the manifestation and development of knowledge and teaching knowledge, by the course takers who took part in the research, allowing, among other things, the development of the autonomy of these teachers by means of the activities proposed in the held course, leading them to look for solutions for the personal difficulties faced by each one of them.

Esta dissertação apresenta modelagem matemática e um método de solução numérica para problemas de conformação eletromagnética de chapas metálicas finas circulares utilizando uma bobina em espiral plana. O método foca especificamente o cálculo do campo eletromagnético gerado pela bobina e análise do circuito que modela o sistema de estampagem eletromagnética. A bobina plana é aproximada por círculos concêntricos carregando a corrente de descarga dos capacitores. Os cálculos das correntes induzidas e perfil da força eletromagnética na chapa e acoplamentos magnéticos entre a bobina e chapa metálica são realizados para o instante inicial, antes da deformação plástica da chapa. O método utiliza a lei de Biot-Savart, sendo que a solução das integrais obtidas para indução magnética é realizada através de métodos numéricos, considerando as simetrias do problema. Para verificação da modelagem matemática, da solução numérica e comprovação da viabilidade técnica deste processo, um dispositivo de estampagem eletromagnética foi desenvolvido e diversos experimentos foram realizados com chapas de alumínio. Os parâmetros investigados foram a espessura da chapa a ser deformada e a influência da presença de vácuo na cavidade da ferramenta. Os resultados experimentais demonstram concordância com os resultados da modelagem proposta. A presença de vácuo também demonstrou um incremento na deformação da chapa. A rotina desenvolvida no software Matlab fornece informações importantes para o processo e permite que se faça ajustes no dispositivo. / This dissertation presents a mathematical model and numerical method to solve the problems of electromagnetic forming of thin circular metal sheets by using a flat spiral coil. The method focuses specifically on the calculation of the electromagnetic field generated by the coil flat and circuit analysis modeling system electromagnetic forming. The flat coil is approximated by concentric circles carrying a discharge current of capacitors. The calculations of induced currents and profile of the electromagnetic force on the plate and magnetic coupling between the coil and sheet metal are made to the initial time, before the plastic deformation of the plate. The method uses the law of Biot-Savart, and the solution of the integral obtained for magnetic induction is performed by numerical methods, considering the symmetries of the problem. To verify the mathematical model, the numerical solution and proving the technical feasibility of this process, a electromagnetic forming device was developed and several experiments were made with aluminum plates. The parameters investigated were the thickness of the plate to be deformed and the influence of the vacuum in the cavity of the tool. The experimental results show agreement with the results of the proposed model. The presence of vacuum also showed an increase in the deformation of the plate. A routine developed in software Matlab provide important information for the process and allow to make adjustments on the device.

[pt] Problemas de geração de grades horárias visam agendar eventos a fim de satisfazer demandas, ao mesmo tempo que satisfazem restrições adicionais. Uma solução é boa se todas as grades horárias resultantes são aceitáveis para todas as pessoas e recursos envolvidos. Para a geração de grades horárias escolares, um número conhecido de aulas, envolvendo estudantes, professores e salas de aula, deve ser agendado ao longo da semana, enquanto limitações operacionais, institucionais, pedagógicas e pessoais devem ser satisfeitas. A alta dificuldade do problema tem levado muitos pesquisadores a trabalhar em abordagens de resolução para o mesmo desde o início dos anos 60. Encontrar uma solução aplicável em um cenário do mundo real implica em satisfazer vários requisitos de qualidade e em não ignorar questões políticas, o que torna o problema clássico muito mais intrincado. Este trabalho descreve uma abordagem baseada em programação inteira mista (MIP) desenvolvida para resolver um problema real de geração de grades horárias escolares e discute ideias e desafios encarados durante a fase de implantação da solução em algumas escolas brasileiras. Em contraste com outros trabalhos na área, o compartilhamento de professores entre diferentes unidades de uma escola é considerado. Experimentos computacionais foram realizados para cenários cujo número de unidades varia de 2 a 15, o número de professores de 35 a 471, e o número de turmas de 16 a 295. Diferentes estratégias foram combinadas, visando a convergência da procura por boas soluções. Por fim, os resultados são avaliados e as melhores abordagens são destacadas. / [en] Timetabling problems look to schedule meetings in order to satisfy a set of demands, while respecting additional constraints. In a good solution the resulting timetables are acceptable to all people and resources involved. In school timetabling, a given number of lectures, involving students, teachers and classrooms, need to be scheduled over the week, while having to satisfy operational, institutional, pedagogical and personal restrictions. The difficulty of the problem has driven many researchers to work on solving approaches for it since the early 1960 s. Finding an actual solution to a real world scenario implies satisfying many quality requirements and not ignoring the political issues, which turns the classical problem much more intricate. This work describes an approach based on mixed integer programming (MIP) developed for solving a real-world school timetabling problem and discusses ideas and issues faced during solution deployment phase for some Brazilian schools. In contrast to other works on school timetabling, teaching staff sharing between distinct school units are considered. Computational experiments were performed for scenarios whose number of school units varies from 2 to 15, number of teachers varies from 35 to 471 and number of classes varies from 16 to 295. Different strategies were combined aiming at converging to good solutions. Finally, results are evaluated and the best approaches are highlighted.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-08-21T23:56:25Z No. of bitstreams: 1 RAMON VIANA DE SOUSA – DISSERTAÇÃO (PPGEP) 2017.pdf: 4546181 bytes, checksum: 1ade137231c59d3b97ff1efa12a0f8c8 (MD5) / Made available in DSpace on 2018-08-21T23:56:25Z (GMT). No. of bitstreams: 1 RAMON VIANA DE SOUSA – DISSERTAÇÃO (PPGEP) 2017.pdf: 4546181 bytes, checksum: 1ade137231c59d3b97ff1efa12a0f8c8 (MD5) Previous issue date: 2017-08-30 / O presente trabalho de pesquisa teve como objetivos estudar o comportamento das massas específicas aparente e real; porosidade intergranular pelo método do deslocamento de líquidos e o calor específico determinado pelo método das misturas para teores de água variando de 11,6 a 30,06%, base úmida; determinar as isotermas de dessorção de equilíbrio higroscópico pelo método estático com uso de solução saturadas de sais, utilizando-se quatros níveis de temperatura 10, 20, 30 e 40 °C e cinco níveis de umidade relativa do ar variando entre 11,15 a 84,32%; para análise dos dados experimentais foram utilizados sete modelos matemáticos: Henderson modificada por Cavalcanti Mata, Henderson modificada por Thompson, Chung–Pfost, Halsey modificada, Cavalcanti Mata e Henderson; determinar, experimentalmente, o calor latente de vaporização da água do arroz vermelho em função do teor de água e temperatura, utilizando o método Othmer ; analisar a cinética de secagem em camada fina utilizando um secador de leito fixo com ventilação forçada em cinco temperaturas: 40, 50, 60, 70 e 80 °C para teores de água inicial de 20, 25 e 30% aplicando-se aos dados experimentais cinco modelos matemáticos: Henderson modificada por Cavalcanti Mata, Henderson modificada por Thompson, Henderson, Fick, Page e Thompson; realizar a secagem e simulação matemática em camada espessa para temperaturas de 40, 50, 60 e 70 °C e teores de água estabelecidos na camada fina . Os resultados obtidos permitiram concluir que as massas específicas aparente e real, a porosidade intergranular e calor específico aumentaram com a elevação do teor de água e que o comportamento das propriedades físicas do arroz vermelho podem ser representadas em função do teor de água pelo modelo linear simples. Observou-se que o teor de água de equilíbrio higroscópico, para uma mesma umidade relativa, diminuiu com a elevação de temperatura, assim como, para uma mesma temperatura, o teor de água de equilíbrio higroscópico aumenta com o aumento da umidade relativa do ar, seguindo a mesma tendência da maioria dos produtos agrícolas. Baseando -se em parâmetros estatísticos, os modelos de Henderson modificada por Cavalcanti Mata e Henderson modificada por Thompson foram os que melhor representaram a higroscopicidade dos grãos de arroz vermelho em casca. A difusividade efetiva dos grãos de arroz vermelho, estimada pelo modelo Fick, aumentou com a elevação da temperatura do ar de secagem. Verificou-se também, que para cada temperatura analisada a difusividade efetiva aumenta com o aumento do teor de água inicial. Através das curvas de cinética de secagem, constatou-se que quando se aumenta a temperatura ocorre uma diminuição do tempo de secagem, enquanto para o teor de água inicial, quanto maior seu valor maior será a taxa de secagem no início do processo. Dentre os modelos analisados na cinética de secagem, o de Cavalcanti Mata foi o que melhor ajustou-se aos dados experimentais em todas as temperaturas e teores de água iniciais estudados. A simulação da secagem em camada espessa utilizou o modelo de Thompson, no qual apresentou uma concordância entre os dados experimentais e simulados para os valores médios das camadas, tendo o menor desvio médio final com temperatura de 60 °C e teor de água inicial equivalente a 20% b.u. / The present research work had as objectives to study the behavior of the apparent and real specific masses; intergranular porosity by liquid displacement method and the specific heat determined by the method of mixtures for water contents ranging from 11.6 to 30.06%, wet basis; determining the equilibrium desorption isotherms hygroscopic by the static method with use of saturated salt solution, using four temperature levels 10, 20, 30 and 40 ° C and five levels of relative humidity of t he air ranging from 11.15 to 84,32%; for the analysis of experimental data seven mathematical models were used: Henderson modified by Cavalcanti Mata, Henderson modified by Thompson, Chung-Pfost, modified Halsey, Cavalcanti Mata and Henderson; determining, experimentally, the latent heat of vaporization of water from red rice as a function of water content and temperature , using the method Othmer; analyzing the drying kinetics of a thin layer using a fixed bed drier with forced ventilation in five temperatures: 40, 50, 60, 70 and 80 ° C for initial water contents of 20, 25 and 30% by applying to the experimental data five mathematical models: Henderson modified by Cavalcanti Mata, Henderson modified by Thompson, Henderson, Fick, Page and Thompson; to perform drying and mathematical simulation in a thick layer at temperatures of 40, 50, 60 and 70 ° C and water levels established in the thin layer. The results showed that the apparent and real specific masses, the intergranular porosity and specific heat increased with increasing water content and that the behavior physical properties of red rice can be represented depending on the water content of the simple linear model. It was observed that the equilibrium water content, to the same hygroscopic relative humidity, decreased with temperature elevation, as to the same temperature, the hygroscopic equilibrium water content increases with increasin g relative humidity, following the same trend of most agricultural products. Based on statistical parameters, models Henderson modified by Cavalcanti Mata and Henderson modified by Thompson were the best represented the hygroscopicity of red grains of rice in husk. The effective diffusivity of red rice grains, estimated by Fick model, increased with increasing drying air temperature. It was also found that for each temperature examined the effective diffusivity increases with increasing initial water content. Through the drying kinetics curves, it was found that increasing temperature is a decrease in drying time, while for the initial water content, the greater will be its highest drying rate early in the process. Among the models analyzed in the drying kinetics, the Cavalcanti Mata was the best set to the experimental data at all temperatures and initial water contents studied. The simulation of the thick layer drying used the Thompson model, in which it showed a concordance between the experimental and simulated datas for the average values of the layers, having the lowest average final deviation with temperature of 60 ° C and initial water content equivalent to 20% b.u.

No Brasil, as hortaliças são produzidas, em diferentes épocas do ano, por milhares de agricultores familiares, distribuídos por todo o país. Por ser uma atividade que admite maior complexidade que as demais atividades agrícolas, esta tese propõe um sistema de planejamento da produção olerícola (SPPO) para as unidades de produção familiar (UPFs). Para o desenvolvimento do SPPO utilizou-se uma metodologia, dividida em quatro fases. A primeira fase consistiu no levantamento de fatores e variáveis intervenientes no processo decisório (para quem, o que, quando e quanto produzir) utilizando-se a análise de conteúdo. Os resultados encontrados foram submetidos ao crivo dos especialistas em olericultura e olericultores familiares, por meio de entrevistas individuais, para definir quais elementos incorporar ao SPPO. Na segunda fase estruturou-se o banco de dados do SPPO de acordo com os resultados da primeira fase. A terceira fase, denominada processo de filtragem, além de contemplar a experiência do olericultor na escolha dos canais de distribuição, hortaliças e confrontar as recomendações agrotécnicas com as condições edafoclimáticas da localidade, busca reduzir a dimensão do problema de planejamento do sequenciamento de produção. A quarta fase consistiu na modelagem matemática para a definição da combinação de produção que será recomendado para a UPF em estudo. Ainda, nesta fase é proposta uma metodologia multiíndice para analisar a viabilidade econômica da produção recomendada pelo SPPO. Entre as vantagens do SPPO, destacam-se: (i) consideração dos fatores mercadológicos, agroecológicos, agrotécnicos, agrotecnológicos, capacidade (área, recursos humanos, hídricos e financeiros) e de base ecológico-sustentável que são incorporados em função das escolhas do olericultor; (ii) maior entendimento da complexidade que envolve o desenvolvimento da atividade; (iii) levantamento das despesas e receitas semanais durante o horizonte de planejamento; e (iv) visualização das atividades (tarefas) que devem ser realizadas para o desenvolvimento do planejado. Foram realizados estudos de caso, utilizando dados reais adaptados de UPFs do município de Pato Branco/PR, para mostrar a viabilidade do SPPO como ferramenta auxiliar no planejamento da produção de hortaliças nas UPFs. / In Brazil, vegetables are produced in different year seasons by thousands of family farms distributed throughout the country. Being an activity that allows bigger complexity than other agricultural activities, this thesis proposes a olericultural production planning system (SPPO) for the family production units (UPFs). For the development of the SPPO it was applied a methodology divided into four phases. The first phase consisted in collecting the factors and variables intervenient in the decisive process (to whom, what, when, and how much to produce) using the content analysis. The results found were submitted to the appreciation of olericulture specialists and family olericulturists, by means of individual interviews, to define which elements to incorporate to the SPPO. In the second phase the SPPO data bank was structured according to the first phase results. The third phase, denominated filtration process, besides contemplating the olericulturist´s experience in the choice of the distribution canals, vegetables, and in confronting the agrotechnical recommendations with the edafoclimatical conditions of the place aims at reducing the dimension of the problem of production sequencing planning. The fourth phase consisted in the mathematical modeling to the definition of production combination which will be recommended to the UPF being studied. In this phase it is still proposed a multiindex methodology to analyze the economical viability of the production recommended by the SPPO. Among the SPPO advantages can be mentioned: (i) consideration of market agroecological, agrotechnical, agrotechnological factors, capacity (area; human, hydric, and financial resources), and of ecological-sustainable basis that are incorporated according to the olericulturist´s choices; (ii) greater understanding of the complexity that involves the activity development; (iii) calculating the weekly expenses and revenue during the planning horizon; and (iv) visualization of the activities (tasks) that must be performed to the development of what has been planned. Case studies were performed, using actual data adapted to the UPFs in the city of Pato Branco/PR to show the viability of the SPPO as an auxiliary tool in planning vegetables production in the UPFs.

Nesse trabalho apresentamos a modelagem matemática do Projeto de Rede da Cadeia de Suprimentos (Supply Chain Network Design) de uma empresa responsável pela produção e distribuição de commodities. O investimento em uma nova fábrica exige que a empresa tenha seu projeto logístico readequado. O desenvolvimento das formulações matemáticas é baseado no trabalho de Jayaraman e Pirkul (2001). Foram realizadas 3 (três) formulações matemáticas de diferentes abordagens para solução do projeto logístico. As implementações computacionais foram realizadas no CPLEX© Optimization Studio Academic Research versão 12.2. As experiências computacionais foram desenvolvidas através de cenários que buscaram representar problemas de dimensões reais. Ainda na etapa de experimentação foram realizadas análises de sensibilidade dos modelos. Um estudo para identificar as demandas de mercado e os custos de transporte foi realizado, sendo assim, foi possível aplicar os modelos no estudo de caso a partir de dados reais de demanda e custos. Para execução das instâncias reais foram selecionadas 2 (duas) abordagens distintas: Single-source e Arcbased. Diferentes market shares foram definidos para construção de novos cenários e instâncias reais foram executadas dentro de limites computacionais de tempo satisfatórios. Os resultados encontrados para cada cenário foram comparados e analisados em relação à resolução do problema proposto. A dissertação contribui para a área de modelagem da cadeia de suprimentos fornecendo modelos que apresentaram resultados satisfatórios para a tomada de decisão nessa fase do projeto logístico da indústria tema dessa pesquisa. / We present a mathematical modeling of the Supply Chain Network Design (SCND) for a company responsible for producing and distributing commodities. Investment in a new plant requires that the company has reconfigured its logistics project. The development of mathematical formulations is based on the work of Jayaraman and Pirkul (2001). Were performed three (3) mathematical formulations for different approaches to solving the logistics project. Computational implementations were done in CPLEX© Optimization Academic Research Studio version 12.2. Computational experiments were developed through scenarios that sought to represent problems of the real dimensions. Still in the experimentation fase were performed sensitivity analysis of models. A study to identify market demands and transportation costs was made, so the models could be applied in the case study data from actual demand and costs. For carrying out the actual instances were selected 2 (two) different approaches: Single-source-based and Arc. Different market shares were set to build new scenarios and actual instances have been implemented within limits satisfactory computational time. The results for each scenario were compared and analyzed for solving the proposed problem. The thesis contributes to modeling area of supply chain models that provide satisfactory results for decision making in this phase of the project's logistics industry theme of this research.