A Teoria dos Jogos é amplamente utilizada no estudo de fenômenos de interação estratégica, em especial na análise de mercados de commodities. Esse trabalho faz uma análise preliminar do mercado brasileiro de eteno e propeno sob a ótica de um modelo baseado na Teoria dos Jogos, representado matematicamente através de um problema de complementaridade mista. Neste modelo, as empresas atuam em uma competição de Cournot e os custos de produção são parâmetros incertos, representados através de cenários, sendo que, no equilíbrio, três decisões devem ser tomadas: i) o portifólio de tecnologias para produção, ii) a capacidade de produção de cada tecnologia e iii) o nível de produção de cada tecnologia em cada cenário. Considerando as diversas limitações do estudo, as simulações realizadas com o modelo proposto mostram que o comportamento dos agentes da indústria petroquímica brasileira está mais próximo de tomadores de preços, sem possibilidade de regulação de preços através das quantidades produzidas. / Game Theory is widely used in the study of strategic interaction, especially in the analysis of commodity markets. This work makes a preliminary analysis of the Brazilian ethylene and propylene market from the perspective of a model based on game theory, represented mathematically by a mixed complementarity problem. In this model, firms behave as Cournot players and production costs are uncertain parameters, represented by scenarios, and in equilibrium three decisions must be made: i) the portfolio of technologies for production, ii) technologies capacity and iii) the level of production for each technology in each scenario. Considering the limitations of the study, the simulations carried out with the proposed model show that the behavior of the Brazilian petrochemical industry agents is closer to price takers, without possibility of price regulation by the quantities produced.

A Teoria dos Jogos é amplamente utilizada no estudo de fenômenos de interação estratégica, em especial na análise de mercados de commodities. Esse trabalho faz uma análise preliminar do mercado brasileiro de eteno e propeno sob a ótica de um modelo baseado na Teoria dos Jogos, representado matematicamente através de um problema de complementaridade mista. Neste modelo, as empresas atuam em uma competição de Cournot e os custos de produção são parâmetros incertos, representados através de cenários, sendo que, no equilíbrio, três decisões devem ser tomadas: i) o portifólio de tecnologias para produção, ii) a capacidade de produção de cada tecnologia e iii) o nível de produção de cada tecnologia em cada cenário. Considerando as diversas limitações do estudo, as simulações realizadas com o modelo proposto mostram que o comportamento dos agentes da indústria petroquímica brasileira está mais próximo de tomadores de preços, sem possibilidade de regulação de preços através das quantidades produzidas. / Game Theory is widely used in the study of strategic interaction, especially in the analysis of commodity markets. This work makes a preliminary analysis of the Brazilian ethylene and propylene market from the perspective of a model based on game theory, represented mathematically by a mixed complementarity problem. In this model, firms behave as Cournot players and production costs are uncertain parameters, represented by scenarios, and in equilibrium three decisions must be made: i) the portfolio of technologies for production, ii) technologies capacity and iii) the level of production for each technology in each scenario. Considering the limitations of the study, the simulations carried out with the proposed model show that the behavior of the Brazilian petrochemical industry agents is closer to price takers, without possibility of price regulation by the quantities produced.

The aims of this thesis are to study the fracture behaviour in unreinforced masonry, to carry out a limited experimental program on three-point bending (TPB) masonry panels and to develop a time-dependent fracture formulation for the study of mode I fracture in quasi-brittle materials. A micro-model for fracture in unreinforced masonry is developed using the concept of the discrete crack approach. All basic masonry failure modes are taken into account. To capture brick diagonal tensile cracking and masonry crushing, a linear compression cap is proposed with a criterion for defining the compression cap. The failure surface for brick and brick-mortar interfaces are modelled using a Mohr-Coulomb failure surface with a tension cut-off and a linear compression cap. The fracture formulation, in nonholonomic rate form within a quasi-prescribed displacement approach, is based on a piecewise-linear constitutive law and is in the form of a so-called ?linear complementarity problem? (LCP). The proposed model has been applied to simulating fracture in masonry shear walls and masonry TPB panels. An experimental program was undertaken to investigate the failure behaviour of masonry panels under TPB with relatively low strength mortar. The basic material parameters were obtained from compression, TPB and shear tests on bricks, mortar and brick-mortar interfaces. The experimental results showed that the failure of masonry TPB panels is governed by both tensile and shear failure rather than just tensile failure. The simulation of the masonry TPB tests compared well with the experimental results. In addition, the LCP fracture formulation is enhanced to study the time-dependent mode I fracture in quasi-brittle materials. Two main time-dependent sources, the viscoelasticity of the bulk material and the crack rate dependent opening, are taken into account. A simplified crack rate model is proposed to include the rate-dependent crack opening. The model is applied to predicting time-dependent crack growth in plain concrete beams under sustained loading. The model captures the essential features including the observed strength increase with loading rate, the load-deflection and load-CMOD responses, the deflection-time and CMOD-time curves, the predicted time to failure and the stress distributions in the fracture zone.

Suppliers in competitive electricity markets regularly respond to prices that change hour by hour or even more frequently, but most consumers respond to price changes on a very different time scale, i. e. they observe and respond to changes in price as reflected on their monthly bills. This thesis examines mixed complementarity programming models of equilibrium that can bridge the speed of response gap between suppliers and consumers, yet adhere to the principle of marginal cost pricing of electricity. It develops a computable equilibrium model to estimate the time-of-use (TOU) prices that can be used in retail electricity markets. An optimization model for the supply side of the electricity market, combined with a price-responsive geometric distributed lagged demand function, computes the TOU prices that satisfy the equilibrium conditions. Monthly load duration curves are approximated and discretized in the context of the supplier's optimization model. The models are formulated and solved by the mixed complementarity problem approach. It is intended that the models will be useful (a) in the regular exercise of setting consumer prices (i. e. , TOU prices that reflect the marginal cost of electricity) by a regulatory body (e. g. , Ontario Energy Board) for jurisdictions (e. g. , Ontario) where consumers' prices are regulated, but suppliers offer into a competitive market, (b) for forecasting in markets without price regulation, but where consumers pay a weighted average of wholesale price, (c) in evaluation of the policies regarding time-of-use pricing compared to the single pricing, and (d) in assessment of the welfare changes due to the implementation of TOU prices.

Suppliers in competitive electricity markets regularly respond to prices that change hour by hour or even more frequently, but most consumers respond to price changes on a very different time scale, i. e. they observe and respond to changes in price as reflected on their monthly bills. This thesis examines mixed complementarity programming models of equilibrium that can bridge the speed of response gap between suppliers and consumers, yet adhere to the principle of marginal cost pricing of electricity. It develops a computable equilibrium model to estimate the time-of-use (TOU) prices that can be used in retail electricity markets. An optimization model for the supply side of the electricity market, combined with a price-responsive geometric distributed lagged demand function, computes the TOU prices that satisfy the equilibrium conditions. Monthly load duration curves are approximated and discretized in the context of the supplier's optimization model. The models are formulated and solved by the mixed complementarity problem approach. It is intended that the models will be useful (a) in the regular exercise of setting consumer prices (i. e. , TOU prices that reflect the marginal cost of electricity) by a regulatory body (e. g. , Ontario Energy Board) for jurisdictions (e. g. , Ontario) where consumers' prices are regulated, but suppliers offer into a competitive market, (b) for forecasting in markets without price regulation, but where consumers pay a weighted average of wholesale price, (c) in evaluation of the policies regarding time-of-use pricing compared to the single pricing, and (d) in assessment of the welfare changes due to the implementation of TOU prices.

The aims of this thesis are to study the fracture behaviour in unreinforced masonry, to carry out a limited experimental program on three-point bending (TPB) masonry panels and to develop a time-dependent fracture formulation for the study of mode I fracture in quasi-brittle materials. A micro-model for fracture in unreinforced masonry is developed using the concept of the discrete crack approach. All basic masonry failure modes are taken into account. To capture brick diagonal tensile cracking and masonry crushing, a linear compression cap is proposed with a criterion for defining the compression cap. The failure surface for brick and brick-mortar interfaces are modelled using a Mohr-Coulomb failure surface with a tension cut-off and a linear compression cap. The fracture formulation, in nonholonomic rate form within a quasi-prescribed displacement approach, is based on a piecewise-linear constitutive law and is in the form of a so-called ?linear complementarity problem? (LCP). The proposed model has been applied to simulating fracture in masonry shear walls and masonry TPB panels. An experimental program was undertaken to investigate the failure behaviour of masonry panels under TPB with relatively low strength mortar. The basic material parameters were obtained from compression, TPB and shear tests on bricks, mortar and brick-mortar interfaces. The experimental results showed that the failure of masonry TPB panels is governed by both tensile and shear failure rather than just tensile failure. The simulation of the masonry TPB tests compared well with the experimental results. In addition, the LCP fracture formulation is enhanced to study the time-dependent mode I fracture in quasi-brittle materials. Two main time-dependent sources, the viscoelasticity of the bulk material and the crack rate dependent opening, are taken into account. A simplified crack rate model is proposed to include the rate-dependent crack opening. The model is applied to predicting time-dependent crack growth in plain concrete beams under sustained loading. The model captures the essential features including the observed strength increase with loading rate, the load-deflection and load-CMOD responses, the deflection-time and CMOD-time curves, the predicted time to failure and the stress distributions in the fracture zone.

Dans cette thèse, nous présentons un modèle granulaire décrivant la dynamique d'un assemblage de floes rigides de tailles et de formes diverses, soumis aux forces de traînée dues aux courants atmosphérique et océanique. Ce modèle est basé sur les équations des moments linéaire et angulaire pour décrire la dynamique régulière des floes et sur la résolution de problèmes linéaires de complémentarité pour traiter les collisions entre les floes. Entre les collisions, le mouvement d'un floe isolé satisfait la conservation des équations des moments linéaire et angulaire écrites à partir des formulations classiques des traînées dues au vent et à l'océan. Nous décrivons les collisions entre les floes comme des événements instantanés et les traitons avant qu'elles n'entraînent une interpénétration. Cela implique la notion d'impulsion de contact et la mise sous la forme de problèmes linéaires de complémentarité basés sur la condition de Signorini pour la non interpénétration et la loi de Coulomb. La nature du contact est représentée à travers un coefficient de friction et un coefficient de restitution décrivant la perte d'énergie cinétique durant la collision. Dans cette présente version du modèle, le coefficient de restitution est fixé. Le modèle a été validé en utilisant des données obtenues du mouvement de disques de bois évoluant en bassin de test aussi bien qu'en comparant le comportement des floes simulés avec un comportement attendu dans des scénarios classiques de dérive de glace et de collisions entre des solides rigides. Les résultats de simulations comprenant différents assemblages contenant des floes de tailles et de formes variées, soumis à différents scénarios de forçage, sont aussi discutés. Ils montrent tout le potentiel de notre approche sans qu'une analyse détaillée et complète n'ait encore été proposée. / In this thesis, we present a model describing the dynamics of a population of ice floes with arbitrary shapes and sizes, which are exposed to atmospheric and oceanic skin drag. The granular model presented is based on simplified momentum equations for ice floe motion between collisions and on the resolution of linear complementarity problems to deal with ice floe collisions. Between collisions, the motion of an individual ice floe satisfies the linear and angular momentum conservation equations, with classical formula applied to account for atmospheric and oceanic skin drag. To deal with collisions, before they lead to interpenetration, we included a linear complementarity problem based on the Signorini condition and Coulombs law. The nature of the contact is described through a constant coefficient of friction, as well as a coefficient of restitution describing the loss of kinetic energy during the collision. In the present version of our model, this coefficient is fixed. The model was validated using data obtained from the motion of interacting artificial wood floes in a test basin. The results of simulations comprising few hundreds of ice floes of various shapes and sizes, exposed to different forcing scenarios, and under different configurations, are also discussed. They show that the progressive clustering of ice floes as the result of kinetic energy dissipation during collisions is well captured, and suggest a collisional regimes of floe dispersion at small scales, different from a large-scale regime essentially driven by wind forcing.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-18T13:11:24Z No. of bitstreams: 1 danielalexisgutierrezpachas.pdf: 1333600 bytes, checksum: f9b6cf486d282ebbca315b17f7d4c92c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-19T11:56:41Z (GMT) No. of bitstreams: 1 danielalexisgutierrezpachas.pdf: 1333600 bytes, checksum: f9b6cf486d282ebbca315b17f7d4c92c (MD5) / Made available in DSpace on 2016-08-19T11:56:41Z (GMT). No. of bitstreams: 1 danielalexisgutierrezpachas.pdf: 1333600 bytes, checksum: f9b6cf486d282ebbca315b17f7d4c92c (MD5) Previous issue date: 2013-01-29 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho realizamos um estudo teórico das Inequações Variacionais e sua aplicação no Problema do Obstáculo. Fazemos o estudo de regularidade para este problema, e observamos que quando as condições de regularidade são satisfeitas, o Problema do Obstáculo torna-se um Problema de Complementaridade. Apresentamos os resultados de equivalência entre o Problema do Obstáculo e o Problema do Dique Retangular. Descrevemos o funcionamento do Algoritmo FDA-NCP, e resolvemos numericamente o Problema do Obstáculo usando complementaridade. / In this work, we perform a theoretical study on Variational Inequalities and their application to the Obstacle Problem. We study the regularity for this problem, and observe that when the regularity conditions are satis ed the Obstacle Problem becomes a Complementarity Problem. We present the equivalence results between the Obstacle Problem and the Square Dam Problem. We describe how the algorithm FDA-NCP works and numerically to solve the Obstacle Problem employing complementarity.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-04-17T20:10:32Z No. of bitstreams: 1 danielrodriguespereira.pdf: 736772 bytes, checksum: d15b2f08bb14ed58ae985f6123258ed5 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-04-18T13:51:41Z (GMT) No. of bitstreams: 1 danielrodriguespereira.pdf: 736772 bytes, checksum: d15b2f08bb14ed58ae985f6123258ed5 (MD5) / Made available in DSpace on 2017-04-18T13:51:41Z (GMT). No. of bitstreams: 1 danielrodriguespereira.pdf: 736772 bytes, checksum: d15b2f08bb14ed58ae985f6123258ed5 (MD5) Previous issue date: 2017-02-07 / Apresentamos neste trabalho o algoritmo de pontos interiores e direções viáveis denominado FDIPA para resolução de problemas de otimização definido por uma função diferenciável e por restrições de desigualdades. O algoritmo gera uma sequência de pontos interiores a partir de um dado ponto inicial também de interior e converge globalmente com ordem superlinear para um par Karush-Kuhn-Tucker do problema. A cada iteração uma direção de descida da função potencial é calculada inicialmente pela resolução de um sistema nas variáveis dual e primal. Apresentamos também o algoritmo FDA para resolução de problemas de complementaridade definido por uma função diferenciável e não linear. Mostramos a equivalência entre os dois métodos no sentido de gerarem as mesmas direções de descida, viável e de restauração a partir de uma atualização dos multiplicadores de Lagrange do problema de otimização. Realizamos uma comparação entre os métodos em uma coletânea de problemas de complementaridade. / In this work we present the algorithm of internal points and viable directions denominated FDIPA to solve optimization problems defined by a differentiable function and by inequalities restrictions. The algorithm generates a sequence of interior points from a given interior starting point and converges globally with superlinear order to a Karush-Kuhn-Tucker pair of the problem. At each iteration a descent direction of the potential function is calculated initially by the solution of a system in the dual and primal variables. We also present the FDA algorithm to solve complementarity problems defined by a non-linear differentiable function. We show the equivalence between the two methods in the sense that they generate the same descent, feasible and restoring directions from an update to the Lagrange multipliers of the optimization problem. We perform a comparison between the two methods in a collection of complementarity problems.

Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2017 / Operations Research (OR) is a scientific method for developing quantitatively well-grounded recommendations for decision making. While it is true that it uses a variety of mathematical techniques, OR has a much broader scope. It is in fact a systematic approach to solving problems, which uses one or more analytical tools in the process of analysis. Over the years, OR has evolved through different stages. This study is motivated by new real-world challenges needed for efficiency and innovation in line with the aims and objectives of OR – the science of better, as classified by the OR Society of the United Kingdom. New real-world challenges are encountered on a daily basis from problems arising in the fields of water, energy, agriculture, mining, tourism, IT development, natural phenomena, transport, climate change, economic and other societal requirements. To counter all these challenges, new techniques ought to be developed. The growth of global markets and the resulting increase in competition have highlighted the need for OR techniques to be improved. These developments, among other reasons, are an indication that new techniques are needed to improve the day-to-day running of organisations, regardless of size, type and location. The principal aim of this study is to modify and develop new OR techniques that can be used to solve emerging problems encountered in the areas of linear programming, integer programming, mixed integer programming, network routing and travelling salesman problems. Distribution models, resource allocation models, travelling salesman problem, general linear mixed integer ii programming and other network problems that occur in real life, have been modelled mathematically in this thesis. Most of these models belong to the NP-hard (non-deterministic polynomial) class of difficult problems. In other words, these types of problems cannot be solved in polynomial time (P). No general purpose algorithm for these problems is known. The thesis is divided into two major areas namely: (1) network models and (2) resource allocation and distribution models. Under network models, five new techniques have been developed: the minimum weight algorithm for a non-directed network, maximum reliability route in both non-directed and directed acyclic network, minimum spanning tree with index less than two, routing through 0k0 specified nodes, and a new heuristic to the travelling salesman problem. Under the resource allocation and distribution models section, four new models have been developed, and these are: a unified approach to solve transportation and assignment problems, a transportation branch and bound algorithm for the generalised assignment problem, a new hybrid search method over the extreme points for solving a large-scale LP model with non-negative coefficients, and a heuristic for a mixed integer program using the characteristic equation approach. In most of the nine approaches developed in the thesis, efforts were done to compare the effectiveness of the new approaches to existing techniques. Improvements in the new techniques in solving problems were noted. However, it was difficult to compare some of the new techniques to the existing ones because computational packages of the new techniques need to be developed first. This aspect will be subject matter of future research on developing these techniques further. It was concluded with strong evidence, that development of new OR techniques is a must if we are to encounter the emerging problems faced by the world today. Key words: NP-hard problem, Network models, Reliability, Heuristic, Largescale LP, Characteristic equation, Algorithm.