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The purpose of this work aims to develop and explore a nonlinear multiperiod petroleum refinery model based on a real-world model. Due to the inherent complexity and interconnected nature of petroleum refineries, various studies are implemented to describe the multiperiod model. The model is based around maximizing the profit of a petroleum refinery, starting from the crude inputs through the crude distillation unit, to the intermediate product processing through various unit operations, and finally to the blending of the final products. The model begins as a single period model, and is re-formulated as a multiperiod model by incorporating intermediate product tanks and dividing the model into partitions. In solving the multiperiod model, the termination criteria for convergence was varied in order to investigate the effect on the solution; it was found that it is acceptable to terminate at a relaxed tolerance due to minimal differences in solution. Several case studies, defined as deviations from normal operation, are implemented in order to draw comparisons between the real-world model and the model studied in this thesis. The thesis model, solved by CONOPT and IPOPT, resulted in significant gains over the real-world model. Next, a Lagrangean decomposition scheme was implemented in an attempt to decrease computation times. The decomposition was unable to find feasible solutions for the subproblems, as the nonlinear and nonconvex nature of the problem posed difficulty in finding feasibilities. However, in the case of a failed decomposition, the point where the decomposition ends may be used as an initial guess to solve the full space problem, regardless of feasibility of the subproblems. It was found that running the decomposition fewer times provided better initial guesses due to lower constraint violations from the infeasibilities, and then combined with the shorter decomposition time resulted in faster computation times. / Thesis / Master of Applied Science (MASc) / Petroleum refineries consist of complex units that serve a certain purpose, such as separating components of a mixed stream or blending intermediate products, in order to create final commercial products, e.g. gasoline and diesel. Due to the complexity and interconnectivity in a refinery, it is difficult to determine the optimal mode of operation. Thus, by formulating the refinery in mathematical form, optimization techniques may be used to find optimal operation. Furthermore, optimization problems can be formulated in a multiperiod fashion, where the problem is repeated over a set time horizon in partitions. The advantage is a higher detail in the operation of the refinery but this comes at a cost of higher computation time. In this work, a multiperiod refinery is formulated and studied by exploring model size, computation times, comparison of solvers, and solution strategies such as decomposition.

Inicialmente neste trabalho são apresentados os conceitos básicos de média e variância e como estes se aplicam na caracterização de um ativo ou carteira de investimento. Posteriormente são apresentadas as estratégias ótimas de investimento para o modelo de Markowitz sem posições a descoberto em ativos de risco, e sem tal restrição. Ainda neste trabalho é apresentada uma breve revisão do modelo de tempo contínuo para o problema de média-variância sem posições a descoberto em ativos de risco, e como objetivo principal do mesmo é proposto um modelo em tempo discreto multiperíodo a partir do modelo de tempo contínuo, o qual é implementado computacionalmente para o mercado de capitais brasileiro. O resultado obtido é comparado com a estratégia de período único do modelo de Markowitz sem posições a descoberto em ativos de risco, sendo este modelo aplicado sequencialmente no horizonte de tempo considerado para o modelo multiperíodo. / Initially in this work are presented the basics concepts of mean and variance and how they are applied to quantify an asset or a portfolio. After this we present the optimal investment strategy of the Markowitz no-shorting constraints mean-variance portfolio selection in single period and the Markowitz optimal investment strategy without such constrain. Following this, we present a short review of the continuous-time dynamic model for the mean-variance portfolio selection with no-shorting constraints in risky assets problem. As the main objective of this work we propose a discrete time multiperiod model based on the continuous-time portfolio selection with no-shorting constraints in risky assets, that is applied to the Brazilian financial market. This result is compared with the investment strategy of the Markowitz no-shorting constraints mean-variance portfolio selection in single period applied sequentially in the multiperiod case.

Most of the literature on scheduling of multi-product batch process does not consider the uncertainties in demand and variability in processing times. We develop a simulation based variable production schedule model for a multi-product batch facility assuming zero wait transfer policy and single product campaign. The model incorporates the demand uncertainties and processing time variability. The impact of demand uncertainties is evaluated in terms of total annual cost, which comprises of the backorder and inventory costs per year. The effect of variability in processing time is measured by the annual production time. We also develop a constant production schedule model that has uncertain demand arrival, but the schedule is independent of demand variations. We compare the variable production schedule model with constant production schedule model in terms of the total annual cost incurred and subsequent results are presented. The conclusion drawn from this comparison is that the total annual cost can be significantly reduced when the demand uncertainties are accounted for in the production schedule.

Inicialmente neste trabalho são apresentados os conceitos básicos de média e variância e como estes se aplicam na caracterização de um ativo ou carteira de investimento. Posteriormente são apresentadas as estratégias ótimas de investimento para o modelo de Markowitz sem posições a descoberto em ativos de risco, e sem tal restrição. Ainda neste trabalho é apresentada uma breve revisão do modelo de tempo contínuo para o problema de média-variância sem posições a descoberto em ativos de risco, e como objetivo principal do mesmo é proposto um modelo em tempo discreto multiperíodo a partir do modelo de tempo contínuo, o qual é implementado computacionalmente para o mercado de capitais brasileiro. O resultado obtido é comparado com a estratégia de período único do modelo de Markowitz sem posições a descoberto em ativos de risco, sendo este modelo aplicado sequencialmente no horizonte de tempo considerado para o modelo multiperíodo. / Initially in this work are presented the basics concepts of mean and variance and how they are applied to quantify an asset or a portfolio. After this we present the optimal investment strategy of the Markowitz no-shorting constraints mean-variance portfolio selection in single period and the Markowitz optimal investment strategy without such constrain. Following this, we present a short review of the continuous-time dynamic model for the mean-variance portfolio selection with no-shorting constraints in risky assets problem. As the main objective of this work we propose a discrete time multiperiod model based on the continuous-time portfolio selection with no-shorting constraints in risky assets, that is applied to the Brazilian financial market. This result is compared with the investment strategy of the Markowitz no-shorting constraints mean-variance portfolio selection in single period applied sequentially in the multiperiod case.

In the push for clean and renewable fuels, timber derived biomass is a promising frontier for biofuel production in the United States. This thesis approaches the established timberlands biofuel implementation problem with three different mathematical programming studies, each testing feasibility and sustainability in different economic and supply related situations. In the first study, a competitive game theory approach was utilized to provide new insights into the behavior within a timberlands supply chain. We utilized Stackelberg game theory modeled with bilevel programming to represent the competing harvesting and manufacturing sectors. In the second study, the initial bilevel model was utilized in a larger two stage multiperiod model with parameter uncertainty. In this more realistic model, the first stage contained logistical decisions around biorefinery investments, such as location and capacity, while the second stage was composed of multiple discrete bilevel scenarios representing potential situations in the timberlands system. The final study focused on long term land management strategies for the timberlands supply chain. Introduction of a new biorefinery investment meant that management strategies must be altered to ensure consistent material flows to manufacturers as well as sustain the new production facility. A modified cyclic scheduling formulation was used to model a timberlands system and its planting and harvesting schedule to accommodate a new biorefinery. This cyclic model added an initial startup period to initiate biofuel production and provide time to adapt land management. The overall contribution of these studies was to analyze a biorefinery's impact on the established behavior in a timberlands supply chain. In particular, the goals of these models were to develop introductory decision making tools for timberlands supply chain managers.

Este estudo considera o modelo de controle ótimo estocástico sob um critério de média-variância para sistemas lineares a tempo discreto sujeitos a saltos Markovianos e ruídos multiplicativos sob dois critérios. Inicialmente, consideramos como critério de desempenho a minimização multiperíodo de uma combinação entre a média e a variância da saída do sistema sem restrições. Em seguida, consideramos o critério de minimização multiperíodo da variância da saída do sistema ao longo do tempo com restrições sobre o valor esperado mínimo. Condições necessárias e suficientes explícitas para a existência de um controle ótimo são determinadas generalizando resultados anteriores existentes na literatura. O controle ótimo é escrito como uma realimentação de estado adicionado de um termo constante. Esta solução é obtida através de um conjunto de equações generalizadas a diferenças de Riccati interconectadas com um conjunto de equações lineares recursivas. Como aplicação, apresentamos alguns exemplos numéricos práticos para um problema de seleção de portfólio multiperíodo com mudança de regime, incluindo uma estratégia de ALM (Asset and Liability Management). Neste problema, deseja-se obter a melhor alocação de portfólio de forma a otimizar seu desempenho entre risco e retorno em cada passo de tempo até o nal do horizonte de investimento e sob um dos dois critérios citados acima. / In this work we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under two criterions. First, we consider an unconstrained multiperiod mean-variance trade-off performance criterion. In the sequence, we consider a multiperiod minimum variance criterion subject to constraints on the minimum expected output along the time. We present explicit necessary and sufficient conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. The optimal control law is written as a state feedback added with a deterministic sequence. This solution is derived from a set of coupled generalized Riccati difference equations interconnected with a set of coupled linear recursive equations. As an application, we present some practical numerical examples on a multiperiod portfolio selection problem with regime switching, including an Asset and Liability Management strategy. In this problem it is desired to nd the best portfolio allocation in order to optimize its risk-return performance in every time step along the investment horizon, under one of the two criterions stated above.In this work we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under two criterions. First, we consider an unconstrained multiperiod mean-variance trade-off performance criterion. In the sequence, we consider a multiperiod minimum variance criterion subject to constraints on the minimum expected output along the time. We present explicit necessary and sufficient conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. The optimal control law is written as a state feedback added with a deterministic sequence. This solution is derived from a set of coupled generalized Riccati difference equations interconnected with a set of coupled linear recursive equations. As an application, we present some practical numerical examples on a multiperiod portfolio selection problem with regime switching, including an Asset and Liability Management strategy. In this problem it is desired to nd the best portfolio allocation in order to optimize its risk-return performance in every time step along the investment horizon, under one of the two criterions stated above.

<p>The transportation cost of logs from forest to customers is a large part of the overall cost for the Swedish forestry industry. Finding good routes from harvesting points to saw and pulp mills is a complex task, where the total number of feasible routes is extremely high. In this thesis we present two methods for log truck scheduling. </p><p>The first is to, from a given set of routes, find the most valuable subset that fulfils the customers demand. We use a model that is similar to the set partitioning problem and a method that is referred to as a composite pricing coupled with Branch and Bound. The composite pricing based method prices the routes (columns) and chooses the most valuable ones that are then added to the LP relaxation. Once an LP optimum is found, the Branch and Bound method is used to find an integer optimum solution. We have tested this on a case of realistic size. </p><p>The second method is a tabu search heuristic. Here, the purpose is to create efficient and qualitative routes from a given number of trips (referred to as predefined trips). From a start solution tabu search systematically generates new solutions. This method was tested on a small problem and on a five times larger problem to study how the size of the problem affected the result. It was also tested and compared on two cases in which the backhauling possibilities (i.e. instead of traveling empty the truck picks up another load on the return trip) had and had not been studied. The composite pricing based method and the tabu search method proved to be very useful for this kind of scheduling.</p>

The transportation cost of logs from forest to customers is a large part of the overall cost for the Swedish forestry industry. Finding good routes from harvesting points to saw and pulp mills is a complex task, where the total number of feasible routes is extremely high. In this thesis we present two methods for log truck scheduling. The first is to, from a given set of routes, find the most valuable subset that fulfils the customers demand. We use a model that is similar to the set partitioning problem and a method that is referred to as a composite pricing coupled with Branch and Bound. The composite pricing based method prices the routes (columns) and chooses the most valuable ones that are then added to the LP relaxation. Once an LP optimum is found, the Branch and Bound method is used to find an integer optimum solution. We have tested this on a case of realistic size. The second method is a tabu search heuristic. Here, the purpose is to create efficient and qualitative routes from a given number of trips (referred to as predefined trips). From a start solution tabu search systematically generates new solutions. This method was tested on a small problem and on a five times larger problem to study how the size of the problem affected the result. It was also tested and compared on two cases in which the backhauling possibilities (i.e. instead of traveling empty the truck picks up another load on the return trip) had and had not been studied. The composite pricing based method and the tabu search method proved to be very useful for this kind of scheduling.

Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-10-11T20:12:25Z No. of bitstreams: 1 DissTSK.pdf: 3524235 bytes, checksum: 7f004fb5c47d3a888f9b19f884f38946 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-21T12:58:59Z (GMT) No. of bitstreams: 1 DissTSK.pdf: 3524235 bytes, checksum: 7f004fb5c47d3a888f9b19f884f38946 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-21T12:59:07Z (GMT) No. of bitstreams: 1 DissTSK.pdf: 3524235 bytes, checksum: 7f004fb5c47d3a888f9b19f884f38946 (MD5) / Made available in DSpace on 2016-10-21T12:59:15Z (GMT). No. of bitstreams: 1 DissTSK.pdf: 3524235 bytes, checksum: 7f004fb5c47d3a888f9b19f884f38946 (MD5) Previous issue date: 2016-05-19 / Não recebi financiamento / This dissertation studies the application of a periodic review inventory model based on the multiperiod newsboy problem, as an effective alternative to reach a well balanced inventory planning policy of subcontractors primary parts area of the aerospace industry. In Brazil, the aerospace industry is responsible for a large amount of the country exports and this industry competes with other globally aerospace supply chains in a scenario increasingly turbulent and demanding for fast deliveries, with high quality levels and low cost. The purpose of this work is to study and propose this alternative for optimizing the inventory planning by means of a quantitative approach, applied in a primary parts sector of the aerospace industry, it will focus in a specific group of items with high annual demand value. The main objective of this approach is to balance the high inventory costs with a high service level demanded in this industry, and efficiently respond the stakeholders expectations, with superior performance of the usual models adopted by this industry, and give a better support to the decision makers in a tactical-operational level. The result obtained show the potential of the method to improve the performance of these inventory management and planning systems. / Este trabalho estuda a aplicação de um modelo analítico de revisão periódica de estoques, baseado no problema do jornaleiro multiperíodo (Multiperiod Newsboy Problem), como uma alternativa efetiva para determinação da política de planejamento de estoques do setor de peças primárias subcontratadas da indústria aeroespacial. No Brasil, a indústria aeroespacial é responsável por grande parte das exportações do país e compete globalmente com outras cadeias aeroespaciais num cenário cada vez mais turbulento e exigente por entregas rápidas, com altos níveis de qualidade e baixos custos. O objetivo deste trabalho é estudar e propor essa alternativa para otimizar o planejamento de estoques por meio de uma abordagem quantitativa, aplicada no setor de peças primárias da indústria aeroespacial, para um grupo de peças com características especificas, principalmente as de alto valor para demanda anual. O intuito desta abordagem é equilibrar os altos custos de estoque com os altos níveis de serviço exigidos por esta indústria, e responder de forma eficiente às expectativas dos stakeholders, com desempenho superior aos modelos atualmente utilizados no setor e auxiliar de forma mais precisa e sistematizada a tomada de decisão no nível tático-operacional. Os resultados obtidos mostram o potencial do método para melhorar o desempenho desses sistemas de gestão e planejamento de estoques.