The scheduling of the converter aisle of a nickel smelting plant is a non-trivial task with significant consequences to plant profitability and production. An optimization-based scheduling formulation is developed using a continuous-time paradigm to accurately represent event timings. The formulation accounts for environmental restrictions on sulfur dioxide emissions using event timing constraints. The formulation includes novel semi-continuous modeling to represent flash furnaces which operate with a continuous inlet flow and intermittent discrete material removal, as well as, a novel sequencing and symmetry-breaking scheme to account for identical units operating in parallel. A rolling horizon feature is included in the formulation to accommodate multi-period optimization. Tightening constraints are developed and used to improve the computational performance of the optimization and demonstrate the capacity of the proposed methodology to function as a real-time decision-support tool. A solution procedure is presented where an aggregate model is used to bound the objective function of the master problem in a two layer optimization scheme. Finally, a novel multi-tiered procedure is presented to enhance the optimization solution by re-optimizing for objectives of decreasing priority in order to minimize task start times and penalize deviations in the furnace flow rate. To address the closed-loop properties of scheduling, a reactive scheduling mechanism is included to allow for rescheduling to account the impact of process disturbances on the operating schedule. A methodology for reducing radical scheduling changes due to the optimization during reactive scheduling is presented. The reactive scheduling algorithm utilizes a tiered optimization approach that progressively increases the degrees of freedom available, as required, in order to achieve a feasible production schedule. The use of the reactive scheduling algorithm demonstrates the ability to reject disturbances and transition plant operation in an agile manner. / Thesis / Master of Applied Science (MASc)

Additional electricity meters behind the grid access point can improve understanding of energy consumption patterns and thus, adjust consumption behavior. For this study, smart meters were installed in three hostels, out of which two are analyzed further in this paper. Starting from an onsite inspection, all appliances were assigned to reasonable groups for sub-metering. Based on data for the year 2021, the sites are characterized according to the sub-metering concept. In addition, load profiles for type-days are derived, which allows to establish a baseload during COVID lockdown and compare it to consumption patterns for normal occupation. In the prescriptive part, the demand profiles are analyzed regarding their economic potential for load shifting. Consumption data for one week with normal occupation is used as input for techno-economic modeling. The mixed-integer model minimizes electricity purchasing costs for different scenarios including dynamic tariffs and onsite generation from photovoltaics.

This study derives the levelized cost of heat (LCOH) for exemplary post-fossil district heating (DH) scenarios. The DH system of Leipzig in 2040 under the assumption of a completely climate-neutral heat supply is considered. Accordingly, four generation scenarios (GS) are proposed based on different energy carriers that are characterized as follows: (1) natural gas with carbon capture and storage, (2) hydrogen, (3) diversified mix of biomass, waste heat and solar, and (4) electricity. In addition, the scenarios’ robustness toward commodity prices is investigated using a sensitivity analysis. A modeling environment was used to optimize the hourly economic dispatch. Based on this, levelized costs are determined. For the reference case, the LCOH of the GS 1 and 2 exceeds the LCOH of GS 3 and 4. Furthermore, the results indicate that relying on singular energy carriers as opposed to diversified generation portfolios leads to less robust LCOH regarding price sensitivities.

Portfolio optimization is a crucial practice in finance aimed at maximizing the return while minimizing the risk through strategic asset allocation. This paper explores two distinct approaches to modeling robust portfolio optimization, comparing their efficacy in balancing the return and the risk. The first approach focuses on diversifying the portfolio by varying the number of stocks and sector allocation, while the second approach emphasizes minimizing risk by selecting stocks with low correlation. Theoretical foundations and mathematical formulations underpinning these approaches are discussed, incorporating concepts from Modern Portfolio Theory and Mixed Integer Linear Programming. Practical implementation involves data collection from Yahoo Finance API and computational analysis using Python and the optimization tool Gurobi. The results of these methodologies are evaluated, considering factors such as budget constraints, maximum and minimum investment limits, binary constraints, and correlation thresholds. The study concludes by discussing the implications of these findings and their relevance in contemporary financial decision-making processes.

[pt] No Brasil, as três principais fontes renováveis de energia elétrica são eólica, pequenas centrais hidrelétricas (PCHs) e biomassa. A comercialização da energia proveniente dessas fontes ocorre majoritariamente no ambiente de contratação regulada (ACR), através de leilões, em detrimento do ambiente de contratação livre (ACL). Isso devido ao fato de seus recursos naturais serem sazonais, estabelecendo o risco de preço-quantidade no ACL, em que o excesso ou déficit de energia gerada em relação à quantidade contratada é liquidado ao preço de liquidação de diferenças (PLD), uma variável sistêmica e altamente volátil. Contudo, a complementaridade dessas fontes permite reduzir esses riscos quando a energia é comercializada de forma conjunta, através de um fundo de energia que gera aumento do valor do portfólio com relação à comercialização individual. Esta dissertação utiliza a teoria de jogos cooperativos para analisar formas de repartir o benefício gerado, através da alocação de quotas financeiras. O conjunto de soluções onde o resultado individual das fontes no fundo é maior do que o resultado individual em qualquer subcoalisão define o núcleo do jogo. Assim, a complexidade de encontrar uma solução dentro do núcleo depende do número de subcoalizões, que cresce exponencialmente com o número de jogadores. Nesse contexto, este trabalho se propôs a apresentar: (i) um modelo de portfólio que incentiva a participação de fontes renováveis no ACL; (ii) um modelo de programação linear que busca o núcleo do jogo; (iii) uma metodologia eficiente baseada em decomposição de Benders, capaz de suprimir a questão da explosão combinatória do problema. / [en] In Brazil, the three main sources of renewable energy are wind, small run-of-river hidros (SH) and biomass. The energy sale of such sources occurs mainly in the Regulated Trading Environment (RTE), through auctions, with shy occurrences in the Free Trading Environment (FTE). This is due to the fact that their natural resources are seasonal, establishing the so-called price-quantity risk in the FTE, as the surplus or deficit of energy generated relative to the contracted amount is settled at the market’s spot price, a systemic and highly volatile variable. However, the complementary nature of these sources allows risk reduction if their energy are trade jointly, through an energy hedge pool that increases the value of the portfolio in comparison to individual strategies. This work makes use of cooperative games theory to analyze ways of sharing the generated benefit, through financial quotas allocation. The set of solutions where the individual sources results in the pool are greater than its results at any possible subcoalition defines the core of the game. Thus, the challenge of finding a solution inside the core depends on the number of subcoalitions, which grows exponentially with the number of players. In this context, this work proposes to present: (i) a model of portfolio that encourages the penetration of renewable sources in the FTE; (ii) a linear programming model that pursuits the game’s core; (iii) an efficient methodology based on Benders decomposition that is capable of suppress the problem of combinatorial explosion, typical of cooperative games with many players.

Este trabalho apresenta um modelo linearizado para ser utilizado em problemas de planejamento da expansão de sistemas de distribuição de energia elétrica (SDEE) com geração distribuída (GD), em um horizonte de curto prazo. O ponto de operação em regime permanente é calculado através de um modelo linearizado da rede, sendo as cargas e geradores representados por injeções constantes de corrente, o que torna possível calcular as correntes nos ramos e as tensões nas barras através de expressões lineares. As alternativas de expansão consideradas são: (i) alocação de bancos de capacitores; (ii) alocação de reguladores de tensão; e (iii) recondutoramento. Ainda, o modelo considera a possibilidade de seleção do tap dos transformadores de distribuição como alternativa para a redução das violações de tensão. A flexibilidade do modelo permite obter soluções considerando a contribuição das GDs no controle de tensão e potência reativa sem a necessidade de especificar uma tensão para a barra da subestação. O modelo de otimização proposto para a solução destes problemas utiliza uma função objetivo linear, além de restrições lineares e variáveis contínuas e binárias. Dessa forma, o modelo de otimização pode ser representado como um problema de programação linear inteira mista (PLIM) A função objetivo considera a minimização dos custos de investimento (aquisição, instalação e remoção de equipamentos e aquisição de condutores) e dos custos de operação, que correspondem aos custos anuais de manutenção somados aos custos das perdas de energia e das violações dos limites de tensão. A variação da carga é representada através de curvas de duração, sendo que os custos das perdas e das violações são ponderados pela duração de cada nível de carregamento. Utilizando uma abordagem de PLIM, sabe-se que existem condições suficientes que garantem a otimalidade de uma dada solução factível, além de permitir que a solução seja obtida através de métodos de otimização clássica. O modelo proposto foi implementado na linguagem de programação OPL e resolvido utilizando o solver comercial CPLEX. O modelo foi validado através da comparação dos resultados obtidos para cinco sistemas de distribuição com os resultados obtidos utilizando um fluxo de carga convencional. Os casos analisados e os resultados obtidos demonstram a precisão do modelo proposto e seu potencial de aplicação. / This work presents a linearized model to be used in short-term expansion planning problems of power distribution systems (PDS) with distributed generation (DG). The steady state operation point is calculated through a linearized model of the network, being the loads and generators modeled as constant current injections, which makes it possible to calculate the branch currents and bus voltages through linear expressions. The alternatives considered for expansion are: (i) capacitor banks placement; (ii) voltage regulators placement; and (iii) reconductoring. Furthermore, the model considers the possibility of adjusting the taps of the distribution transformers as an alternative to reduce voltage violations. The flexibility of the model enables solutions that includes the contribution of DGs in the control of voltage and reactive power without the need to specify the substation voltage. The optimization model proposed to solve these problems uses a linear objective function, along with linear constraints, binary and continuous variables. Thus, the optimization model can be represented as a mixed integer linear programming problem (MILP) The objective function considers the minimization of the investment costs (acquisition, installation and removal of equipment and acquisition of conductors) and the operation costs, which corresponds to the annual maintenance cost plus the costs related to energy losses and violation of voltage limits. The load variation is represented by discrete load duration curves and the costs of losses and voltage violations are weighted by the duration of each load level. Using a MILP approach, it is known that there are sufficient conditions that guarantee the optimality of a given feasible solution, besides allowing the solution to be obtained by classical optimization methods. The proposed model was written in the programming language OPL and solved by the commercial solver CPLEX. The model was validated through the comparison of the results obtained for five distribution systems with the results obtained through conventional load flow. The analyzed cases and the obtained results show the accuracy of the proposed model and its potential for application.

A presente pesquisa considera o problema de programação de uma frota de embarcações de lançamentos de dutos, conhecidas como Pipe Layer Support Vessel (PLSVs), as quais fazem parte da frota de apoio marítimo de uma operação offshore. As embarcações do tipo PLSVs são responsáveis pelas tarefas de lançamento de dutos submarinos, que escoam a produção dos poços de petróleo, e pela interligação destes dutos à infraestrutura submarina. A programação da frota deve atender uma demanda de serviço conhecida, em um horizonte de médio prazo, respeitando restrições operacionais, visando minimizar o atraso ponderado total das tarefas ou evitar que existam atrasos. Foi desenvolvido um método para estimar o valor da solução ótima do problema, baseado na técnica de relaxação Lagrangiana, e um conjunto de heurísticas para gerar soluções viáveis para o problema. / This research considers the problem of scheduling a fleet of specialized vessels used for launching pipes and connecting them to the subsea infrastructure, in an offshore oil production environment. The Pipe Layer Support Vessels (PLSV) must be scheduled such that the demand is fully attended within the planning horizon, observing other operational constraints, with the purpose of minimizing the total weighted tardiness. The solution method is based on constructive and local search heuristics. Bounds on the optimal solution were derived by a Lagrangean relaxation algorithm.

本論文研究股票分類與否對投資組合報酬有無差別，因此以目標規畫方式提出兩個混合整數線性規劃模型建立投資組合。在考量市場風險上，兩模型的差別在於一個是單股比重的限制，另一個是類股數目的限制。兩模型中均考慮交易數量為整數與實務中的交易成本，且採用了0-1決策變數，決定股票及類股的選取與否。並以台灣股票市場作為實證研究對象，探討兩模型投資組合在市場不同走勢下的表現，同時也觀察股票分類後，探討選幾個類股數會有較佳的績效，並分析投資組合建立後多久應該進行調整。 / This thesis studies the effect of return of a portfolio while restricting the number of asset category. Two mixed-integer linear programming models are proposed by using the goal programming technique. In consideration of the risk, the difference between these two models is that one focuses on a single stock restriction, and the other is on the asset category restriction. The integer restriction and transaction cost are included in the model while using binary decision variable to indicate the selection of an asset and the selection a category. Finally, an empirical study will be presented by applying to Taiwan’s stock market. The performances of these two models are discussed. Moreover, the best number of category in the portfolio and the best timing of rebalance are also investigated.

As more owners seek to develop sustainable buildings, the construction industry is adapting to new requirements in order to meet owner's concerns. Material selection has been identified as an area where designers and contractors can have a significant impact on the sustainable performance of a building. Objective factors such as design considerations and cost constraints can play a role in the selection of materials. However, there may be subjective factors that could also impact the selection of materials. Building upon the potential impact of sustainability perceptions in an optimization model that can be used to help decision makers to select materials, this study defines and tests an instrument to identify and measure such perceptions. The purpose of this dissertation is to develop a conceptual instrument that measures the user-based assessment of product sustainability and validates decision-maker's perceptions in order to evaluate the contribution of subjective characteristics in materials selection. A survey of design and construction students and practitioners is carried out to capture the subjective factors included in the instrument. A Factor Analysis approach is used to refine and validate the measurement instrument and predict decision-makers' sustainability appraisal due to the factors considered.

Χωροθέτηση μονάδας επεξεργασίας ΑΣΑ σε συνδιασμό με τον απαραίτητο ΧΥΤΥ, με μικτό ακέραιο γραμμικό προγραμματισμό, για τη βελτιστοποίηση των ακολουθούμενων διαδρομών των απορριμματοφόρων προς την μονάδα επεξεργασίας και απο την μονάδα προς τον ΧΥΤΥ.Εγινε με εφαρμογή GIS στη Μεσσηνία. / The current thesis is about optimum siting of a MSW treatment plant combined with a landfill for residues based on mixed integer linear programming (MILP) and GIS methodology.