指數基金係提供投資者追隨市場指數成長的投資工具，且投資者僅需考量市場風險即可，其建構方式有完全複製法、分層法、抽樣法、及最佳化法。本論文使用目標規劃模型建構指數基金，此法可歸類為最佳化法。由於模型中每種股票的投資數量設為整數變數，加上控制股票種類數量的0-1變數，因此所建構的目標規劃模型為混合型整數線性規劃問題。此問題在大尺度模型時往往無法求得其最佳解，我們研究此模型的結構提出一組縮小解集合空間的合理不等式，應用切面法加入必需的不等式後再根據本模型的對偶性質發展出有效率的啟發式演算法，最後將此模型及演算法應用在模擬台灣發行量加權股價指數。 / Index fund is an investment tool which tracks a stock-market index and thus is associated with market risk only. Its attraction to investors is low investment risk and low administrative expenses. Four different approaches to index fund construction can be classified as full replication, stratification, sampling, and optimizing respectively. In this thesis, we construct an index fund via the goal programming model with the optimizing approach. The model can be formulated as a mixed integer linear programming. The exact optimal solution can not be obtained when the model becomes large. We then develop a valid inequality and use this valid inequality to develop a cutting plane method. We also propose an efficient heuristic by adopting the dual property. Finally, an empirical study applying to the Taiwan Stock Exchange Capitalization Weighted Stock Index is given to show the efficiency of the algorithm.

Sistemas de Distribuição de Energia Elétrica (SDEE) estão, pelas próprias condições de funcionamento, sujeitos a perdas de energia e quedas nos níveis de tensão. Uma das formas de reduzir as perdas e ao mesmo tempo melhorar o perfil de tensão do SDEE consiste na utilização de bancos de capacitores e reguladores de tensão ao longo dos alimentadores. Para isto a alocação ótima destes equipamentos torna-se de fundamental importância, logo este trabalho tem por objetivo a utilização de um método quadrático de programação por metas multiobjetivo para a ótima alocação desses equipamentos visando a redução de perdas (meta 1) com o menor custo de investimento (meta 2) sujeito a restrições do fluxo de potência, limites técnicos de operação, mudança no controle dos capacitores chaveados e dos taps dos reguladores de tensão. O constante aumento na penetração da geração distribuída traz novos desafios para o controle e a operação dos SDEE. A metodologia proposta considera os efeitos destas fontes de geração e os seus impactos na alocações ótima dos bancos de capacitores e reguladores de tensão. Com o intuito de resolver o problema de otimização em programas comerciais como Gurobi e Cplex uma metodologia linear de cálculo de fluxo de potência é utilizada. Os algoritmos foram desenvolvidos no software Matlab, e posteriormente foi realizada a conversão para linguagem GAMS (Generic Algebraic Modeling System) para utilização dos solvers na plataforma NEOS (Network Enabled Optimization System). / Power distribution systems (DS) are susceptible to energy loss and voltage drops, mainly because of the way that they are operated and built. One way to minimize system loss and improve the voltage profile of DS is with the use of capacitor banks and voltage regulators (VRs) along the distribution feeders. In this scenario, the optimal placement of these devices becomes crucial. In this paper, a quadratic multi objective goal programming method is proposed to obtain the optimal placement of these devices, where the goals are energy loss (goal 1) and the total investment cost (goal 2). The model is subject to system operation constraints, such as power flow demands, limits of voltages and currents, number of stages of switched capacitors and the tap control of VRs. The increase of distributed generation penetration brings new challenges for control and operation of DS. The proposed methodology considers the effects of these power sources and their impact on optimal allocations of capacitors and VRs. With the aim of solving the optimization problem in commercial programs, a linear power flow is used. The algorithms were developed with Matlab software and the conversion was made to a General Algebraic Modeling System (GAMS) language and solved in the NEOS (Network Enabled Optimization System) platform.

Sistemas de Distribuição de Energia Elétrica (SDEE) estão, pelas próprias condições de funcionamento, sujeitos a perdas de energia e quedas nos níveis de tensão. Uma das formas de reduzir as perdas e ao mesmo tempo melhorar o perfil de tensão do SDEE consiste na utilização de bancos de capacitores e reguladores de tensão ao longo dos alimentadores. Para isto a alocação ótima destes equipamentos torna-se de fundamental importância, logo este trabalho tem por objetivo a utilização de um método quadrático de programação por metas multiobjetivo para a ótima alocação desses equipamentos visando a redução de perdas (meta 1) com o menor custo de investimento (meta 2) sujeito a restrições do fluxo de potência, limites técnicos de operação, mudança no controle dos capacitores chaveados e dos taps dos reguladores de tensão. O constante aumento na penetração da geração distribuída traz novos desafios para o controle e a operação dos SDEE. A metodologia proposta considera os efeitos destas fontes de geração e os seus impactos na alocações ótima dos bancos de capacitores e reguladores de tensão. Com o intuito de resolver o problema de otimização em programas comerciais como Gurobi e Cplex uma metodologia linear de cálculo de fluxo de potência é utilizada. Os algoritmos foram desenvolvidos no software Matlab, e posteriormente foi realizada a conversão para linguagem GAMS (Generic Algebraic Modeling System) para utilização dos solvers na plataforma NEOS (Network Enabled Optimization System). / Power distribution systems (DS) are susceptible to energy loss and voltage drops, mainly because of the way that they are operated and built. One way to minimize system loss and improve the voltage profile of DS is with the use of capacitor banks and voltage regulators (VRs) along the distribution feeders. In this scenario, the optimal placement of these devices becomes crucial. In this paper, a quadratic multi objective goal programming method is proposed to obtain the optimal placement of these devices, where the goals are energy loss (goal 1) and the total investment cost (goal 2). The model is subject to system operation constraints, such as power flow demands, limits of voltages and currents, number of stages of switched capacitors and the tap control of VRs. The increase of distributed generation penetration brings new challenges for control and operation of DS. The proposed methodology considers the effects of these power sources and their impact on optimal allocations of capacitors and VRs. With the aim of solving the optimization problem in commercial programs, a linear power flow is used. The algorithms were developed with Matlab software and the conversion was made to a General Algebraic Modeling System (GAMS) language and solved in the NEOS (Network Enabled Optimization System) platform.

Sistemas de Distribuição de Energia Elétrica (SDEE) estão, pelas próprias condições de funcionamento, sujeitos a perdas de energia e quedas nos níveis de tensão. Uma das formas de reduzir as perdas e ao mesmo tempo melhorar o perfil de tensão do SDEE consiste na utilização de bancos de capacitores e reguladores de tensão ao longo dos alimentadores. Para isto a alocação ótima destes equipamentos torna-se de fundamental importância, logo este trabalho tem por objetivo a utilização de um método quadrático de programação por metas multiobjetivo para a ótima alocação desses equipamentos visando a redução de perdas (meta 1) com o menor custo de investimento (meta 2) sujeito a restrições do fluxo de potência, limites técnicos de operação, mudança no controle dos capacitores chaveados e dos taps dos reguladores de tensão. O constante aumento na penetração da geração distribuída traz novos desafios para o controle e a operação dos SDEE. A metodologia proposta considera os efeitos destas fontes de geração e os seus impactos na alocações ótima dos bancos de capacitores e reguladores de tensão. Com o intuito de resolver o problema de otimização em programas comerciais como Gurobi e Cplex uma metodologia linear de cálculo de fluxo de potência é utilizada. Os algoritmos foram desenvolvidos no software Matlab, e posteriormente foi realizada a conversão para linguagem GAMS (Generic Algebraic Modeling System) para utilização dos solvers na plataforma NEOS (Network Enabled Optimization System). / Power distribution systems (DS) are susceptible to energy loss and voltage drops, mainly because of the way that they are operated and built. One way to minimize system loss and improve the voltage profile of DS is with the use of capacitor banks and voltage regulators (VRs) along the distribution feeders. In this scenario, the optimal placement of these devices becomes crucial. In this paper, a quadratic multi objective goal programming method is proposed to obtain the optimal placement of these devices, where the goals are energy loss (goal 1) and the total investment cost (goal 2). The model is subject to system operation constraints, such as power flow demands, limits of voltages and currents, number of stages of switched capacitors and the tap control of VRs. The increase of distributed generation penetration brings new challenges for control and operation of DS. The proposed methodology considers the effects of these power sources and their impact on optimal allocations of capacitors and VRs. With the aim of solving the optimization problem in commercial programs, a linear power flow is used. The algorithms were developed with Matlab software and the conversion was made to a General Algebraic Modeling System (GAMS) language and solved in the NEOS (Network Enabled Optimization System) platform.

Inventory management under uncertainty is a widely researched field and many different types of inventory models have been used to address inventory problems in practice [1, 10, 11, 26, 50, 35]. However, there is a lack of published studies focusing on inventory planning in environments, such as the military, that are characterised by uncertainty as a result of extreme events. A critical area in military decision support is inventory management. Planning for stock levels in particular can be a daunting task, due to the uncertainty associated with the future. The military is typically an environment where improbable events can have massive impacts on operations; and the availability of the correct amount of stock can enhance the responsiveness, efficiency, and preparedness of the military, and ultimately save human lives. On the other hand, excessive stock - especially ammunition - can result in huge monetary losses through damages, stock degradation, and stock obsolescence. Excessive ammunition also poses a risk to public safety, and can ultimately challenge a country's ability to control the use of force. It is therefore very important to provide proper attention to determining the required stock levels during military inventory management. This dissertation aims, therefore, to develop a reliable decision support tool that can assist with inventory management in the military. To achieve this, a mixed multi-objective mathematical model is used that attempts to minimise cost, shortages, and stock while incorporating demand uncertainty by means of probability distributions and fuzzy numbers. The model considers three different scenarios, and determines the minimum required stock level and the best order quantity for three different stock categories, for a single ammunition item. The model is converted into its crisp, non-fuzzy, and deterministic counterpart first by transforming the fuzzy constraints into their crisp versions and then deriving the deterministic model of the crisp recourse stochastic model. The corresponding crisp, deterministic model is then solved using exact branch-and-bound embedded in the LINGO 10.0 optimisation software package and the reliability of the solutions in different scenarios is tested by means of discrete event simulation. The reliability of the model is then compared with the reliabilities of the well known (r;Q) and (s; S) inventory models in the literature. The comparison indicates that the mixed model proposed in this dissertation is more reliable in extreme scenarios than the (r;Q) and (s; S) inventory models in the literature. A sensitivity analysis is then performed and results indicate that the model yields reliable solutions with a reliability that varies between 74.54% and 100%, depending on the scenario investigated. The lower reliability is during the high demand scenario, this is caused by the ability of the inventory model to prioritise different scenarios based on their estimated possibility to ensure that stock levels are not unneccessary escalated for highly improbable events. It can be concluded that the proposed mixed multi-objective mathematical model that aims to minimise inventory cost, surplus stock, and shortages is a reliable inventory decision support model for the uncertain military environment. / Dissertation (MEng)--University of Pretoria, 2011. / Industrial and Systems Engineering / unrestricted

In this thesis I consider possibility to spend my vacation in one of the three countries: Spain, France, Italy. In each country I chose ten cities, which I would like to visit. I will use Travel Salesman Problem to decide the best route inside each country according to three criteria: Cost, Minutes and Transport. There is also a possibility to choose the type of transport: train or combination of train and airplane. Also I will use Weighted goal programming and Chebyshev goal programming to optimize all criteria simultaneously. In the end I will use multiple -- criteria decision analysis to compare results. According to three methods (ORESTE, ELECTRE III, TOPSIS) I will choose one of the states for my vacation. I will make all calculation in program MPL and in Excel using solver SANNA.

Goal programming is an approach for solving decision problems. The aim of this doctoral thesis is to show the practical use of this approach for solving real problems. The first chapter brings a brief introduction to multicriteria decision making. The second chapter is devoted to goal programming, its history, theory, criticism and also to its practical applications. The third chapter deals with description of a model for optimisation of white mass production. This model utilises the goal programming principle to deal with measuring deviations of raw materials' composition. A part of this chapter is a presentation of OPTIPROT, an application that implements the mentioned model. In the fourth chapter there are described three mathematical models for timetabling at a department level; two multistage models and one complex model. All three models are formulated utilising goal programming. In this chapter there is also described an application that implements the complex model for timetabling.

Les travaux présentés dans cette thèse portent sur la notion de performance environnementale comme cadre analytique pour l’étude des impacts des activités agricoles sur l’environnement. Après avoir mis en évidence un manque de formalisation de cette notion dans la littérature, nous la définissons comme la distance entre l’état environnemental d’un écosystème à un moment donné et un état environnemental à atteindre pour cet écosystème, dit « de haute performance environnementale ». Dans cette étude, l’état environnemental est approché par trois critères liés à la ressource « eau » : les concentrations en nitrates et en matières en suspension, et les débits.Suite à la description de l’état initial, nous proposons une méthode d’optimisation de la performance environnementale des activités agricoles basée sur un couplage entre un modèle agro-hydrologique (SWAT) et un modèle d’optimisation multicritère (Weighted Goal Programming). La démarche d’optimisation considère la réaffectation spatialisée de systèmes de culture sur l’espace considéré comme facteur d’amélioration, les différents critères de l’optimisation étant examinés simultanément.La méthode est implémentée sur le bassin versant de la Boulouze (coteaux de Gascogne). Les résultats montrent une amélioration de la performance environnementale du système étudié. L’analyse de la nouvelle occupation des sols souligne qu’au-delà des évolutions quantitatives des surfaces allouées aux systèmes de culture, la spatialisation des changements d’un système vers un autre influe également sur la performance environnementale à l’échelle du bassin versant. Enfin, nous interrogeons l’applicabilité de cette méthode et mettons en évidence l’intérêt qu’elle présente comme outil à la fois de modélisation de scénarios et de communication. / We introduce in this thesis the notion of environmental performance as an analytical framework aimed at studying the impacts of agricultural activities on the environment. We outline first a need to formalize this notion and then define it as the distance between the “environmental” state of a system at a specific time and a state of “high environmental performance” to achieve. Focus is on water management at the watershed level with three criteria: nitrogen, sediments (water quality) and water flows (water quantity).Our aim is to optimize the environmental performance of agricultural activities at the watershed scale. First the initial status of the watershed is described, then a method is proposed. This method is based on a coupling between an agro-hydrological model, the Soil and Water Assessment Tool (SWAT), and the Weighted Goal Programming optimization method. Our purpose is the reallocation of farming systems within the watershed when considering the optimization criteria simultaneously.We implement this method on the Boulouze watershed (coteaux de Gascogne, in the southwestern part of France). Results outline an improvement of the environmental performance. The analysis of the new land-use plan emphasizes the fact that the changes of farming systems are not only due to evolutions of the surfaces where they are implemented, but that the environmental performance at watershed scale is also affected by their location.Finally we explore the applicability of the method used highlighting its attributes as a relevant tool for modeling scenarios and for communicating.

Submitted by Secretaria Pós de Produção (tpp@vm.uff.br) on 2017-07-27T20:00:22Z No. of bitstreams: 1 D2016 - Ana Paula dos Santos.pdf: 1475202 bytes, checksum: 995f3768e015149be9bbdbae4aff8e20 (MD5) / Made available in DSpace on 2017-07-27T20:00:22Z (GMT). No. of bitstreams: 1 D2016 - Ana Paula dos Santos.pdf: 1475202 bytes, checksum: 995f3768e015149be9bbdbae4aff8e20 (MD5) / A baixa discriminação e o esquema de multiplicadores pouco realistas são frequentemente apontadas como limitações da Análise Envoltória de Dados (DEA, de Data Envelopment Analysis). Com o propósito de amenizá-las, o modelo MCDEA (Multiple Criteria DEA) foi desenvolvido sob uma perspectiva multiobjetivo. Como na maioria dos problemas multiobjetivo, o modelo MCDEA não costuma gerar uma solução ótima única, mas um conjunto de soluções não dominadas. Buscando obter uma solução, que, tanto quanto possível, otimize conjuntamente as funções objetivo do modelo MCDEA, foram propostas abordagens baseadas na metodologia de programação por metas (GP, de Goal Programming). Dentre elas, destacam-se os modelos GPDEA, que usam programação por metas do tipo soma ponderada. Contudo, recentemente, os modelos GPDEA foram considerados inválidos, sem que nenhuma formulação alternativa baseada em programação por metas fosse proposta. Visando preencher tal lacuna, esta tese tem o objetivo de desenvolver formulações que solucionem, apropriadamente, o modelo MCDEA, para o caso de retornos constantes e variáveis de escala, mediante o uso de programação por metas do tipo soma ponderada. Essas formulações foram denominadas modelos WGP-MCDEA (Weighted GP-MCDEA), e englobam tanto a orientação a inputs como a outputs. Os modelos propostos geram as soluções básicas não dominadas dos modelos MCDEA correspondentes, quando os níveis de aspiração para as metas são precisamente definidos com este fim. Quando esses níveis são relaxados, em geral, os modelos WGP-MCDEA geram as soluções não dominadas dos modelos MCDEA correspondentes que cobrem a maior área na região de indiferença dos pesos. / Low discrimination and unrealistic multipliers schemes are often cited as limitations of DEA. To mitigate those limitations, the MCDEA model was developed under a multi-objective perspective. As in most multiple objective problems, MCDEA model does not usually result in a unique optimal solution, but in a set of non-dominated solutions. In an attempt to obtain a satisfactory solution, which, as far as possible, jointly optimizes MCDEA´s objective functions, some goal-programming-based approaches were proposed. Among those proposals, we highlight the GPDEA models, which use weighted goal programming. However, recently, GPDEA models were considered invalid, without any alternative goal-programming-based formulation being proposed. Seeking to fill this gap, the objective of this dissertation is to develop formulations that appropriately solve MCDEA model for the cases of constant and variable returns-to-scale, by means of weighted goal programming. These formulations were called WGP-MCDEA models, and include both input and output orientations. The proposed models generate the basic non-dominated solutions of the corresponding MCDEA models when the goals´ aspiration levels are specifically defined for this purpose. When those aspiration levels are smoothened, the WP-MCDEA models generally produce the non-dominated solution of the corresponding MCDEA models that cover the largest area in the indifference region.

本論文使用大中取小原則及目標規劃技術，提出建構投資組合的數學規劃模型。要求此投資組合面對於不確定的股市，能夠在控制風險最小的情況下穩定且具有成長性的獲利。論文內探討如何透過數學的限制式來控制風險，而又能兼顧穩定且具有成長性的獲利，同時模型也可針對不同投資者的需求設定其數學規劃模型。最後以台灣股票市場做為實證分析的對象，給予不同的參數設定來驗證投資組合的表現。實證發現若以期初的配置比重持有到投資期間結束，此投資方式的績效欠佳。因此論文中進一步探討最佳的調整週期，實證顯示每經過8週，根據最新的資訊，重新調整建立新的投資組合，投資績效最好。 / This thesis proposed a mathematic programming model to construct a growth portfolio by using the mini-max principle and goal programming technique. The constructed portfolio is required to minimize the risk and to earn a stable profit under uncertain market. In the thesis, we discussed how to control the risk and maintain the growth of the portfolio by using the linear constraints. The proposed model also provides several parameters setting to meet the different investors' requirement. Finally, an empirical study will be provided by using the data from Taiwan’s stock market. The portfolios are constructed by giving different parameters and the performances are reported. The empirical study showed that holding a portfolio through the entire investment period without rebalance yield the performances that are not good. Therefore, the rebalance timing is investigated and the empirical study showed that a portfolio with rebalance strategy by every 8 weeks yield the best performance.