建立指數基金時，通常是利用追蹤指數的技巧，選取少量的股票建構指數基金使得報酬率與標的指數(benchmark index)報酬率同步的投資組合。如果能建立包含少量股票的投資組合，就可達到指數追蹤的效果，那麼也能利用少量的股票建立績效可以超越指數基金的投資組合。本論文利用建構指數基金的方法以及大中取小的概念，挑選出一個績效可以超越標的指數的投資組合。本論文提出的模型亦考慮實務上交易所需的各項成本、整數交易單位與資產總類數等限制。因此，模型包含整數變數與二元變數。最後以台灣加權股價指數的相關資料做為實證研究的對象，實證結果顯示本論文提出的模型所建立的投資組合超越標的指數的績效平均年化報酬率25%。 / Setting up an index fund usually uses techniques of index-tracking that choosing few stocks forming a portfolio to obtain the same return rate as the benchmark index. Similarly we can use the same concept to set up a portfolio such that the performance is better than index’s. In this thesis we use index-tracking methods and minimax rule to obtain a portfolio which outperforms the benchmark index. In the proposed mathematical model we will consider the transaction costs, integer trading unit volume, and the total number of assets in the portfolio. Therefore the resulting model is a mixed integer nonlinear programming including integer variables and binary variables. Finally, the empirical study will be performed by using the data from the Taiwan stock market to verify the performance of our model. The empirical study shows that the portfolios created by our models outperform the benchmark index up to 25% in average.

Submitted by Augusto Cesar Pereira (augusto.pereira@feb.unesp.br) on 2017-12-20T09:42:45Z No. of bitstreams: 1 Dissertação_Augusto_Repositorio.pdf: 2651783 bytes, checksum: 084f19f166b7161411ec58baa4ecf206 (MD5) / Approved for entry into archive by Maria Marlene Zaniboni null (zaniboni@bauru.unesp.br) on 2017-12-20T10:54:46Z (GMT) No. of bitstreams: 1 pereira_ac_me_bauru.pdf: 2651783 bytes, checksum: 084f19f166b7161411ec58baa4ecf206 (MD5) / Made available in DSpace on 2017-12-20T10:54:46Z (GMT). No. of bitstreams: 1 pereira_ac_me_bauru.pdf: 2651783 bytes, checksum: 084f19f166b7161411ec58baa4ecf206 (MD5) Previous issue date: 2017-12-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho propõe um modelo de Procedimento de Equilíbrio de Mercado com Restrições de Segurança Estocásticas (PEMRSE) que pode ser utilizado como um modelo de leilão de energia e reserva do dia seguinte por operadores de sistemas hidrotérmicos. O modelo de PEMRSE tem o objetivo de minimizar o custo esperado da operação, considerando os custos associados aos excedentes de geração e consumo, partidas, contratação de reservas e a penalização econômica associada aos cortes involuntários de carga. O PEMRSE considera vários aspectos que dificultam a resolução de problemas de leilão: i) representação detalhada dos sistemas de geração hidrelétrico e termelétrico; ii) perdas na transmissão; e iii) restrições de segurança pré e pós-contingência. São propostas técnicas de linearização que não demandam o uso de variáveis binárias para a função de produção hidráulica e para as funções de potência e engolimento máximo de geradores hidrelétricos. A estrutura estocástica permite cortes involuntários de carga, isto é, o operador pode optar por não contratar a totalidade das reservas necessárias para cobrir as falhas associadas às contingências, ponderando sua decisão pela probabilidade de ocorrência destas falhas e pelo valor da penalização econômica associada ao corte de carga. Propõe-se também uma técnica para a resolução de modelos de PEMRSE em tempos computacionais menores com relação à sua resolução direta. Simulações em um sistema-teste de três barras e no sistema IEEE de 24 barras evidenciam a eficiência do modelo, das técnicas de linearização e da técnica de resolução propostos. As simulações também mostram os impactos dos aspectos complicadores nos resultados do leilão e no tempo computacional de resolução. O modelo de PEMRSE proposto pode ser resolvido de maneira eficiente por meio de pacotes computacionais disponíveis comercialmente por meio da técnica de resolução proposta. / This work proposes a Market Clearing Procedure with Stochastic Security Constraints (MCPSSC) model that can be used as an energy and reserve day-ahead auction model by hydrothermal systems operators. The MCPSSC aims to minimize the expected cost of the operation, considering the costs associated with the generation and consumption surpluses, start-ups, contracting of reserves and the economic penalization associated with involuntary load shedding events. The MCPSSC model considers several aspects that complicate the resolution of auction problems: i) detailed representation of the hydrothermal generating systems; ii) transmission losses; and iii) pre- and post-contingency security constraints. We propose linearization techniques that does not require the use of binary variables for the hydro production function and for the maximum power output and maximum water discharge functions of hydro generators. The stochastic structure allows some load shedding, ie, the operator can choose not to contract the total reserve requirements to cover the failures associated with the contingencies, weighting its decision by the probability of occurrence of these failures and by the value of lost load. We also propose a technique for the resolution of MCPSSC models in lower computational times regarding its direct resolution. Simulations in a three-bus test system and in the IEEE 24-bus system show the efficiency of the model, the linearization techniques and the resolution technique proposed. The simulations also show the the impact of the complicating aspects in the auction outcomes and in the computational time. The proposed MCPSSC model can be efficiently solved by commercially available solvers by means of the proposed resolution technique.

Cette thèse a pour objectif de modéliser et résoudre des problèmes d’optimisation d’un système d’auto-partage avec des voitures électriques dit « à un seul sens », où les utilisateurs peuvent prendre une voiture dans une station et la laisser ensuite dans une autre. Ce fonctionnement conduit généralement à une situation de déséquilibre dans la répartition des voitures avec certaines stations pleines et d’autres vides. Une des solutions utilisées par les opérateurs d’autopartage pour pallier ce problème est le recours à des agents pour déplacer les voitures selon le besoin. Identifier et répondre à ce besoin est un problème d’optimisation non trivial, notamment à cause de l’usage de véhicules électriques, ce qui engendre des contraintes de rechargement de batteries et d’autonomie. Le problème d’optimisation est décomposé en deux sous-problèmes : le premier est le problème d’affectation des voitures aux clients, ainsi que leurs routages, que nous nommons ROCSP pour Recharging One way Car Sharing Problem ; le second problème est celui du planning des agents et leurs routages que nous nommons ESRP pour Employee Scheduling Routing Problem. 1. Résolution du ROCSP : deux modélisations en Programmation Linéaire en Nombres Entiers (PLNE) sont proposées, la première basée sur les flots et la deuxième sur les chemins, ce qui fait que les deux modèles intègrent de manière différente les contraintes de recharge électrique. Comme la résolution exacte à travers les modèles PLNE s’avère très gourmande en temps de calcul et non adaptée aux instances d’auto-partage de taille réelle, nous proposons des heuristiques qui permettent dans un temps raisonnable d’optimiser la redistribution des voitures et la gestion du service. Ces heuristiques permettent de calculer le nombre de voitures et les différentes opérations de relocalisation (redistribution des voitures) à réaliser sur une journée donnée. 2. Résolution du ESRP : un modèle PLNE est proposé pour la résolution exacte du ESRP, et, en complément, des heuristiques sont proposées pour une résolution approchée et relativement rapide. L’objectif est la détermination du nombre minimal d’agents nécessaire pour effectuer les opérations de relocalisation qui découlent du premier problème, le ROCSP. Dans une partie prospective, et une fois les ROCSP et ESRP résolus dans leur version statique, nous nous focaliserons sur une autre variante du problème avec réservation dynamique. Nous proposons également d’explorer un nouveau concept - l’auto-copartage - qui se veut une hybridation entre autopartage et covoiturage. Les algorithmes proposés ont été validés sur le réseau Auto Bleue de la ville de Nice essentiellement, qui gère une flotte de véhicules électriques, en s’appuyant sur des modèles de génération de flux pour estimer la demande, mais aussi d’autres instances que nous avons générées pour simuler d’autres villes, au sein d’un Système d’Information Géographique. / This thesis aims at modelling and solving optimization problems related to the management of one-way-electric-car-sharing systems, where users can take a car from a station, use it, and then return it to another station. This generally leads to an imbalanced distribution of cars, with some full stations and other empty ones. A solution to this problem, implemented by car-sharing operators, is to employ staff agents to move cars as needed. However, identifying this need is a non-trivial optimization problem, especially since the system may be more constrained when the vehicles used are electric, which generates battery recharging and autonomy constraints. The global optimization problem addressed is then divided into two sub-problems. The first one is assigning the cars to customers, as well as their routing; it is denoted by ROCSP (Recharging OneWay Car Sharing Problem). The second problem involves agents planning and routing; it is denoted by ESRP (Employee Scheduling Routing Problem). 1. For the ROCSP, we propose two Mixed-integer linear programming (MILP) modelizations of the problem: One based on flows and the other based on paths. This means that the two models include the battery-recharging constraints in two different ways. As the exact resolution through the MILP models is quite expensive in terms of computational time and is not adapted for the resolution of real-size car-sharing instances, we introduce heuristics that enable the optimization of cars-redistribution and service management of the service within a reasonable amount of time. These heuristics allows the calculation of the number of cars and the various redistribution operations to be performed on a given day. 2. For the ESRP, this second problem is also addressed with MILP models for the exact resolution, and some heuristics are suggested for an approximate resolution. This process has reasonable calculation time and aims at finding the minimum number of agents to perform the necessary relocation operations that stem from the first problem, namely, the ROCSP. Once the ROCSP and ESRP solved in their static versions, we then focus on the ROCSP by exploring another variant of the problem : ROCSP with dynamic reservation. We also suggest to explore a new concept : Auto-CoPartage, which is a hybridization of car-sharing and carpooling. The stated algorithms are validated on the Auto Bleue electrical vehicles fleet in the network of the city of Nice, essentially by relying on flow generation models to estimate the demand, but also using other instances that we have generated for other cities. All the data are handled using a Geographical Information System.