Portfolio Management is the process of allocating an investor's wealth to in­ vestment opportunities over a given planning period. Not only should Portfolio Management be treated within a multi-period framework, but one should also take into consideration the stochastic nature of related parameters. After a short review of key concepts from Finance Theory, e.g. utility function, risk attitude, Value-at-rusk estimation methods, a.nd mean-variance efficiency, this work describes a framework for the formulation of the Portfolio Management problem in a Stochastic Programming setting. Classical solution techniques for the resolution of the resulting Stochastic Programs (e.g. L-shaped Decompo­ sition, Approximation of the probability function) are presented. These are discussed within both the two-stage and the multi-stage case with a special em­ phasis on the former. A description of how Importance Sampling and EVPI are used to improve the efficiency of classical methods is presented. Postoptimality Analysis, a sensitivity analysis method, is also described. / Statistics / M. Sc. (Operations Research)

There is a need for a fuel-optimal required time of arrival (RTA) mode for aircraft flight management systems capable of enabling controlled time of arrival functionality in the presence of wind speed forecast uncertainty. A computationally tractable two-stage stochastic algorithm utilizing a data-driven, location-specific forecast uncertainty model to generate forecast uncertainty scenarios is proposed as a solution. Three years of Aircraft Communications Addressing and Reporting Systems (ACARS) wind speed reports are used in conjunction with corresponding wind speed forecasts from the Rapid Update Cycle (RUC) forecast product to construct an inhomogeneous Markov model quantifying forecast uncertainty characteristics along specific route through the national airspace system. The forecast uncertainty modeling methodology addresses previously unanswered questions regarding the regional uncertainty characteristics of the RUC model, and realizations of the model demonstrate a clear tendency of the RUC product to be positively biased along routes following the normal contours of the jet stream. A two-stage stochastic algorithm is then developed to calculate the fuel optimal stage one cruise speed given a required time of arrival at a destination waypoint and wind forecast uncertainty scenarios generated using the inhomogeneous Markov model. The algorithm utilizes a quadratic approximation of aircraft fuel flow rate as a function of cruising Mach number to quickly search for the fuel-minimum stage one cruise speed while keeping computational footprint small and ensuring RTA adherence. Compared to standard approaches to the problem utilizing large scale linear programming approximations, the algorithm performs significantly better from a computational complexity standpoint, providing solutions in fractional power time while maintaining computational tractability in on-board systems.

Renewable energy is key to a sustainable future. However, the intermittency of most renewable sources and lack of sufficient storage in the current power grid means that reliable integration of significantly more renewables will be a challenging task. Moreover, increased integration of renewables not only increases uncertainty, but also reduces the fraction of traditional controllable generation capacity that is available to cope with supply-demand imbalances and uncertainties. Less traditional generation also means less rotating mass that provides very short term, yet very important, kinetic energy storage to the system and enables mitigation of the frequency drop subsequent to major contingencies but before controllable generation can increase production. Demand, on the other side, has been largely regarded as non-controllable and inelastic in the current setting. However, there is strong evidence that a considerable portion of the current and future demand, such as electric vehicle load, is flexible. That is, the instantaneous power delivered to it needs not to be bound to a specific trajectory. In this thesis, we focus on harnessing demand flexibility as a key to enabling more renewable integration and cost reduction. We start with a data driven analysis of the potential of flexible demands, particularly plug-in electric vehicle (PEV) load. We first show that, if left unmanaged, these loads can jeopardize grid reliability by exacerbating the peaks in the load profile and increasing the negative correlation of demand with wind energy production. Then, we propose a simple local policy with very limited information and minimal coordination that besides avoiding undesired effects, has the positive side-effect of substantially increasing the correlation of flexible demand with wind energy production. Such local policies could be readily implemented as modifications to existing "grid friendly" charging modes of plug-in electric vehicles. We then propose improved localized charging policies that counter balance intermittency by autonomously responding to frequency deviations from the nominal frequency and show that PEV load can offer a substantial amount of such ancillary services. Next, we consider the case where real-time prices are employed to provide incentives for demand response. We consider a flexible load under such a pricing scheme and obtain the optimal policy for responding to stochastic price signals to minimize the expected cost of energy. We show that this optimal policy follows a multi-threshold form and propose a recursive method to obtain these thresholds. We then extend our results to obtain optimal policies for simultaneous energy consumption and ancillary service provision by flexible loads as well as optimal policies for operation of storage assets under similar real-time stochastic prices. We prove that the optimal policy in all these cases admits a computationally efficient form. Moreover, we show that while optimal response to prices reduces energy costs, it will result in increased volatility in the aggregate demand which is undesirable. We then discuss how aggregation of flexible loads can take us a step further by transforming the loads to controllable assets that help maintain grid reliability by counterbalancing the intermittency due to renewables. We explore the value of load flexibility in the context of a restructured electricity market. To this end, we introduce a model that economically incentivizes the load to reveal its flexibility and provides cost-comfort trade-offs to the consumers. We establish the performance of our proposed model through evaluation of the price reductions that can be provided to the users compared to uncontrolled and uncoordinated consumption. We show that a key advantage of aggregation and coordination is provision of "regulation" to the system by load, which can account for a considerable price reduction. The proposed scheme is also capable of preventing distribution network overloads. Finally, we extend our flexible load coordination problem to a multi-settlement market setup and propose a stochastic programming approach in obtaining day-ahead market energy purchases and ancillary service sales. Our work demonstrates the potential of flexible loads in harnessing renewables by affecting the load patterns and providing mechanisms to mitigate the inherent intermittency of renewables in an economically efficient manner. / text

Les services de soins hospitaliers sont soumis à de nombreux évènements de natures aléatoires rendant leur gestion et leur pilotage difficiles. Ces difficultés organisationnelles reposent essentiellement sur l'incertitude permanente pesant sur les évolutions futurs, principalement en termes d'arrivées et de départs de patients. Pourtant, une prise en charge rapide et efficace des patients est primordiale pour des services tels que les urgences. Ces services doivent pouvoir placer rapidement leurs patients ce qui n'est possible uniquement si (i) les arrivées ont été anticipées et des places sont laissées vacantes dans les services pour recevoir les patients urgents et/ou (ii) le planning d'occupation des services est construit de telle manière que l'insertion d'un nouveau patient est facilitée.Notre objectif va être de gérer les flux de patients séjournant dans les services de courts-séjours de l'hôpital, depuis le choix d'admission d'un nouveau patient jusqu'à sa sortie, et ce, en s'inspirant des deux postulats précédant. A l'aide de modèles d'optimisation stochastique, une succession de problèmes de décisions, ayant pour but de garantir le bon fonctionnement des structures hospitalières, est résolue. Une hiérarchie en trois niveaux est appliquée pour résoudre le problème de gestion: 1. Planification des admissions des patients réguliers, 2. Affectation des patients aux unités de soins et insertion des urgences, 3. Affectation des patients d'un service aux chambres.Les études de cas sont basées sur les données d'un établissement partenaire, le Centre Hospitalier de Firminy (France). / Hospitals have to deals with a lot of random events making their management hard to realize. Those difficulties are mainly due to the uncertainty relative to future evolutions of demand, in particular in term of future arrivals and departures. Despite those difficulties, a fast and efficient hospitalization is required especially for some units like the emergency department. This department has to find quick solution to the problem of hospitalized of their patients. This can only be possible if (i) emergency arrivals are forecasted and so a bed is remaining free for them and/or (ii) the planning of beds occupation is made in a way allowing easy allocations of emergency patients.Our purpose is going to manage the patient flow in short stay unit (medicine and surgery) starting form the choice of an admission date for each patient until their discharge by keeping in mind the two previous assumptions. By using some stochastic optimization models, we solve a succession of decision problems in order to grant the good state of hospitals. Three level of decision are solved: 1. Admission scheduling for elective patients, 2. Patient assignment to hospital floors, 3. Patient assignment to rooms.Cases of study are based on data provided by a french hospital partner of this work, Firminy's Hospital Center

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

O planejamento da produção em indústrias moveleiras de pequeno porte é comumente constituído por decisões referentes ao volume de produção e à política de estoque, com o objetivo de minimizar o desperdício de material, os atrasos e as horas-extras utilizadas ao longo do horizonte de planejamento. Administrar tais decisões de uma maneira tratável e eficiente é, em geral, um desafio, especialmente considerando a natureza incerta dos dados. Nessa tese, são desenvolvidos modelos de otimização para apoiar tais decisões no contexto do problema combinado de dimensionamento de lotes e corte de estoque sob incertezas que surge em indústrias moveleiras. Para lidar com as incertezas dos dados, são investigadas duas metodologias: programação estocástica e otimização robusta. Dessa maneira, são propostos modelos de programação estocástica de dois estágios com recurso, assim como modelos estocásticos robustos que incorporam aversão ao risco. A motivação em também desenvolver modelos baseados em otimização robusta é considerar casos práticos em que não há uma descrição probabilística explícita dos dados de entrada, assim como evitar trabalhar com numerosos cenários, o que pode tornar o modelo estocástico computacionalmente intratável. Os experimentos numéricos baseados em exemplares reais de uma empresa moveleira de pequeno porte mostram que as soluções obtidas pelos modelos de programação estocástica fornecem planos de produção robustos e que o (a) decisor (a) pode designar suas preferências em relação ao risco aos modelos, assim como controlar o tradeoff entre o custo total esperado e a robustez da solução. Em relação aos resultados dos modelos de otimização robusta, são obtidos alguns insights entre os chamados budgets de incerteza, as taxas de atendimento da demanda e os valores ótimos. Além disso, evidências numéricas indicam que budgets de incerteza menos conservadores resultam em níveis de serviço razoáveis com baixos custos globais, enquanto a abordagem de pior caso gera, relativamente, boas taxas de atendimento da demanda, mas com custos globais elevados / Production planning procedures in small-size furniture companies commonly consist of decisions with respect to production level and inventory policy, while attempting to minimize trim-loss, backlogging and overtime usage throughout the planning horizon. Managing these decisions in a tractable and efficient way is often a challenge, especially when the uncertainty of data is taken into account. In this thesis, we develop optimization models to support these decisions in the context of the combined lot-sizing and cutting-stock problem that arises in furniture companies. To deal with data uncertainty, we investigate two methodologies: stochastic programming and robust optimization. In the former case, we propose two-stage stochastic programming models with recourse, as well as robust stochastic models to incorporate risk-aversion. In the latter case, our motivation to investigate robust optimization models is the lack of an explicit probabilistic description of the input data. Furthermore, we want to avoid dealing with a large number of scenarios, which typically lead to computationally intractable stochastic programming models. Numerical experiments based on real data from a small-size furniture plant show that the solutions of the stochastic programming models provide robust production plans so that the decision-maker can assign his or her risk preferences to the model and control the tradeoff between the expected total cost and solution robustness. Regarding the results from the robust optimization models, we provide some insights into the relationship among budgets of uncertainty, fill rates and optimal values. Moreover, numerical evidence indicate that less conservative budgets of uncertainty result in reasonable service levels with cheaper global costs, while worst case deterministic approaches lead to relatively good fill rates, but with prohibitive global costs

O presente trabalho desenvolve uma extensão do problema de corte de estoque unidimensional no caso em que a demanda pelos vários tipos de itens não é exatamente conhecida. Para considerar a aleatoriedade, foi proposto um modelo de programação estocástica de dois estágios com recurso. As varáveis de primeiro estágio são os números de barras cortadas por padrão de corte, e as variáveis de segundo estágio, os números de itens produzidos em escassez e em escassez. O objetivo do modelo é minimizar o custo total esperado. Para resolver a relaxação linear do modelo, foram propostos um método exato baseado no método Simplex com geração de colunas e uma estratégia heurística, que considera o valor esperado da demanda na resolução do problema de corte de estoque. As duas estratégias foram comparadas, assim como a possibilidade de resolver o problema de corte ignorando as incertezas. Finalmente, observou-se que é mais interessante determinar o valor ótimo do modelo recurso quando o problema sofre mais influência da aleatoriedade / This paper presents an integer linear optimization model of large scale for the one-dimensional cutting stock problem in the case which a demand is considered a random variable. To take this randomness into account, the problem was formulated as a two-stage stochastic linear program with recourse. The first stage decision variables are given by the number of bars that has to be cut according to each pattern, and the second stage decision variables by the number of holding items or backordering items production. The model objective is minimizes the total expected cost. We propose two methods to solve the model linear relaxation, one of them it is a Simplex-based method with column generation. The second method is a heuristic strategy that adopted the expected value of demand. We compare both strategies and the possibly of ignoring uncertainties on model. Finally, we observe that is much more interesting to determine the optimal recourse model solution when we have problems that are more afected by randomness

Cette thèse propose un nouveau processus de réservation d'examens IRM (Imagerie par Résonance Magnétique) afin de réduire les temps d’attente d’examens d'imagerie des patients atteint d'un AVC (Accident Vasculaire Cérébral) soignés dans une unité neurovasculaire. Le service d’imagerie réserve chaque semaine pour l'unité neurovasculaire un nombre donné de créneaux d'examens IRM appelés CTS afin d’assurer un diagnostic rapide aux patients. L'unité neurovasculaire garde la possibilité de réservations régulières appelées RTS pour pallier les variations des flux de patients.Nous donnons d'abord une formulation mathématique du problème d'optimisation pour déterminer le nombre et la répartition des créneaux CTS appelée contrat et une politique d'affectation des patients entre les créneaux CTS ou les réservations RTS. L'objectif est de trouver le meilleur compromis entre le délai d'examens et le nombre de créneaux CTS non utilisés. Pour un contrat donné, nous avons mis en évidence les propriétés et la forme des politiques d'affectation optimales à l'aide d'une approche de processus de décision markovien à coût moyen et coût actualisé. Le contrat est ensuite déterminé par une approche d'approximation Monté Carlo et amélioré par des recherches locales. Les expérimentations numériques montrent que la nouvelle méthode de réservation permet de réduire de manière importante les délais d'examens au prix des créneaux inutilisés.Afin de réduire le nombre de CTS inutilisé, nous explorons ensuite la possibilité d’annuler des créneaux CTS un ou deux jours en avance. Une approche de processus de décision markovien est de nouveau utilisée pour prouver les propriétés et la forme de la politique optimale d’annulation. Les expérimentations numériques montrent que l'annulation avancée des créneaux CTS permet de réduire de manière importante les créneaux CTS inutilisés avec une augmentation légère des délais d'attente. / This research is motivated by our collaborations with a large French university teaching hospital in order to reduce the Length of Stay (LoS) of stroke patients treated in the neurovascular department. Quick diagnosis is critical for stroke patients but relies on expensive and heavily used imaging facilities such as MRI (Magnetic Resonance Imaging) scanners. Therefore, it is very important for the neurovascular department to reduce the patient LoS by reducing their waiting time of imaging examinations. From the neurovascular department perspective, this thesis proposes a new MRI examinations reservation process in order to reduce patient waiting times without degrading the utilization of MRI. The service provider, i.e., the imaging department, reserves each week a certain number of appropriately distributed contracted time slots (CTS) for the neurovascular department to ensure quick MRI examination of stroke patients. In addition to CTS, it is still possible for stroke patients to get MRI time slots through regular reservation (RTS). This thesis first proposes a stochastic programming model to simultaneously determine the contract decision, i.e., the number of CTS and its distribution, and the patient assignment policy to assign patients to either CTS or RTS. To solve this problem, structure properties of the optimal patient assignment policy for a given contract are proved by an average cost Markov decision process (MDP) approach. The contract is determined by a Monte Carlo approximation approach and then improved by local search. Computational experiments show that the proposed algorithms can efficiently solve the model. The new reservation process greatly reduces the average waiting time of stroke patients. At the same time, some CTS cannot be used for the lack of patients.To reduce the unused CTS, we further explore the possibility of the advance cancellation of CTS. Structure properties of optimal control policies for one-day and two-day advance cancellation are established separately via an average-cost MDP approach with appropriate modeling and advanced convexity concepts used in control of queueing systems. Computational experiments show that appropriate advance cancellations of CTS greatly reduce the unused CTS with nearly the same waiting times.

O planejamento da produção em indústrias moveleiras de pequeno porte é comumente constituído por decisões referentes ao volume de produção e à política de estoque, com o objetivo de minimizar o desperdício de material, os atrasos e as horas-extras utilizadas ao longo do horizonte de planejamento. Administrar tais decisões de uma maneira tratável e eficiente é, em geral, um desafio, especialmente considerando a natureza incerta dos dados. Nessa tese, são desenvolvidos modelos de otimização para apoiar tais decisões no contexto do problema combinado de dimensionamento de lotes e corte de estoque sob incertezas que surge em indústrias moveleiras. Para lidar com as incertezas dos dados, são investigadas duas metodologias: programação estocástica e otimização robusta. Dessa maneira, são propostos modelos de programação estocástica de dois estágios com recurso, assim como modelos estocásticos robustos que incorporam aversão ao risco. A motivação em também desenvolver modelos baseados em otimização robusta é considerar casos práticos em que não há uma descrição probabilística explícita dos dados de entrada, assim como evitar trabalhar com numerosos cenários, o que pode tornar o modelo estocástico computacionalmente intratável. Os experimentos numéricos baseados em exemplares reais de uma empresa moveleira de pequeno porte mostram que as soluções obtidas pelos modelos de programação estocástica fornecem planos de produção robustos e que o (a) decisor (a) pode designar suas preferências em relação ao risco aos modelos, assim como controlar o tradeoff entre o custo total esperado e a robustez da solução. Em relação aos resultados dos modelos de otimização robusta, são obtidos alguns insights entre os chamados budgets de incerteza, as taxas de atendimento da demanda e os valores ótimos. Além disso, evidências numéricas indicam que budgets de incerteza menos conservadores resultam em níveis de serviço razoáveis com baixos custos globais, enquanto a abordagem de pior caso gera, relativamente, boas taxas de atendimento da demanda, mas com custos globais elevados / Production planning procedures in small-size furniture companies commonly consist of decisions with respect to production level and inventory policy, while attempting to minimize trim-loss, backlogging and overtime usage throughout the planning horizon. Managing these decisions in a tractable and efficient way is often a challenge, especially when the uncertainty of data is taken into account. In this thesis, we develop optimization models to support these decisions in the context of the combined lot-sizing and cutting-stock problem that arises in furniture companies. To deal with data uncertainty, we investigate two methodologies: stochastic programming and robust optimization. In the former case, we propose two-stage stochastic programming models with recourse, as well as robust stochastic models to incorporate risk-aversion. In the latter case, our motivation to investigate robust optimization models is the lack of an explicit probabilistic description of the input data. Furthermore, we want to avoid dealing with a large number of scenarios, which typically lead to computationally intractable stochastic programming models. Numerical experiments based on real data from a small-size furniture plant show that the solutions of the stochastic programming models provide robust production plans so that the decision-maker can assign his or her risk preferences to the model and control the tradeoff between the expected total cost and solution robustness. Regarding the results from the robust optimization models, we provide some insights into the relationship among budgets of uncertainty, fill rates and optimal values. Moreover, numerical evidence indicate that less conservative budgets of uncertainty result in reasonable service levels with cheaper global costs, while worst case deterministic approaches lead to relatively good fill rates, but with prohibitive global costs

[pt] A parte mais difícil de modelar os problemas de tomada de decisão do mundo real, é a incerteza associada a realização de eventos futuros. A programação estocástica se encarrega desse assunto; o objetivo é achar soluções que sejam factíveis para todas as possíveis realizações dos dados, otimizando o valor esperado de algumas funções das variáveis de decisão e de incerteza. A abordagem mais estudada está baseada em simulação de Monte Carlo e o método SAA (Sample Average Appmwimation) o qual é uma formulação do problema verdadeiro para cada realização da data incerta, que pertence a um conjunto finito de cenários uniformemente distribuídos. É possível provar que o valor ótimo e a solução ótima do problema SAA converge a seus homólogos do problema verdadeiro quando o número de cenários é suficientemente grande.Embora essa abordagem seja útil ali existem fatores limitantes sobre o custo computacional para obter soluções mais precisas aumentando o número de cenários; no entanto o fato mais importante é que o problema SAA é função de cada amostra gerada e por essa razão é aleatório, o qual significa que a sua solução também é incerta, e para medir essa incerteza e necessário considerar o número de replicações do problema SAA afim de estimar a dispersão da solução, aumentando assim o custo computacional. O propósito deste trabalho é apresentar uma abordagem alternativa baseada em um método de partição que permite obter cotas para estimar deterministicamente a solução do problema original, com aplicação da desigualdade de Jensen e de técnicas de otimização robusta. No final se analisa a convergência dos algoritmos de solução propostos. / [en] The hardest part of modelling decision-making problems in the real world, is the uncertainty associated to realizations of futures events. The stochastic programming is responsible about this subject; the target is finding solutions that are feasible for all possible realizations of the unknown data, optimizing the expected value of some functions of decision variables and random variables. The approach most studied is based on Monte Carlo simulation and the Sample Average Approximation (SAA) method which is a kind of discretization of expected value, considering a finite set of realizations or scenarios uniformly distributed. It is possible to prove that the optimal value and the optimal solution of the SAA problem converge to their counterparts of the true problem when the number of scenarios is sufficiently big. Although that approach is useful, there exist limiting factors about the computational cost to increase the scenarios number to obtain a better solution; but the most important fact is that SAA problem is function of each sample generated, and for that reason is random, which means that the solution is also uncertain, and to measure its uncertainty it is necessary consider the replications of SAA problem to estimate the dispersion of the estimated solution, increasing even more the computational cost. The purpose of this work is presenting an alternative approach based on robust optimization techniques and applications of Jensen s inequality, to obtain bounds for the optimal solution, partitioning the support of distribution (without scenarios creation) of unknown data, and taking advantage of the convexity. At the end of this work the convergence of the bounding problem and the proposed solution algorithms are analyzed.