Cette thèse est composée de deux parties, chacune portant sur un sous-domaine de l'optimisation combinatoire a priori distant de l'autre. Le premier thème de recherche abordé est la programmation biniveau stochastique. Se cachent derrière ce terme deux sujets de recherche relativement peu étudiés conjointement, à savoir d'un côté la programmation stochastique, et de l'autre la programmation biniveau. La programmation mathématique (PM) regroupe un ensemble de méthodes de modélisation et de résolution, pouvant être utilisées pour traiter des problèmes pratiques que se posent des décideurs. La programmation stochastique et la programmation biniveau sont deux sous-domaines de la PM, permettant chacun de modéliser un aspect particulier de ces problèmes pratiques. Nous élaborons un modèle mathématique issu d'un problème appliqué, où les aspects biniveau et stochastique sont tous deux sollicités, puis procédons à une série de transformations du modèle. Une méthode de résolution est proposée pour le PM résultant. Nous démontrons alors théoriquement et vérifions expérimentalement la convergence de cette méthode. Cet algorithme peut être utilisé pour résoudre d'autres programmes biniveaux que celui qui est proposé.Le second thème de recherche de cette thèse s'intitule "problèmes de coupe et de couverture partielles dans les graphes". Les problèmes de coupe et de couverture sont parmi les problèmes de graphe les plus étudiés du point de vue complexité et algorithmique. Nous considérons certains de ces problèmes dans une variante partielle, c'est-à-dire que la propriété de coupe ou de couverture dont il est question doit être vérifiée partiellement, selon un paramètre donné, et non plus complètement comme c'est le cas pour les problèmes originels. Précisément, les problèmes étudiés sont le problème de multicoupe partielle, de coupe multiterminale partielle, et de l'ensemble dominant partiel. Les versions sommets des ces problèmes sont également considérés. Notons que les problèmes en variante partielle généralisent les problèmes non partiels. Nous donnons des algorithmes exacts lorsque cela est possible, prouvons la NP-difficulté de certaines variantes, et fournissons des algorithmes approchés dans des cas assez généraux. / This thesis is composed of two parts, each part belonging to a sub-domain of combinatorial optimization a priori distant from the other. The first research subject is stochastic bilevel programming. This term regroups two research subject rarely studied together, namely stochastic programming on the one hand, and bilevel programming on the other hand. Mathematical Programming (MP) is a set of modelisation and resolution methods, that can be used to tackle practical problems and help take decisions. Stochastic programming and bilevel programming are two sub-domains of MP, each one of them being able to model a specific aspect of these practical problems. Starting from a practical problem, we design a mathematical model where the bilevel and stochastic aspects are used together, then apply a series of transformations to this model. A resolution method is proposed for the resulting MP. We then theoretically prove and numerically verify that this method converges. This algorithm can be used to solve other bilevel programs than the ones we study.The second research subject in this thesis is called "partial cut and cover problems in graphs". Cut and cover problems are among the most studied from the complexity and algorithmical point of view. We consider some of these problems in a partial variant, which means that the cut or cover property that is looked into must be verified partially, according to a given parameter, and not completely, as it was the case with the original problems. More precisely, the problems that we study are the partial multicut, the partial multiterminal cut, and the partial dominating set. Versions of these problems were vertices are

In this thesis, we study three supply chain planning problems. The first two problems fall in the tactical planning level, while the third one falls in the strategic/tactical level. We present a direct application for the first two planning problems in the wind turbines industry. For the third problem, we show how it can be applied to supply chains in the food industry. Many countries and localities have the explicitly stated goal of increasing the fraction of their electrical power that is generated by wind turbines. This has led to a rapid growth in the manufacturing and installation of wind turbines. The globally installed capacity for the manufacturing of different components of the wind turbine is nearly fully utilized. Because of the large penalties for missing delivery deadlines for wind turbines, the effective planning of its supply chain has a significant impact on the profitability of the turbine manufacturers. Motivated by the planning challenges faced by one of the world’s largest manufacturers of wind turbines, we present a comprehensive tactical supply chain planning model for manufacturing of wind turbines in the first part of this thesis. The model is multi-period, multi-echelon, and multi-commodity. Furthermore, the model explicitly incorporates backorder penalties with a general cost structure, i.e., the cost structure does not have to be linear in function of the backorder delay. To the best of our knowledge, modeling-based supply chain planning has not been applied to wind turbines, nor has a model with all the above mentioned features been described in the literature. Based on real-world data, we present numerical results that show the significant impact of the capability to model backorder penalties with general cost structures on the overall cost of supply chains for wind turbines. With today’s rapidly changing global market place, it is essential to model uncertainty in supply chain planning. In the second part of this thesis, we develop a two-stage stochastic programming model for the comprehensive tactical planning of supply chains under supply uncertainty. In the first stage, procurement decisions are made while in the second stage, production, inventory, and delivery decisions are made. The considered supply uncertainty combines supplier random yields and stochastic lead times, and is thus the most general form of such uncertainty to date. We apply our model to the same wind turbines supply chain. We illustrate theoretical and numerical results that show the impact of supplier uncertainty/unreliability on the optimal procurement decisions. We also quantify the value of modeling uncertainty versus deterministic planning. Supplier selection with quantity discounts has been an active research problem in the operations research community. In this the last part of this thesis, we focus on a new quantity discounts scheme offered by suppliers in some industries. Suppliers are selected for a strategic planning period (e.g., 5 years). Fixed costs associated with suppliers’ selection are paid. Orders are placed monthly from any of the chosen suppliers, but the quantity discounts are based on the aggregated annual order quantities. We incorporate all this in a multi-period multi-product multi-echelon supply chain planning problem and develop a mixed integer programming (MIP) model for it. Leading commercial MIP solvers take 40 minutes on average to get any feasible solution for realistic instances of our model. With the aim of getting high-quality feasible solutions quickly, we develop an algorithm that constructs a good initial solution and three other iterative algorithms that improve this initial solution and are capable of getting very fast high quality primal solutions. Two of the latter three algorithms are based on MIP-based local search and the third algorithm incorporates a variable neighborhood Descent (VND) combining the first two. We present numerical results for a set of instances based on a real-world supply chain in the food industry and show the efficiency of our customized algorithms. The leading commercial solver CPLEX finds only a very few feasible solutions that have lower total costs than our initial solution within a three hours run time limit. All our iterative algorithms well outperform CPLEX. The VND algorithm has the best average performance. Its average relative gap to the best known feasible solution is within 1% in less than 40 minutes of computing time.

本論文提出追蹤特定目標線的二階段混合整數非線性隨機規劃模型，以建立追蹤目標線的投資組合。藉由引進情境樹(scenario tree)，我們將此類二階段隨機規劃問題，轉換成為等價的非隨機規劃模型。在金融商品的價格波動及交互作用下，所建立的投資組合在經過一段時間後，其追蹤目標線的能力可能會日趨降低，所以本論文亦提出調整投資組合的規劃模型。為符合實務考量，本論文同時考慮交易成本、股票放空的限制，並且加入期貨進行避險。為了反應投資者的預期心理，也引進了選擇權及情境樹。最後，我們使用台灣股票市場、期貨交易市場及台指選擇權市場的資料進行實證研究，亦探討不同成長率設定之目標線與投資比例對於投資組合的影響。 / To construct a portfolio tracking specific target line, this thesis studies how to do it via two-stage stochastic mixed-integer nonlinear model. We introduce scenario tree to convert this stochastic model into an deterministic equivalent model. Under the volatility of price and the interaction of each financial derivatives, the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical model to rebalance the tracking portfolio. These models consider the transactions cost and the limitation of shorting a stock, and the tracking portfolio will include a futures as a hedge position. To reflect the expectation of investors, we introduce scenario tree and also include a options as a hedge position. Finally, an empirical study will be performed by the data from Taiwan stock market, the futures market and the options market to explore the performance of the proposed models. We will analyze how the different benchmarks settings and invest ratio will affect the value of the tracking portfolio.

[pt] Uma importante questão que se coloca para entidades abertas de previdência complementar e sociedades seguradoras que operam previdência complementar é a definição de uma gestão dos ativos e passivos (do inglês ALM – Asset and Liability Management). Tal questão se torna mais relevante em um cenário de alta competitividade, margens operacionais decrescentes, garantias mínimas de rentabilidade para um passivo estocástico de longo prazo e um período de queda da rentabilidade dos instrumentos financeiros, sendo estes muitas vezes de difícil precificação e pouco previsíveis num mercado volátil como o brasileiro. Somada a estas dificuldades, as companhias deste mercado estão sujeitas a uma regulação baseada em riscos, oriunda de práticas internacionais, adotada pelo órgão superior, Susep, que impõe restrições regulamentares para a manutenção da solvência das companhias, o que eleva a dificuldade da definição de um modelo. Diante deste cenário, esta dissertação apresenta uma proposta de ALM baseada em um modelo de programação estocástica multiestágio que tem como objetivo definir dinamicamente a alocação ótima dos ativos, incluindo títulos com pagamentos de cupons, e mensurar o risco de insolvência da companhia para o horizonte de planejamento. / [en] An important issue of open pension funds and insurance companies that operate supplementary pension is the definition of an asset and liability management (ALM) framework. Such a question becomes more relevant in a scenario of high competition, declining operating margins, minimum guaranteed returns to a stochastic long-term liability and a period of falling returns on financial instruments, these being often difficult to pricing and predictable in a volatile market such as Brazil. Added to these issues, those companies are subject to a risk-based regulation, derived from international practices adopted by the national insurance regulator, Susep, which imposes constraints to maintain solvency of companies and therefore increases the complexity of an ALM framework. Due this condition, this dissertation presents a proposition of ALM based on a multistage stochastic programming model, which aims to define a dynamic optimal asset allocation, including bonds with coupons payment, and measure the company s insolvency risk for the planning horizon.

Made available in DSpace on 2016-06-02T19:53:32Z (GMT). No. of bitstreams: 1 MARTINEZ_Jonathan_2014.pdf: 11989383 bytes, checksum: 96fb53d9544014ea55b1e53ee779c134 (MD5) Previous issue date: 2014-03-14 / Financiadora de Estudos e Projetos / This study presents a pump scheduling problem for the capture, transfer and storage of water supply systems in urban networks, whose objective is to minimize the electricity cost associated to the pumping operations. To deal with the dynamic and random nature of the water-demand, we propose two-stage stochastic programming with recourse models, where the random variables are represented by a finite and discrete set of realizations or scenarios. The developed mathematical models are extensions of previous deterministic models of the literature and they reflect the basic assumption that a fixed cost could be incurred by the turn on/ turn off activities of the hydraulic pumps. In order to control violations of the water-demand constraints in the presence of multiple different scenarios, we also consider a robustness technique in an attempt to obtain almost feasible solutions. Last, but not least, we adopt a risk-aversion criteria so-called mean absolute deviation to obtain second-stage costs less dependent on the realizations of the scenarios. The scenarios were generated according to a Monte-Carlo simulation procedure that may use any probability distributions to produce the empirical probabilities of the random variables. As the proposed pump scheduling problem with fixed cost is a two-stage stochastic mixed 0 − 1 program, we develop a efficient hybrid heuristic to obtain good-quality solutions of practical instances in a plausible running time. Overall results evidence the stability of the scenario generation method, the sensitivity of the solution according to the key parameters of the mathematical model, and the efficiency of the heuristic in solving large instances. Finally, we show that is possible to save resources by solving the stochastic programming model instead of adopting simpler approaches based on the expected value. / Esse estudo apresenta um problema de programação de bombas para a captação, armazenamento e transferência de água em sistemas de abastecimentos de água em redes urbanas, cujo objetivo é minimizar o custo de energia elétrica associado às operações de bombeamento. Para lidar com a natureza dinâmica e aleatória da demanda por água, foram propostos modelos de programação estocástica de dois estágios com recurso, em que a variável aleatória é representada por um conjunto finito de realizações ou cenários. Os modelos matemáticos desenvolvidos são extensões de modelos determinísticos da literatura e refletem a suposição básica de que é possível se incorrer em um custo fixo pelas atividades de liga/desliga das bombas hidráulicas. Para controlar as violações das restrições de demanda por água na presença de múltiplos cenários diferentes, considerou-se também uma técnica de robustez na tentativa de gerar soluções quase factíveis. Por último, mas não menos importante, adotou-se um critério de aversão ao risco denominado desvio médio absoluto para obter custos de segundo estágio menos dependentes das realizações dos cenários. Os cenários foram gerados de acordo com um procedimento baseado em simulação Monte-Carlo que pode utilizar qualquer distribuição de probabilidade para produzir as probabilidades empíricas das variáveis aleatórias. Como o problema de programação de bombas com custo fixo proposto é um programa inteiro misto 0−1 estocástico, desenvolve-se uma heurística híbrida eficiente para obter soluções de boa qualidade de instâncias práticas em um tempo computacional plausível. Os resultados evidenciam a estabilidade do método de geração de cenários, a sensibilidade da solução de acordo com parâmetros-chave do modelo matemático, e a eficiência da heurística na resolução de instâncias de grande porte. Finalmente, foi demonstrado que é possível poupar recursos pela resolução do modelo de programação estocástica, em vez de adotar abordagens mais simples baseadas no valor esperado.

Dans cette thèse, nous étudions le problème d’optimisation des effectifs dans les centres d’appels, dans lequel nous visons à minimiser les coûts d’exploitation tout en offrant aux clients une qualité de service (QoS) élevée. Nous introduisons également l'utilisation de contraintes probabilistes qui exigent que la qualité de service soit satisfaite avec une probabilité donnée. Ces contraintes sont adéquates dans le cas où la performance est mesurée sur un court intervalle de temps, car les mesures de QoS sont des variables aléatoires sur une période donnée. Les problèmes de personnel proposés sont difficiles en raison de l'absence de forme analytique pour les contraintes probabilistes et doivent être approximées par simulation. En outre, les fonctions QoS sont généralement non linéaires et non convexes. Nous considérons les problèmes d’affectation personnel dans différents contextes et étudions les modèles proposés tant du point de vue théorique que pratique. Les méthodologies développées sont générales, en ce sens qu'elles peuvent être adaptées et appliquées à d'autres problèmes de décision dans les systèmes de files d'attente. La thèse comprend trois articles traitant de différents défis en matière de modélisation et de résolution de problèmes d'optimisation d’affectation personnel dans les centres d'appels à compétences multiples. Les premier et deuxième article concernent un problème d'optimisation d'affectation de personnel en deux étapes sous l'incertitude. Alors que dans le second, nous étudions un modèle général de programmation stochastique discrète en deux étapes pour fournir une garantie théorique de la consistance de l'approximation par moyenne échantillonnale (SAA) lorsque la taille des échantillons tend vers l'infini, le troisième applique l'approche du SAA pour résoudre le problème d’optimisation d'affectation de personnel en deux étapes avec les taux d’arrivée incertain. Les deux articles indiquent la viabilité de l'approche SAA dans notre contexte, tant du point de vue théorique que pratique. Pour être plus précis, dans le premier article, nous considérons un problème stochastique discret général en deux étapes avec des contraintes en espérance. Nous formulons un problème SAA avec échantillonnage imbriqué et nous montrons que, sous certaines hypothèses satisfaites dans les exemples de centres d'appels, il est possible d'obtenir les solutions optimales du problème initial en résolvant son SAA avec des échantillons suffisamment grands. De plus, nous montrons que la probabilité que la solution optimale du problème de l’échantillon soit une solution optimale du problème initial tend vers un de manière exponentielle au fur et à mesure que nous augmentons la taille des échantillons. Ces résultats théoriques sont importants, non seulement pour les applications de centre d'appels, mais également pour d'autres problèmes de prise de décision avec des variables de décision discrètes. Le deuxième article concerne les méthodes de résolution d'un problème d'affectation en personnel en deux étapes sous incertitude du taux d'arrivée. Le problème SAA étant coûteux à résoudre lorsque le nombre de scénarios est important. En effet, pour chaque scénario, il est nécessaire d'effectuer une simulation pour estimer les contraintes de QoS. Nous développons un algorithme combinant simulation, génération de coupes, renforcement de coupes et décomposition de Benders pour résoudre le problème SAA. Nous montrons l'efficacité de l'approche, en particulier lorsque le nombre de scénarios est grand. Dans le dernier article, nous examinons les problèmes de contraintes en probabilité sur les mesures de niveau de service. Notre méthodologie proposée dans cet article est motivée par le fait que les fonctions de QoS affichent généralement des courbes en S et peuvent être bien approximées par des fonctions sigmoïdes appropriées. Sur la base de cette idée, nous avons développé une nouvelle approche combinant la régression non linéaire, la simulation et la recherche locale par région de confiance pour résoudre efficacement les problèmes de personnel à grande échelle de manière viable. L’avantage principal de cette approche est que la procédure d’optimisation peut être formulée comme une séquence de simulations et de résolutions de problèmes de programmation linéaire. Les résultats numériques basés sur des exemples réels de centres d'appels montrent l'efficacité pratique de notre approche. Les méthodologies développées dans cette thèse peuvent être appliquées dans de nombreux autres contextes, par exemple les problèmes de personnel et de planification dans d'autres systèmes basés sur des files d'attente avec d'autres types de contraintes de QoS. Celles-ci soulèvent également plusieurs axes de recherche qu'il pourrait être intéressant d'étudier. Par exemple, une approche de regroupement de scénarios pour atténuer le coût des modèles d'affectation en deux étapes, ou une version d'optimisation robuste en distribution pour mieux gérer l'incertitude des données. / In this thesis, we study the staffing optimization problem in multiskill call centers, in which we aim at minimizing the operating cost while delivering a high quality of service (QoS) to customers. We also introduce the use of chance constraints which require that the QoSs are met with a given probability. These constraints are adequate in the case when the performance is measured over a short time interval as QoS measures are random variables in a given time period. The proposed staffing problems are challenging in the sense that the stochastic constraints have no-closed forms and need to be approximated by simulation. In addition, the QoS functions are typically non-linear and non-convex. We consider staffing optimization problems in different settings and study the proposed models in both theoretical and practical aspects. The methodologies developed are general, in the sense that they can be adapted and applied to other staffing/scheduling problems in queuing-based systems. The thesis consists of three articles dealing with different challenges in modeling and solving staffing optimization problems in multiskill call centers. The first and second articles concern a two-stage staffing optimization problem under uncertainty. While in the first one, we study a general two-stage discrete stochastic programming model to provide a theoretical guarantee for the consistency of the sample average approximation (SAA) when the sample sizes go to infinity, the second one applies the SAA approach to solve the two-stage staffing optimization problem under arrival rate uncertainty. Both papers indicate the viability of the SAA approach in our context, in both theoretical and practical aspects. To be more precise, in the first article, we consider a general two-stage discrete stochastic problem with expected value constraints. We formulate its SAA with nested sampling. We show that under some assumptions that hold in call center examples, one can obtain the optimal solutions of the original problem by solving its SAA with large enough sample sizes. Moreover, we show that the probability that the optimal solution of the sample problem is an optimal solution of the original problem, approaches one exponentially fast as we increase the sample sizes. These theoretical findings are important, not only for call center applications, but also for other decision-making problems with discrete decision variables. The second article concerns solution methods to solve a two-stage staffing problem under arrival rate uncertainty. It is motivated by the fact that the SAA version of the two-stage staffing problem becomes expensive to solve with a large number of scenarios, as for each scenario, one needs to use simulation to approximate the QoS constraints. We develop an algorithm that combines simulation, cut generation, cut strengthening and Benders decomposition to solve the SAA problem. We show the efficiency of the approach, especially when the number of scenarios is large. In the last article, we consider problems with chance constraints on the service level measures. Our methodology proposed in this article is motivated by the fact that the QoS functions generally display ``S-shape'' curves and might be well approximated by appropriate sigmoid functions. Based on this idea, we develop a novel approach that combines non-linear regression, simulation and trust region local search to efficiently solve large-scale staffing problems in a viable way. The main advantage of the approach is that the optimization procedure can be formulated as a sequence of steps of performing simulation and solving linear programming models. Numerical results based on real-life call center examples show the practical viability of our approach. The methodologies developed in this thesis can be applied in many other settings, e.g., staffing and scheduling problems in other queuing-based systems with other types of QoS constraints. These also raise several research directions that might be interesting to investigate. For examples, a clustering approach to mitigate the expensiveness of the two-stage staffing models, or a distributionally robust optimization version to better deal with data uncertainty.

Multiobjective Stochastic Linear Programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for Multiobjective Stochastic Linear Programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out. / Decision Sciences

The master’s thesis focuses on the optimization models in logistics with emphasis on the network interdiction problem. The brief introduction is followed by two overview chapters - graph theory and mathematical programming. Important definitions strongly related to network interdiction problems are introduced in the chapter named Basic concepts of graph theory. Necessary theorems used for solving problems are following the definitions. Next chapter named Introduction to mathematical programming firstly contains concepts from linear programming. Definitions and theorems are chosen with respect to the following maximum flow problem and the derived dual problem. Concepts of stochastic optimization follow. In the fifth chapter, we discuss deterministic models of the network interdiction. Stochastic models of the network interdiction follow in the next chapter. All models are implemented in programmes written in the programming language GAMS, the codes are attached.

In this study within quantitative portfolio optimization, stochastic programming is investigated as an investment decision tool. This research takes the direction of scenario based Mean-Absolute Deviation and is compared with the traditional Mean-Variance model and widely used Risk Parity portfolio. Furthermore, this thesis is done in collaboration with the First Swedish National Pension Fund, AP1, and the implemented multi-asset portfolios are thus tailored to match their investment style. The models are evaluated on two different fund management levels, in order to study if the portfolio performance benefits from a more restricted feasible domain. This research concludes that stochastic programming over the investigated time period is inferior to Risk Parity, but outperforms the Mean-Variance Model. The biggest aw of the model is its poor performance during periods of market stress. However, the model showed superior results during normal market conditions. / I denna studie inom kvantitativ portföljoptimering undersöks stokastisk programmering som ett investeringsbeslutsverktyg. Denna studie tar riktningen för scenariobaserad Mean-Absolute Deviation och jämförs med den traditionella Mean-Variance-modellen samt den utbrett använda Risk Parity-portföljen. Avhandlingen görs i samarbete med Första AP-fonden, och de implementerade portföljerna, med era tillgångsslag, är därför skräddarsydda för att matcha deras investeringsstil. Modellerna utvärderas på två olika fondhanteringsnivåer för att studera om portföljens prestanda drar nytta av en mer restrektiv optimeringsmodell. Den här undersökningen visar att stokastisk programmering under undersökta tidsperioder presterar något sämre än Risk Parity, men överträffar Mean-Variance. Modellens största brist är dess prestanda under perioder av marknadsstress. Modellen visade dock något bättre resultat under normala marknadsförhållanden.

Investors constantly seek information that provides an edge over the market. One of the conventional methods is to find factors which can predict asset returns. In this study we improve the Fama and French Five-Factor model with Regime-Switches, student's t distributions and copula dependencies. We also add price momentum as a sixth factor and add a one-day lag to the factors. The Regime-Switches are obtained from a Hidden Markov Model with conditional Student's t distributions. For the return process we use factor data as input, Student's t distributed residuals, and Student's t copula dependencies. To fit the copulas, we develop a novel approach based on the Expectation-Maximisation algorithm. The results are promising as the quantiles for most of the portfolios show a good fit to the theoretical quantiles. Using a sophisticated Stochastic Programming model, we back-test the predictive power over a 26 year period out-of-sample. Furthermore we analyse the performance of different factors during different market regimes.