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

Made available in DSpace on 2016-03-15T19:31:05Z (GMT). No. of bitstreams: 1 Marcio Barros Souza.pdf: 3064012 bytes, checksum: bbb11da9182e6b1ff4c1aee75ce7f916 (MD5) Previous issue date: 2014-05-07 / The aim of this study was to develop an analytical model of full stochastic programming, grounded on the Real Options Theory (ROT) for the analysis of the value of the investment opportunity in project to implement Enterprise Resource Planning (ERP) system. The proposed model is a modified extension of Wu et al. (2008), incorporating the possibility of a catastrophic event (or contingent event), as discussed in Schwartz and Zozaya-Gorostiza (2003). While a programming and stochastic optimization model, it is inserted in the context of Operational Research, whose nature, as the name implies, is the use of analytical scientific method to address operational problems in organizations. The managerial flexibility of the model was treated as a real option, in which there is the right, but not the obligation, to perform an action (for instance, postpone, expand, contract or abandon. The strategic decision concerned the possibility of purchasing and implementing the system as a whole package or through modules. Revenue estimates for the project were modeled as a stochastic process of the Geometric Brownian Motion type, while costs were modeled as a function of the characteristics of each cash outflow type, resulting in the choice of a probability distribution. The model uses Latin hypercube simulation to obtain the expected values of the parameters for generating a decision tree that guides the optimization process. Given the parameters and constraints of the model, the optimization searches for the optimal investment decision. Considering the model configuration and parameters adopted, the figures indicate that the process of purchasing and implementing the modules result in an optimal decision for the value of the investment opportunity. Furthermore, the sensitivity analysis of the parameters allowed the identification of the most sensitive parameters in the model that need careful analysis, to avoid distortions in the projections. / Neste trabalho, objetivou-se a desenvolver um modelo analítico de programação estocástica inteira, fundamentada pela Teoria de Opções Reais (TOR), para a análise do valor da oportunidade de investimento em projeto para implementação de sistema ERP - Enterprise Resource Planning. O modelo proposto é uma extensão modificada de Wu et. al. (2008), com a incorporação da possibilidade de ocorrência de um evento catastrófico (ou contingente), como em Schwartz e Zozaya-Gorostiza (2003). Enquanto modelo de programação estocástica e de otimização, está inserido no contexto de Pesquisa Operacional, cuja natureza, como o próprio nome indica, é o uso do método científico analítico para tratar dos problemas operacionais nas organizações. A flexibilidade gerencial do projeto é tratada como uma opção real, na qual há um direito, mas não uma obrigação, para realizar uma ação (por exemplo, adiar, expandir, contrair ou abandonar). A decisão estratégica relacionou-se com a possibilidade de comprar e implementar o sistema pelo pacote completo, ou então por módulos. As estimativas de receitas do projeto foram modeladas como um processo estocástico do tipo Movimento Browniano Geométrico, enquanto os custos foram modelados em função da particularidade de cada tipo de saída de caixa, resultando na escolha de uma distribuição de probabilidades. O modelo utiliza simulação por hipercubos latinos para obtenção dos valores esperados dos parâmetros, os quais alimentam uma árvore de decisão que baliza o processo de otimização. Dados os parâmetros e as restrições do modelo, a otimização busca a decisão ótima de investimento. Os resultados obtidos, considerando a configuração do modelo e os parâmetros adotados, apontam que a compra e implementação por módulos resulta em uma decisão ótima para o valor da oportunidade de investimento. Ademais, a análise de sensibilidade dos parâmetros possibilitou a identificação dos parâmetros mais sensíveis no modelo e que precisam ser analisados com atenção, para evitar distorções nas projeções.

This thesis concerns solutions to problems that arise in optimizing fixed interval scheduling under situations of uncertainty such as when there are random delays in job process times. These problems can be solved by using a vertex coloring with random edges and problems can be formulated using integer linear, quadratic and stochastic programming. In this thesis is propo- sed a new integer linear formulation. Under certain conditions there is proved its equivalence with stochastic formulation, where is maximized the schedule reliability. Moreover, we modified the proposed formulation to obtain bet- ter corresponding to real life situations. In a numerical study we compared computational time of individual formulations. It turns out that the propo- sed formulation is able to solve scheduling problems considerably faster than other formulations. 1

The main objective of this thesis is to build a multi-stage stochastic pro- gram within an asset-liability management problem of a leasing company. At the beginning, the business model of such a company is introduced and the stochastic programming formulation is derived. Thereafter, three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint are applied to the model to control for riski- ness of the optimal strategy. Their properties and their effects on the optimal decisions are thoroughly investigated, while various risk limits are considered. In order to obtain solutions of the problems, random elements in the model formulation had to be approximated by scenarios. The Hull - White model calibrated by a newly proposed method based on maximum likelihood esti- mation has been used to generate scenarios of future interest rates. In the end, the performances of the optimal solutions of the problems for unconsid- ered and unfavourable crisis scenarios were inspected. The used methodology of such a stress test has not yet been implemented in stochastic programming problems within an asset-liability management. 1

La présente thèse s’intéresse aux modèles d’allocation stratégiques d’actifs et à leurs applications pour la gestion des réserves financières des régimes de retraite par répartition, en particulier ceux partiellement provisionnés. L’étude de l’utilité des réserves pour un système par répartition et a fortiori de leur gestion reste un sujet peu exploré. Les hypothèses classiques sont parfois jugées trop restrictives pour décrire l'évolution complexe des réserves. De nouveaux modèles et de nouveaux résultats sont développés à trois niveaux : la génération de scénarios économiques (GSE), les techniques d’optimisation numérique et le choix de l’allocation stratégique optimale dans un contexte de gestion actif-passif (ALM). Dans le cadre de la génération de scénarios économiques et financiers, certains indicateurs de mesure de performance du GSE ont été étudiés. Par ailleurs, des améliorations par rapport à ce qui se pratique usuellement lors de la construction du GSE ont été apportées, notamment au niveau du choix de la matrice de corrélation entre les variables modélisées. Concernant le calibrage du GSE, un ensemble d’outils permettant l’estimation de ses différents paramètres a été présenté. Cette thèse a également accordé une attention particulière aux techniques numériques de recherche de l'optimum, qui demeurent des questions essentielles pour la mise en place d'un modèle d'allocation. Une réflexion sur un algorithme d’optimisation globale d’une fonction non convexe et bruitée a été développée. L’algorithme permet de moduler facilement, au moyen de deux paramètres, la réitération de tirages dans un voisinage des points solutions découverts, ou à l’inverse l’exploration de la fonction dans des zones encore peu explorées. Nous présentons ensuite des techniques novatrices d'ALM basées sur la programmation stochastique. Leur application a été développée pour le choix de l’allocation stratégique d’actifs des régimes de retraite par répartition partiellement provisionnés. Une nouvelle méthodologie pour la génération de l’arbre des scénarios a été adoptée à ce niveau. Enfin, une étude comparative du modèle d’ALM développé avec celui basé sur la stratégie Fixed-Mix a été effectuée. Différents tests de sensibilité ont été par ailleurs mis en place pour mesurer l’impact du changement de certaines variables clés d’entrée sur les résultats produits par notre modèle d’ALM / This thesis focuses on the strategic asset allocation models and on their application for the financial reserve management of a pay-as-you-go (PAYG) retirement schemes, especially those with partial provision. The study of the reserve utility for a PAYG system and of their management still leaves a lot to be explored. Classical hypothesis are usually considered too restrictive for the description of the complex reserve evolution. New models and new results have been developed over three levels : economic scenario generation (ESG), numerical optimization techniques and the choice of optimal strategic asset allocation in the case of an Asset-Liability Management (ALM). For the generation of financial and economic scenarios, some ESG performance indicators have been studied. Also, we detailed and proposed to improve ESG construction, notably the choice of the correlation matrix between modelled variables. Then, a set of tools were presented so that we could estimate ESG parameters variety. This thesis has also paid particular attention to numerical techniques of optimum research, which is an important step for the asset allocation implementation. We developed a reflexion about a global optimisation algorithm of a non convex and a noisy function. The algorithm allows for simple modulating, through two parameters, the reiteration of evaluations at an observed point or the exploration of the noisy function at a new unobserved point. Then, we presented new ALM techniques based on stochastic programming. An application to the strategic asset allocation of a retirement scheme with partial provision is developed. A specific methodology for the scenario tree generation was proposed at this level. Finally, a comparative study between proposed ALM model and Fixed-Mix strategy based model was achieved. We also made a variety of a sensitivity tests to detect the impact of the input values changes on the output results, provided by our ALM model

Ce travail de thèse de doctorat est dédié à l'étude de problèmes d'optimisation combinatoire du domaine des architectures massivement parallèles avec la prise en compte des données incertaines tels que les temps d'exécution. On s'intéresse aux programmes sous contraintes probabilistes dont l'objectif est de trouver la meilleure solution qui soit réalisable avec un niveau de probabilité minimal garanti. Une analyse quantitative des données incertaines à traiter (variables aléatoires dépendantes, multimodales, multidimensionnelles, difficiles à caractériser avec des lois de distribution usuelles), nous a conduit à concevoir une méthode qui est non paramétrique, intitulée "approche binomiale robuste". Elle est valable quelle que soit la loi jointe et s'appuie sur l'optimisation robuste et sur des tests d'hypothèse statistique. On propose ensuite une méthodologie pour adapter des algorithmes de résolution de type approchée pour résoudre des problèmes stochastiques en intégrant l'approche binomiale robuste afin de vérifier la réalisabilité d'une solution. La pertinence pratique de notre démarche est enfin validée à travers deux problèmes issus de la compilation des applications de type flot de données pour les architectures manycore. Le premier problème traite du partitionnement stochastique de réseaux de processus sur un ensemble fixé de nœuds, en prenant en compte la charge de chaque nœud et les incertitudes affectant les poids des processus. Afin de trouver des solutions robustes, un algorithme par construction progressive à démarrages multiples a été proposé ce qui a permis d'évaluer le coût des solution et le gain en robustesse par rapport aux solutions déterministes du même problème. Le deuxième problème consiste à traiter de manière globale le placement et le routage des applications de type flot de données sur une architecture clustérisée. L'objectif est de placer les processus sur les clusters en s'assurant de la réalisabilité du routage des communications entre les tâches. Une heuristique de type GRASP a été conçue pour le cas déterministe, puis adaptée au cas stochastique clustérisé. / This PhD thesis is devoted to the study of combinatorial optimization problems related to massively parallel embedded architectures when taking into account uncertain data (e.g. execution time). Our focus is on chance constrained programs with the objective of finding the best solution which is feasible with a preset probability guarantee. A qualitative analysis of the uncertain data we have to treat (dependent random variables, multimodal, multidimensional, difficult to characterize through classical distributions) has lead us to design a non parametric method, the so-called "robust binomial approach", valid whatever the joint distribution and which is based on robust optimization and statistical hypothesis testing. We also propose a methodology for adapting approximate algorithms for solving stochastic problems by integrating the robust binomial approach when verifying for solution feasibility. The paractical relevance of our approach is validated through two problems arising in the compilation of dataflow application for manycore platforms. The first problem treats the stochastic partitioning of networks of processes on a fixed set of nodes, by taking into account the load of each node and the uncertainty affecting the weight of the processes. For finding stochastic solutions, a semi-greedy iterative algorithm has been proposed which allowed measuring the robustness and cost of the solutions with regard to those for the deterministic version of the problem. The second problem consists in studying the global placement and routing of dataflow applications on a clusterized architecture. The purpose being to place the processes on clusters such that it exists a feasible routing, a GRASP heuristic has been conceived first for the deterministic case and afterwards extended for the chance constrained variant of the problem.

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Magisterská práce se zabývá stochastickou optimalizací síťových úloh. Teoretická část pokrývá tři témata - teorii grafů, optimalizaci a progressive hedging algoritmus. V rámci optimalizace je hlavní část věnována stochastickému programování a dvoustupňovému programování. Progressing hedging algoritmus zahrnuje také metodu přiřazování scénářů a modifikaci obecného algoritmu na dvou stupňové úlohy. Praktická část je věnována modelům na reálných datech z oblasti svozu odpadu v rámci České republiky. Data poskytl Ústav procesního inženýrství.

The aim of this diploma thesis is to design and efficiently implement a framework to support optimization modelling. The emphasis is placed on two-stage stochastic optimization problems and performing calculations on large data. The computing core uses the GAMS system and with using its application interface and Python programming language, the user will be able to efficiently acquire and process input and output data. The separation of the data logic and the application logic then offers a wide range of options for testing and experimenting with a general model on dynamically changing input data. The thesis is also focused on an evaluation of the framework complexity. The framework performance was evaluated by measuring the time required to complete the required task for various use cases, on the increasing sample size of input data.

The diploma thesis deals with the modeling of selected risks in healthcare. Motivated by the current pandemic situation, it focuses on analysis of risks associated with the vaccination center in Brno. The theoretical part is mainly devoted to the issue of risk management with a focus on risks in healthcare, where the methods that are used in the practical part are defined. Furthermore, the thesis presents selected topics of mathematical programming. Especially, the newsvendor problem is introduced as inspiring case for further modelling. The brief description of the covid-19 pandemic situation later serves as one of the data sources. The practical part deals with the description and risk analysis of the vaccination process using the methods "What If?" and the FMEA method. Appropriate decisions are then proposed for selected risk situations using the GAMS optimization system. Based on the results of the calculations, specific recommendations are proposed.