The past few decades have witnessed a growing interest in the engineering communities to approach the handling of imperfect information from a quantitatively justifiable angle. In the aerospace engineering domain, the movement to develop creative avenues to nondeterministically solving engineering problems has emerged in the field of aerospace systems design. Inspired by statistical data modeling and numerical analysis techniques that used to be relatively foreign to the designers of aerospace systems, a variety of strategies leveraging upon the probabilistic treatment of uncertainty has been, and continue to be, reported. Although each method differs in the sequence in which probabilistic analysis and numerical optimization are performed, a common motif in all of them is the lack of any built-in provisions to compensate for infeasibilities that occur during optimization. Constraint violations are either strictly prohibited or striven to be held to an acceptable probability threshold, implying that most hitherto developed probabilistic design methods promote an avoid-failure approach to developing aerospace systems under uncertainty. It is the premise of this dissertation that such a dichotomous structure of addressing imperfections is hardly a realistic model of how product development unfolds in practice. From a time-phased view of engineering design, it is often observed that previously unknown parameters become known with the passing of each design milestone, and their effects on the system are realized. Should these impacts happen to be detrimental to critical system-level metrics, then a compensatory action is taken to remedy any unwanted deviations from the target or required bounds, rather than starting the process completely anew. Anecdotal accounts of numerous real-world design projects confirm that such remedial actions are commonly practiced means to ensure the successful fielding of aerospace systems. Therefore, formalizing the remedial aspect of engineering design into a new methodological capability would be the next logical step towards making uncertainty handling more pragmatic for this generation of engineers. In order to formulate a nondeterministic solution approach that capitalizes on the practice of compensatory design, this research introduces the notion of recourse. Within the context of engineering an aerospace system, recourse is defined as a set of corrective actions that can be implemented in stages later than the current design phase to keep critical system-level figures of merit within the desired target ranges, albeit at some penalty. The terminology is inspired by the concept of the same name in the field of statistical decision analysis, where it refers to an action taken by a decision maker to mitigate the unfavorable consequences caused by uncertainty realizations. Recourse programs also introduce the concept of stages to optimization formulations, and allow each stage to encompass as many sequences or events as determined necessary to solve the problem at hand. Together, these two major premises of classical stochastic programming provide a natural way to embody not only the remedial, but also the temporal and nondeterministic aspects of aerospace systems design. A two-part strategy, which partitions the design activities into stages, is proposed to model the bi-phasal nature of recourse. The first stage is defined as the time period in which an a priori design is identified before the exact values of the uncertain parameters are known. In contrast, the second stage is a period occurring some time after the first stage, when an a posteriori correction can be made to the first-stage design, should the realization of uncertainties impart infeasibilities. Penalizing costs are attached to the second-stage corrections to reflect the reality that getting it done right the first time is almost always less costly than fixing it after the fact. Consequently, the goal of the second stage becomes identifying an optimal solution with respect to the second-stage penalty, given the first-stage design, as well as a particular realization of the random parameters. This two-stage model is intended as an analogue of the traditional practice of monitoring and managing key Technical Performance Measures (TPMs) in aerospace systems development settings. Whenever an alarmingly significant discrepancy between the demonstrated and target TPM values is noted, it is generally the case that the most cost-effective recourse option is selected, given the available resources at the time, as well as scheduling and budget constraints. One obvious weakness of the two-stage strategy as presented above is its limited applicability as a forecasting tool. Not only cannot the second stage be invoked without a first-stage starting point, but also the second-stage solution differs from one specific outcome of uncertainties to another. On the contrary, what would be more valuable given the time-phased nature of engineering design is the capability to perform an anticipatory identification of an optimum that is also expected to incur the least costly recourse option in the future. It is argued that such a solution is in fact a more balanced alternative than robust, probabilistically maximized, or chance-constrained solutions, because it represents trading the design optimality in the present with the potential costs of future recourse. Therefore, it is further proposed that the original two-stage model be embedded inside a larger design loop, so that the realization of numerous recourse scenarios can be simulated for a given first-stage design. The repetitive procedure at the second stage is necessary for computing the expected cost of recourse, which is equivalent to its mathematical expectation as per the strong law of large numbers. The feedback loop then communicates this information to the aggregate-level optimizer, whose objective is to minimize the sum total of the first-stage metric and the expected cost of future corrective actions. The resulting stochastic solution is a design that is well-hedged against the uncertain consequences of later design phases, while at the same time being less conservative than a solution designed to more traditional deterministic standards. As a proof-of-concept demonstration, the recourse-based solution approach is presented as applied to a contemporary aerospace engineering problem of interest - the integration of fuel cell technology into uninhabited aerial systems. The creation of a simulation environment capable of designing three system alternatives based on Proton Exchange Membrane Fuel Cell (PEMFC) technology and another three systems leveraging upon Solid Oxide Fuel Cell (SOFC) technology is presented as the means to notionally emulate the development process of this revolutionary aeropropulsion method. Notable findings from the deterministic trade studies and algorithmic investigation include the incompatibility of the SOFC based architectures with the conceived maritime border patrol mission, as well as the thermodynamic scalability of the PEMFC based alternatives. It is the latter finding which justifies the usage of the more practical specific-parameter based approach in synthesizing the design results at the propulsion level into the overall aircraft sizing framework. The ensuing presentation on the stochastic portion of the implementation outlines how the selective applications of certain Design of Experiments, constrained optimization, Surrogate Modeling, and Monte Carlo sampling techniques enable the visualization of the objective function space. The particular formulations of the design stages, recourse, and uncertainties proposed in this research are shown to result in solutions that are well compromised between unfounded optimism and unwarranted conservatism. In all stochastic optimization cases, the Value of Stochastic Solution (VSS) proves to be an intuitively appealing measure of accounting for recourse-causing uncertainties in an aerospace systems design environment.

Thesis (Ph. D.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 459-469). Also available via the World Wide Web.

[pt] Esta tese apresenta uma nova proposta para modelagem das funções de custo futuro, utilizadas na Programação Dinâmica Estocástica (PDE). A técnica proposta é aplicada ao planejamento da operação de médio prazo de sistemas elétricos de potência. Através da discretização do espaço de estados, o algoritmo de fechos convexos (convex hull) é utilizado na obtenção de uma série de hiperplanos que compõe um conjunto convexo. Estes planos representam uma aproximação linear por partes da função de custo futuro. O custo operacional médio utilizando a metodologia proposta considerando-se um único cenário de afluências foi comparado com o custo obtido da programação dinâmica dual determinística para o mesmo cenário de afluências. Esta análise mostra a convergência das duas metodologias e é utilizada para determinar o nível mínimo de discretização necessário para modelagem das funções de custo futuro. A partir deste resultado é feita a extensão da análise para diversos cenários de afluências utilizando-se a metodologia proposta, sendo a função de custo futuro obtida através da média do custo de operação para os diversos cenários, em cada discretização. A aplicabilidade do método é mostrada utilizando um caso exemplo de duas usinas hidrelétricas reais em cascata. Adicionalmente, um estudo de caso analisa as vantagens da paralelização do código de programação, onde métricas tais como fator de aceleração e eficiência são analisadas. Por fim, é apresentada uma simulação contendo todo o sistema elétrico brasileiro, representado por reservatórios equivalentes. / [en] This thesis presents a new approach for the expected-cost-to-go functions modeling used in the stochastic dynamic programming (SDP) algorithm. The proposed technique is applied to the long-term operation planning of electrical power systems. Using state space discretization, the convex hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a piecewise linear approximation for the expected-cost-to-go functions. The mean operation costs obtained by the proposed methodology for a single water inflow scenario were compared with those from the deterministic dual dynamic programming for the same inflow scenario.This sensitivity analysis shows the convergence of both methods and is used to determine the minimum discretization level necessary to model the expected-cost-to-go functions. From the obtained result the proposed methodology is extended to the analysis of a set of water inflow scenarios, where the expected-cost-to-go function is obtained by the mean operation cost to all the considered scenario in each discretization level. The applicability of the proposed methodology for two hydro plants in a cascade is demonstrated. Additionally, a case study using code parallelization is presented aiming at gaining computational performance, where the parallelization performance, as speedup and efficiency are measured. To finish with a simulation with the whole Brazilian electrical system considering aggregated reservoir is presented.

Este trabalho propõe um modelo para a simulação do passivo atuarial de um fundo de pensão brasileiro. As principais fontes de incertezas que influenciam a avaliação do passivo atuarial foram especificadas como variáveis aleatórias e parâmetros do modelo. Diversos cenários são gerados utilizando a técnica de simulação de Monte Carlo e a microssimulação no intuito de determinar o status de cada participante do fundo de pensão modelo para períodos futuros em diferentes nós de uma árvore de cenários. A situação de vida de cada participante, simulada individualmente a cada nó, está condicionada ao seu estado no nó imediatamente antecessor. O resultado é um modelo flexível, que permite a configuração de parâmetros a níveis individuais e possibilita trabalhar com diversas tábuas biométricas, mostrando-se capaz de gerar cenários consistentes, realistas e variados, capturando a essência da incerteza inerente às entidades de previdência complementar e produzindo não só valores únicos e determinísticos de reservas matemáticas e fluxos de caixa atuariais, mas intervalos de valores possíveis com distribuições conhecidas, importantes para a gestão eficiente de um fundo de pensão. A metodologia proposta serve como alternativa ao cálculo atuarial tradicional, que utiliza diretamente as probabilidades das tábuas biométricas, fixas por idade e sexo, para a mensuração dos fluxos de caixa previdenciários e reservas matemáticas. Os dados gerados a partir das simulações servem como dados de entrada para um modelo estocástico completo de Asset-Liability Management (ALM). / This study proposes a model to simulate actuarial liabilities from a pension fund in Brazil. The main uncertainties that affect the liabilities have been specified as random variables and parameters of the developed model. Many scenarios are generated using Monte Carlo simulation and micro-simulation techniques in order to determine the status of each member of the pension fund for future periods in different nodes of a scenario tree. The future of each participant, simulated individually at each node, is conditioned to its status in the immediately predecessor node. The result is a flexible model which allows the parameters configuration at individual levels and that can work with several actuarial tables, showing to be itself able to generate consistent, realistic and sorted scenarios, capturing the uncertainty inherent in pension funds environment and producing not only single and deterministic values for actuarial liabilities and cash flows, but ranges of possible values with known distributions, becoming an important tool for the efficient management of the pension fund. The methodology applied is an alternative to the classic actuarial techniques, that use directly the probabilities from actuarial tables, fixed by age and gender, to calculate the liabilities and the cash flow of the pension fund. The data generated by this model were thought to be inputs for a full multistage stochastic Asset-Liability Management (ALM) model.

abstract: One of the greatest 21st century challenges is meeting the needs of a growing world population expected to increase 35% by 2050 given projected trends in diets, consumption and income. This in turn requires a 70-100% improvement on current production capability, even as the world is undergoing systemic climate pattern changes. This growth not only translates to higher demand for staple products, such as rice, wheat, and beans, but also creates demand for high-value products such as fresh fruits and vegetables (FVs), fueled by better economic conditions and a more health conscious consumer. In this case, it would seem that these trends would present opportunities for the economic development of environmentally well-suited regions to produce high-value products. Interestingly, many regions with production potential still exhibit a considerable gap between their current and ‘true’ maximum capability, especially in places where poverty is more common. Paradoxically, often high-value, horticultural products could be produced in these regions, if relatively small capital investments are made and proper marketing and distribution channels are created. The hypothesis is that small farmers within local agricultural systems are well positioned to take advantage of existing sustainable and profitable opportunities, specifically in high-value agricultural production. Unearthing these opportunities can entice investments in small farming development and help them enter the horticultural industry, thus expand the volume, variety and/or quality of products available for global consumption. In this dissertation, the objective is three-fold: (1) to demonstrate the hidden production potential that exist within local agricultural communities, (2) highlight the importance of supply chain modeling tools in the strategic design of local agricultural systems, and (3) demonstrate the application of optimization and machine learning techniques to strategize the implementation of protective agricultural technologies. As part of this dissertation, a yield approximation method is developed and integrated with a mixed-integer program to estimate a region’s potential to produce non-perennial, vegetable items. This integration offers practical approximations that help decision-makers identify technologies needed to protect agricultural production, alter harvesting patterns to better match market behavior, and provide an analytical framework through which external investment entities can assess different production options. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2017

Este trabalho propõe um modelo para a simulação do passivo atuarial de um fundo de pensão brasileiro. As principais fontes de incertezas que influenciam a avaliação do passivo atuarial foram especificadas como variáveis aleatórias e parâmetros do modelo. Diversos cenários são gerados utilizando a técnica de simulação de Monte Carlo e a microssimulação no intuito de determinar o status de cada participante do fundo de pensão modelo para períodos futuros em diferentes nós de uma árvore de cenários. A situação de vida de cada participante, simulada individualmente a cada nó, está condicionada ao seu estado no nó imediatamente antecessor. O resultado é um modelo flexível, que permite a configuração de parâmetros a níveis individuais e possibilita trabalhar com diversas tábuas biométricas, mostrando-se capaz de gerar cenários consistentes, realistas e variados, capturando a essência da incerteza inerente às entidades de previdência complementar e produzindo não só valores únicos e determinísticos de reservas matemáticas e fluxos de caixa atuariais, mas intervalos de valores possíveis com distribuições conhecidas, importantes para a gestão eficiente de um fundo de pensão. A metodologia proposta serve como alternativa ao cálculo atuarial tradicional, que utiliza diretamente as probabilidades das tábuas biométricas, fixas por idade e sexo, para a mensuração dos fluxos de caixa previdenciários e reservas matemáticas. Os dados gerados a partir das simulações servem como dados de entrada para um modelo estocástico completo de Asset-Liability Management (ALM). / This study proposes a model to simulate actuarial liabilities from a pension fund in Brazil. The main uncertainties that affect the liabilities have been specified as random variables and parameters of the developed model. Many scenarios are generated using Monte Carlo simulation and micro-simulation techniques in order to determine the status of each member of the pension fund for future periods in different nodes of a scenario tree. The future of each participant, simulated individually at each node, is conditioned to its status in the immediately predecessor node. The result is a flexible model which allows the parameters configuration at individual levels and that can work with several actuarial tables, showing to be itself able to generate consistent, realistic and sorted scenarios, capturing the uncertainty inherent in pension funds environment and producing not only single and deterministic values for actuarial liabilities and cash flows, but ranges of possible values with known distributions, becoming an important tool for the efficient management of the pension fund. The methodology applied is an alternative to the classic actuarial techniques, that use directly the probabilities from actuarial tables, fixed by age and gender, to calculate the liabilities and the cash flow of the pension fund. The data generated by this model were thought to be inputs for a full multistage stochastic Asset-Liability Management (ALM) model.

Orientador: Vinicius Amaral Armentano / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-11T06:29:58Z (GMT). No. of bitstreams: 1 Shiguemoto_AndreLuis_D.pdf: 2284701 bytes, checksum: 01f64264e516fb8e883b2f2632cace5b (MD5) Previous issue date: 2008 / Resumo: Este trabalho aborda a otimização de dois problemas integrados de uma seção de uma cadeia de suprimento. O primeiro é um problema de produção-distribuição ao longo de períodos de um horizonte de planejamento finito. Uma planta com restrições de capacidade processa vários produtos e uma frota homogênea de veículos está disponível para distribuição de produtos para atender a demanda dos clientes. Em cada período, o problema de produção determina quanto processar de cada produto, e o problema de distribuição define a quantidade de cada produto a ser entregue aos clientes e as rotas dos veículos. O objetivo é minimizar os custos de produção e estoque na planta, custos de estoque no cliente e custos de distribuição. O problema é resolvido pela meta-heurística busca tabu integrada com um procedimento de religamento de caminho, que permite soluções infactíveis durante a busca. O segundo problema envolve a seção estoque-produção com demanda estocástica de um único produto, especificada por uma distribuição discreta de probabilidades. O fornecedor deve definir quando visitar os clientes, quanto entregar, e as rotas de cada período, de forma a maximizar o rendimento pelas quantidades entregues e minimizar os custo de estoque nos clientes, custos de demanda perdida e custos de distribuição. O problema é modelado por meio de uma árvore de cenários que aproxima um processo de decisão markoviano. Uma heurística baseada em horizonte rolante é desenvolvida, de forma que em cada passo, o modelo definido em uma janela de tempo é resolvido de forma ótima pelo software de otimização CPLEX / Abstract: This work addresses the optimization of two integrated problems in a section of a suppy chain. The first is a production-distribution problem along periods of a finite planning horizon. A plant with capacity constraints processes several products and a homogeneous fleet of vehicles is available for the distribution of the products in order to satisfy the customers¿ demand. In each period, the production problem determines how much to process of each product, and the distribution problem defines the quantity of the product that should be delivered, and the vehicle routes. The objective is to minimize the production and inventory cost at the plant, inventory costs at the clients and the distribution costs. The problem is solved by the tabu search meta-heuristic integrated with a path relinking procedure, and infeasible solutions are allowed during the search. The second problem involves the section inventory-distribution with stochastic demand defined by a discrete probability distribution. The supplier must define when to visit the clients, how much to deliver, and the routes of each period in order to maximize the reward from delivering the delivered quantities and minimize the inventory costs at the clients, costs for lost demand and distribution costs. The problem is modeled as a scenario tree that approximates a markovian decision process. A heuristic based on a rolling horizon is developed, such that at each step, the model defined in a sliding time window is solved optimally by the optimization software CPLEX / Doutorado / Automação / Doutor em Engenharia Elétrica

The operational scheduling at coal handling facilities is of the utmost importance to ensure that the coal consuming processes are supplied with a constant feed of good quality coal. Although the Sasol Coal Handling Facility (CHF) were not designed to perform coal blending during the coal handling process, CHF has to blend the different sources to ensure that the quality of the feed supplied is of a stable nature. As a result, the operation of the plant has become an extremely complex process. Consequently, human intelligence is no longer sufficient to perform coal handling scheduling and therefore a scheduling model is required to ensure optimal plant operation and optimal downstream process performance. After various attempts to solve the scheduling model optimally, i.e. with exact solution methods, it was found that it is not possible to accurately model the complexities of CHF in such a way that the currently available exact solvers can solve it in an acceptable operational time. Various alternative solution approaches are compared, in terms of solution quality and execution speed, using a simplified version of the CHF scheduling problem. This investigation indicates that the Simulated Annealing (SA) metaheuristic is the most efficient solution method to provide approximate solutions. The metaheuristic solution approach allows one to model the typical sequential thoughts of a control room operator and sequential operating procedures. Thus far, these sequential rules could not be modelled in the simultaneous equation environment required for exact solution methods. An SA metaheuristic is developed to solve the practical scheduling model. A novel SA approach is applied where, instead of the actual solution being used for neighbourhood solution representation, the neighbours are indirectly represented by the rules used to generate neighbourhood solutions. It is also found that the initial temperature should not be a fixed value, but should be a multiple of the objective function value of the initial solution. An inverse arctan-based cooling schedule function outperforms traditional cooling schedules as it provides the required diversification and intensification behaviour of the SA. The scheduling model solves within 45 seconds and provides good, practically executable results. The metaheuristic approach to scheduling is therefore successful as the plant complexities and intricate operational philosophies can be accurately modelled using the sequential nature of programming languages and provides good approximate optimal solutions in a short solution time. Tests done with live CHF data indicate that the metaheuristic solution outperforms the current scheduling methodologies applied in the business. The implementation of the scheduler will lead to a more stable factory feed, which will increase production yields and therefore increase company profits. By reducing the amount of coal re-handling (in terms of throw-outs and load-backs at mine bunkers), the scheduler will reduce the coal handling facility’s annual operating cost by approximately R4.6 million (ZAR). Furthermore, the approaches discussed in this document can be applied to any continuous product scheduling environment. Additional information available on a CD stored at Level 3 of the Merensky Library. / Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2011. / Industrial and Systems Engineering / unrestricted

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

Este trabalho propõe um modelo para a simulação do passivo atuarial de um fundo de pensão brasileiro. As principais fontes de incertezas que influenciam a avaliação do passivo atuarial foram especificadas como variáveis aleatórias e parâmetros do modelo. Diversos cenários são gerados utilizando a técnica de simulação de Monte Carlo e a microssimulação no intuito de determinar o status de cada participante do fundo de pensão modelo para períodos futuros em diferentes nós de uma árvore de cenários. A situação de vida de cada participante, simulada individualmente a cada nó, está condicionada ao seu estado no nó imediatamente antecessor. O resultado é um modelo flexível, que permite a configuração de parâmetros a níveis individuais e possibilita trabalhar com diversas tábuas biométricas, mostrando-se capaz de gerar cenários consistentes, realistas e variados, capturando a essência da incerteza inerente às entidades de previdência complementar e produzindo não só valores únicos e determinísticos de reservas matemáticas e fluxos de caixa atuariais, mas intervalos de valores possíveis com distribuições conhecidas, importantes para a gestão eficiente de um fundo de pensão. A metodologia proposta serve como alternativa ao cálculo atuarial tradicional, que utiliza diretamente as probabilidades das tábuas biométricas, fixas por idade e sexo, para a mensuração dos fluxos de caixa previdenciários e reservas matemáticas. Os dados gerados a partir das simulações servem como dados de entrada para um modelo estocástico completo de Asset-Liability Management (ALM). / This study proposes a model to simulate actuarial liabilities from a pension fund in Brazil. The main uncertainties that affect the liabilities have been specified as random variables and parameters of the developed model. Many scenarios are generated using Monte Carlo simulation and micro-simulation techniques in order to determine the status of each member of the pension fund for future periods in different nodes of a scenario tree. The future of each participant, simulated individually at each node, is conditioned to its status in the immediately predecessor node. The result is a flexible model which allows the parameters configuration at individual levels and that can work with several actuarial tables, showing to be itself able to generate consistent, realistic and sorted scenarios, capturing the uncertainty inherent in pension funds environment and producing not only single and deterministic values for actuarial liabilities and cash flows, but ranges of possible values with known distributions, becoming an important tool for the efficient management of the pension fund. The methodology applied is an alternative to the classic actuarial techniques, that use directly the probabilities from actuarial tables, fixed by age and gender, to calculate the liabilities and the cash flow of the pension fund. The data generated by this model were thought to be inputs for a full multistage stochastic Asset-Liability Management (ALM) model.