Ensaios em matemática aplicada: estimação e trajetórias bootstrap de oferta de sangue e estudo de desempenho de extensões do algoritmo de Programação Dinâmica Dual Estocástica
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Data
2017-09-26
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Guigues, Vincent Gérard Yannick
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We study two topics of applied mathematics. The first topic is devoted to the estimation of blood supply time series and the generation of simulated trajectories. The main goal is to contribute to the literature of stock management of perishable goods. We use Autoregressive Vetors models and two bootstrap techniques when residuals are nonGaussian. We conclude that both techniques are suitable for the problem at hand and are good approaches to enhance predictability of the blood supply time series. The second topic is devoted to the study of different extensions of the Stochastic Dual Dynamic Programming algorithm (SDDP). We compare the computational performance of two algorithms applied to portfolio selection models. The first one is Multicut Decomposition Algorithm (MuDA) which modifies SDDP by including multiple cuts (instead of just one) per stage and per iteration. The second, Cut Selection Multicut Decomposition Algorithms (CuSMuDA), combines MuDA with cut selection strategies and, to the best of our knowledge, has not been proposed so far in the literature. We compare two Cut Selection strategies, CS1 and CS2. We run simulations for 6 different instances of the portfolio problem. Results show the attractiveness of CuSMuDA CS2, which was much quicker than MuDA (between 5,1 and 12,6 times quicker) and much quicker than the other cut selection strategy, CuSMuDA CS1 (between 10,3 and 21,9 times quicker).