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Résolution de grands problèmes stochastiques multi-étapes : Application à un problème de dimensionnement de capacités et de gestion de flux et de stocks

Abstract : In a deterministic setting, data input are considered to be known. However, in real-world applications we're facing problems whose parameters are partially or totally uncertain. The approach where we consider a single scenario, which is supposed to represent a mean case, shows quickly its limits. We consider working in a discretized uncertainty space spreading over several time periods; we therefore consider scenario trees and introduce the multistage models associated. Problems dimensions rise exponentially with the number of stages that render direct solution methods inappropriate. What has motivated our work, is an industrial application arising in a gas market, concerning more precisely capacity reservation in the context of a contractual agreement that has to hold over a certain time horizon. Spot prices and client demands are considered to be uncertain and are modeled using a scenario tree. The problem structure presents strong similarities with a wide family of problems, where variables are coupling with each other in a very characteristic manner. After a literature survey focusing on (but not limited to) solution methods for multistage models, the Nested Decomposition method has been chosen. Over very large cases, even decomposition methods show their limits; this concerns in principle convergence times. This work is mostly devoted to the development of new procedures inside the Nested Decomposition method, in order to work with larger scenario trees in less time. Other aspects, concerning time reduction over a single iteration are also studied. Comparisons between the classic and the newly presented approaches revealed the superiority of the latter over the former.
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Submitted on : Friday, April 25, 2008 - 11:33:22 AM
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Georges Kolomvos. Résolution de grands problèmes stochastiques multi-étapes : Application à un problème de dimensionnement de capacités et de gestion de flux et de stocks. Sciences de l'ingénieur [physics]. Ecole Centrale Paris, 2007. Français. ⟨tel-00275775⟩

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