Abstract

This thesis proposes a heuristic method to approximate multistage sto- chastic convex optimization problem with unconstrained state variables. This is called the ...
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Abstract This thesis proposes a heuristic method to approximate multistage stochastic convex optimization problem with unconstrained state variables. This is called the stochastic programming with step decision rules method (SPSDR). This method is based on the concept of decision rule being adapted to the standard stochastic programming method. The use of step decision rules allows the formulation of an optimisation problem without the support of an event tree. The main advantage being an approach to overcome the curse of dimensionality. To involve performances we adapt the expert advice method. The resulting formulation is well suited to parallel computations. The expert advice method formulation involves the performance of the method on the studied numerical examples. This heuristic approach is proposed as a methodological contribution to the use of the massive multistage stochastic programming method. SPSDR is applied on a 12-stages supply chain optimization problem. Plain stochastic programming and robust optimization methods have been developed to be able to evaluate performances of the approach. A validation phase is used to determine posteriori knowledge on a large set of scenarios. Then, the DET2STO software is used, which is permitted to automatically generate the stochastic version of a deterministic problem and formulate with the GMPL algebraic modeling language. This tool is integrated into a website that permits the user to solve and transform their own problems online, using only free softwares. The two applications are proposed as a technological contribution to the use of stochastic programming. The SPSDR approach is involved in cases of a risk measure objective functions.

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