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Solving two-stage stochastic programming problems with level decomposition

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Abstract

We propose a new variant of the two-stage recourse model. It can be used e.g., in managing resources in whose supply random interruptions may occur. Oil and natural gas are examples for such resources. Constraints in the resulting stochastic programming problems can be regarded as generalizations of integrated chance constraints. For the solution of such problems, we propose a new decomposition method that integrates a bundle-type convex programming method with the classic distribution approximation schemes. Feasibility and optimality issues are taken into consideration simultaneously, since we use a convex programming method suited for constrained optimization. This approach can also be applied to traditional two-stage problems whose recourse functions can be extended to the whole space in a computationally efficient way. Network recourse problems are an example for such problems. We report encouraging test results with the new method.

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Authors and Affiliations

  1. Department of Operations Research, Loránd Eötvös University of Budapest, P.O. Box 120, Budapest, 1518, Hungary

    Csaba I. Fábián

  2. Doctoral School in Applied Mathematics, Loránd Eötvös University of Budapest, Budapest, Hungary

    Zoltán Szőke

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  1. Csaba I. Fábián
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  2. Zoltán Szőke
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Correspondence to Csaba I. Fábián.

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Fábián, C.I., Szőke, Z. Solving two-stage stochastic programming problems with level decomposition. CMS 4, 313–353 (2007). https://doi.org/10.1007/s10287-006-0026-8

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