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Bounds in Multistage Linear Stochastic Programming

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Abstract

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for optimal solution may help in evaluating whether it is worth the additional computations for the stochastic program vs. simplified approaches. In this paper we generalize measures from the two-stage case, based on different levels of available information, to the multistage stochastic programming problems. A set of theorems providing chains of inequalities among the new quantities are proved. Numerical results on a case study related to a simple transportation problem illustrate the described relationships.

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Acknowledgements

The work has been supported under grant by Regione Lombardia: “Metodi di integrazione delle fonti energetiche rinnovabili e monitoraggio satellitare dell’impatto ambientale”, EN-17, ID 17369.10 and by Bergamo and Brescia University grants 2010–2011.

We thank the referees for their helpful comments that improved the quality of the paper.

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Authors and Affiliations

  1. Department of Management, Economics and Quantitative Methods, Bergamo University, Via dei Caniana 2, 24127, Bergamo, Italy

    Francesca Maggioni & Marida Bertocchi

  2. Department of Economics and Management, Brescia University, Contrada S. Chiara 50, Brescia, 25122, Italy

    Elisabetta Allevi

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  1. Francesca Maggioni
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  2. Elisabetta Allevi
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  3. Marida Bertocchi
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Correspondence to Elisabetta Allevi.

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Maggioni, F., Allevi, E. & Bertocchi, M. Bounds in Multistage Linear Stochastic Programming. J Optim Theory Appl 163, 200–229 (2014). https://doi.org/10.1007/s10957-013-0450-1

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  • DOI: https://doi.org/10.1007/s10957-013-0450-1

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