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The value of the right distribution in stochastic programming with application to a Newsvendor problem

Author

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  • Francesca Maggioni

    (University of Bergamo)

  • Matteo Cagnolari

    (University of Bergamo)

  • Luca Bertazzi

    (University of Brescia)

Abstract

In this paper we introduce the concepts of the Value of the Right Distribution (VRD), the Performance Bound (PB) and the Worst-Case Performance Bound (WPB), which allow us to quantify how much we lose if we guess the wrong distribution of the uncertain parameters affecting a stochastic optimization problem. In order to show how they apply, we introduce a cost-based variant of the classical Newsvendor problem and model it as a two-stage stochastic programming model. For this problem, we first provide optimal solutions in closed form for different probability distributions and then compute, both analytically and computationally, the VRD measure and the corresponding performance bounds PB and WPB. Finally, systematic numerical results are provided.

Suggested Citation

  • Francesca Maggioni & Matteo Cagnolari & Luca Bertazzi, 2019. "The value of the right distribution in stochastic programming with application to a Newsvendor problem," Computational Management Science, Springer, vol. 16(4), pages 739-758, October.
    • Handle: RePEc:spr:comgts:v:16:y:2019:i:4:d:10.1007_s10287-019-00356-2
    DOI: 10.1007/s10287-019-00356-2
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    References listed on IDEAS

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    1. Svetlozar T. Rachev & Werner Römisch, 2002. "Quantitative Stability in Stochastic Programming: The Method of Probability Metrics," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 792-818, November.
    2. Francesca Maggioni & Stein Wallace, 2012. "Analyzing the quality of the expected value solution in stochastic programming," Annals of Operations Research, Springer, vol. 200(1), pages 37-54, November.
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    7. Maggioni, Francesca & Cagnolari, Matteo & Bertazzi, Luca & Wallace, Stein W., 2019. "Stochastic optimization models for a bike-sharing problem with transshipment," European Journal of Operational Research, Elsevier, vol. 276(1), pages 272-283.
    8. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2016. "Monotonic bounds in multistage mixed-integer stochastic programming," Computational Management Science, Springer, vol. 13(3), pages 423-457, July.
    9. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
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