IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v16y2019i4d10.1007_s10287-019-00356-2.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-019-00356-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-019-00356-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    3. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2014. "Bounds in Multistage Linear Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 200-229, October.
    4. Dimitris Bertsimas & Aurélie Thiele, 2006. "A Robust Optimization Approach to Inventory Theory," Operations Research, INFORMS, vol. 54(1), pages 150-168, February.
    5. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    6. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    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.
    10. Bita Analui & Georg Pflug, 2014. "On distributionally robust multiperiod stochastic optimization," Computational Management Science, Springer, vol. 11(3), pages 197-220, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Qinghe Sun & Li Chen & Mabel C. Chou & Qiang Meng, 2023. "Mitigating the financial risk behind emission cap compliance: A case in maritime transportation," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 283-300, January.
    2. Hermann, Alexander & Jensen, Tue Vissing & Østergaard, Jacob & Kazempour, Jalal, 2022. "A complementarity model for electric power transmission-distribution coordination under uncertainty," European Journal of Operational Research, Elsevier, vol. 299(1), pages 313-329.
    3. Miguel Angel Muñoz & Pierre Pinson & Jalal Kazempour, 2023. "Online decision making for trading wind energy," Computational Management Science, Springer, vol. 20(1), pages 1-31, December.
    4. Mitridati, Lesia & Kazempour, Jalal & Pinson, Pierre, 2020. "Heat and electricity market coordination: A scalable complementarity approach," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1107-1123.
    5. Peng, Shen & Maggioni, Francesca & Lisser, Abdel, 2022. "Bounds for probabilistic programming with application to a blend planning problem," European Journal of Operational Research, Elsevier, vol. 297(3), pages 964-976.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francesca Maggioni & Elisabetta Allevi & Asgeir Tomasgard, 2020. "Bounds in multi-horizon stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 605-625, September.
    2. Audrius Kabašinskas & Francesca Maggioni & Kristina Šutienė & Eimutis Valakevičius, 2019. "A multistage risk-averse stochastic programming model for personal savings accrual: the evidence from Lithuania," Annals of Operations Research, Springer, vol. 279(1), pages 43-70, August.
    3. Bita Analui & Georg Pflug, 2014. "On distributionally robust multiperiod stochastic optimization," Computational Management Science, Springer, vol. 11(3), pages 197-220, July.
    4. Dimitris Bertsimas & Melvyn Sim & Meilin Zhang, 2019. "Adaptive Distributionally Robust Optimization," Management Science, INFORMS, vol. 65(2), pages 604-618, February.
    5. Gambella, Claudio & Maggioni, Francesca & Vigo, Daniele, 2019. "A stochastic programming model for a tactical solid waste management problem," European Journal of Operational Research, Elsevier, vol. 273(2), pages 684-694.
    6. Ching-Hui Tang, 2018. "Two-stage stochastic modeling of transportation outsourcing plans for transshipment centers," 4OR, Springer, vol. 16(1), pages 67-94, March.
    7. Steffen Rebennack, 2022. "Data-driven stochastic optimization for distributional ambiguity with integrated confidence region," Journal of Global Optimization, Springer, vol. 84(2), pages 255-293, October.
    8. Viet Anh Nguyen & Soroosh Shafiee & Damir Filipovi'c & Daniel Kuhn, 2021. "Mean-Covariance Robust Risk Measurement," Papers 2112.09959, arXiv.org, revised Nov 2023.
    9. Ch. Pflug, Georg, 2023. "Multistage stochastic decision problems: Approximation by recursive structures and ambiguity modeling," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1027-1039.
    10. Birghila, Corina & Pflug, Georg Ch., 2019. "Optimal XL-insurance under Wasserstein-type ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 30-43.
    11. Shie Mannor & Ofir Mebel & Huan Xu, 2016. "Robust MDPs with k -Rectangular Uncertainty," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1484-1509, November.
    12. Kim, Jang Ho & Kim, Woo Chang & Fabozzi, Frank J., 2013. "Composition of robust equity portfolios," Finance Research Letters, Elsevier, vol. 10(2), pages 72-81.
    13. Giovanni Pantuso & Trine K. Boomsma, 2020. "On the number of stages in multistage stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 581-603, September.
    14. Marcio Costa Santos & Michael Poss & Dritan Nace, 2018. "A perfect information lower bound for robust lot-sizing problems," Annals of Operations Research, Springer, vol. 271(2), pages 887-913, December.
    15. Hui Zhao & Qiang Meng & Yadong Wang, 2022. "Robust container slot allocation with uncertain demand for liner shipping services," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 551-579, September.
    16. Hachmi Ben Ameur & Mouna Boujelbène & J. L. Prigent & Emna Triki, 2020. "Optimal Portfolio Positioning on Multiple Assets Under Ambiguity," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 21-57, June.
    17. Jose Blanchet & Lin Chen & Xun Yu Zhou, 2022. "Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances," Management Science, INFORMS, vol. 68(9), pages 6382-6410, September.
    18. Cavagnini, Rossana & Bertazzi, Luca & Maggioni, Francesca, 2022. "A rolling horizon approach for a multi-stage stochastic fixed-charge transportation problem with transshipment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 912-922.
    19. Martin Glanzer & Georg Ch. Pflug & Alois Pichler, 2017. "Incorporating statistical model error into the calculation of acceptability prices of contingent claims," Papers 1703.05709, arXiv.org, revised Jan 2019.
    20. Ameur, H. Ben & Prigent, J.L., 2013. "Optimal portfolio positioning under ambiguity," Economic Modelling, Elsevier, vol. 34(C), pages 89-97.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:comgts:v:16:y:2019:i:4:d:10.1007_s10287-019-00356-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.