IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v200y2012i1p37-5410.1007-s10479-010-0807-x.html
   My bibliography  Save this article

Analyzing the quality of the expected value solution in stochastic programming

Author

Listed:
  • Francesca Maggioni
  • Stein Wallace

Abstract

Stochastic programs are usually hard to solve when applied to real-world problems; a common approach is to consider the simpler deterministic program in which random parameters are replaced by their expected values, with a loss in terms of quality of the solution. The Value of the Stochastic Solution—VSS—is normally used to measure the importance of using a stochastic model. But what if VSS is large, or expected to be large, but we cannot solve the relevant stochastic program? Shall we just give up? In this paper we investigate very simple methods for studying structural similarities and differences between the stochastic solution and its deterministic counterpart. The aim of the methods is to find out, even when VSS is large, if the deterministic solution carries useful information for the stochastic case. It turns out that a large VSS does not necessarily imply that the deterministic solution is useless for the stochastic setting. Measures of the structure and upgradeability of the deterministic solution such as the loss using the skeleton solution and the loss of upgrading the deterministic solution will be introduced and basic inequalities in relation to the standard VSS are presented and tested on different cases. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:200:y:2012:i:1:p:37-54:10.1007/s10479-010-0807-x
    DOI: 10.1007/s10479-010-0807-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0807-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0807-x?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. Julia L. Higle & Stein W. Wallace, 2003. "Sensitivity Analysis and Uncertainty in Linear Programming," Interfaces, INFORMS, vol. 33(4), pages 53-60, August.
    2. Francesca Maggioni & Michal Kaut & Luca Bertazzi, 2009. "Stochastic optimization models for a single-sink transportation problem," Computational Management Science, Springer, vol. 6(2), pages 251-267, May.
    3. Stein W. Wallace, 2000. "Decision Making Under Uncertainty: Is Sensitivity Analysis of Any Use?," Operations Research, INFORMS, vol. 48(1), pages 20-25, February.
    4. F. Maggioni & F. A. Potra & M. I. Bertocchi & E. Allevi, 2009. "Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 309-328, November.
    Full references (including those not matched with items on IDEAS)

    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. Xin Wang & Teodor Gabriel Crainic & Stein W. Wallace, 2019. "Stochastic Network Design for Planning Scheduled Transportation Services: The Value of Deterministic Solutions," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 153-170, February.
    2. E. Borgonovo & L. Peccati, 2011. "Managerial insights from service industry models: a new scenario decomposition method," Annals of Operations Research, Springer, vol. 185(1), pages 161-179, May.
    3. Arnt-Gunnar Lium & Teodor Gabriel Crainic & Stein W. Wallace, 2009. "A Study of Demand Stochasticity in Service Network Design," Transportation Science, INFORMS, vol. 43(2), pages 144-157, May.
    4. Curry, Stewart & Lee, Ilbin & Ma, Simin & Serban, Nicoleta, 2022. "Global sensitivity analysis via a statistical tolerance approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 44-59.
    5. Maskooki, Alaleh & Kallio, Markku, 2023. "A bi-criteria moving-target travelling salesman problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 309(1), pages 271-285.
    6. Biju Thapalia & Stein Wallace & Michal Kaut & Teodor Crainic, 2012. "Single source single-commodity stochastic network design," Computational Management Science, Springer, vol. 9(1), pages 139-160, February.
    7. Stein Wallace, 2010. "Stochastic programming and the option of doing it differently," Annals of Operations Research, Springer, vol. 177(1), pages 3-8, June.
    8. Borgonovo, E., 2010. "Sensitivity analysis with finite changes: An application to modified EOQ models," European Journal of Operational Research, Elsevier, vol. 200(1), pages 127-138, January.
    9. Thapalia, Biju K. & Crainic, Teodor Gabriel & Kaut, Michal & Wallace, Stein W., 2012. "Single-commodity network design with random edge capacities," European Journal of Operational Research, Elsevier, vol. 220(2), pages 394-403.
    10. Julie Ann Stuart Williams & Randall Reid & Philip E. Billings & Natalie C. Belford, 2023. "Engaging Students in Optimization Modeling: Gaining Business Disruption Insights," INFORMS Transactions on Education, INFORMS, vol. 24(1), pages 85-94, September.
    11. Fatemeh Sarayloo & Teodor Gabriel Crainic & Walter Rei, 2021. "A Learning-Based Matheuristic for Stochastic Multicommodity Network Design," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 643-656, May.
    12. Xin Wang & Stein W. Wallace, 2016. "Stochastic scheduled service network design in the presence of a spot market for excess capacity," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(4), pages 393-413, December.
    13. Borgonovo, E. & Peccati, L., 2011. "Finite change comparative statics for risk-coherent inventories," International Journal of Production Economics, Elsevier, vol. 131(1), pages 52-62, May.
    14. Hui, Yer Van & Gao, Jia & Leung, Lawrence & Wallace, Stein, 2014. "Airfreight forwarder’s shipment planning under uncertainty: A two-stage stochastic programming approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 66(C), pages 83-102.
    15. Rolf Golombek & Kjell Arne Brekke & Michal Kaut & Sverre A.C. Kittelsen & Stein W. Wallace, 2016. "Stochastic equilibrium modeling: The Impact of Uncertainty on the European Energy Market," EcoMod2016 9201, EcoMod.
    16. Brekke, Kjell Arne & Golombek, Rolf & Kaut, Michal & Kittelsen, Sverre A.C. & Wallace, Stein W., 2017. "Stochastic energy market equilibrium modeling with multiple agents," Energy, Elsevier, vol. 134(C), pages 984-990.
    17. Leung, Lawrence C. & Wong, Wai Hung & Hui, Yer Van & Wan, Yulai, 2013. "Managing third-party logistics under uncertainty: A decision scheme and managerial implications," International Journal of Production Economics, Elsevier, vol. 145(2), pages 630-644.
    18. Baker, Erin & Bosetti, Valentina & Salo, Ahti, 2016. "Finding Common Ground when Experts Disagree: Belief Dominance over Portfolios of Alternatives," MITP: Mitigation, Innovation and Transformation Pathways 243147, Fondazione Eni Enrico Mattei (FEEM).
    19. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    20. Aikaterini Papapostolou & Charikleia Karakosta & Kalliopi-Anastasia Kourti & Haris Doukas & John Psarras, 2019. "Supporting Europe’s Energy Policy Towards a Decarbonised Energy System: A Comparative Assessment," Sustainability, MDPI, vol. 11(15), pages 1-26, July.

    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:annopr:v:200:y:2012:i:1:p:37-54:10.1007/s10479-010-0807-x. 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.