IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v15y2018i3d10.1007_s10287-018-0312-2.html
   My bibliography  Save this article

Stochastic programs with binary distributions: structural properties of scenario trees and algorithms

Author

Listed:
  • Vit Prochazka

    (NHH Norwegian School of Economics)

  • Stein W. Wallace

    (NHH Norwegian School of Economics)

Abstract

Binary random variables often refer to such as customers that are present or not, roads that are open or not, machines that are operable or not. At the same time, stochastic programs often apply to situations where penalties are accumulated when demand is not met, travel times are too long, or profits too low. Typical for these situations is that the penalties imply a partial order on the scenarios, leading to a partition of the scenarios into two sets: those that can result in penalties for some decisions, and those that never lead to penalties. We demonstrate how this observation can be used to efficiently calculate out-of-sample values, find good scenario trees and generally simplify calculations. Most of our observations apply to general integer random variables, and not just the 0/1 case.

Suggested Citation

  • Vit Prochazka & Stein W. Wallace, 2018. "Stochastic programs with binary distributions: structural properties of scenario trees and algorithms," Computational Management Science, Springer, vol. 15(3), pages 397-410, October.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:3:d:10.1007_s10287-018-0312-2
    DOI: 10.1007/s10287-018-0312-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-018-0312-2
    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/s10287-018-0312-2?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Yifei Zhao & Stein W. Wallace, 2014. "Integrated Facility Layout Design and Flow Assignment Problem Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 798-808, November.
    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. Vit Prochazka & Stein W. Wallace, 2020. "Scenario tree construction driven by heuristic solutions of the optimization problem," Computational Management Science, Springer, vol. 17(2), pages 277-307, June.
    2. Wei Zhang & Kai Wang & Alexandre Jacquillat & Shuaian Wang, 2023. "Optimized Scenario Reduction: Solving Large-Scale Stochastic Programs with Quality Guarantees," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 886-908, July.

    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. Yifei Zhao & Stein W. Wallace, 2016. "Appraising redundancy in facility layout," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 665-679, February.
    2. Zhaoxia Guo & Stein W. Wallace & Michal Kaut, 2019. "Vehicle Routing with Space- and Time-Correlated Stochastic Travel Times: Evaluating the Objective Function," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 654-670, October.
    3. Feizollahi, Mohammad Javad & Feyzollahi, Hadi, 2015. "Robust quadratic assignment problem with budgeted uncertain flows," Operations Research Perspectives, Elsevier, vol. 2(C), pages 114-123.

    More about this item

    Keywords

    Stochastic programming; Scenarios; Binary random variables; Algorithms;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    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:15:y:2018:i:3:d:10.1007_s10287-018-0312-2. 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.