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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. Narum, Benjamin S. & Fairbrother, Jamie & Wallace, Stein W., 2024. "Problem-based scenario generation by decomposing output distributions," European Journal of Operational Research, Elsevier, vol. 318(1), pages 154-166.

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    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

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