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Distributionally robust simple integer recourse

Author

Listed:
  • Weijun Xie

    (Virginia Tech)

  • Shabbir Ahmed

    (Georgia Institute of Technology)

Abstract

The simple integer recourse (SIR) function of a decision variable is the expectation of the integer round-up of the shortage/surplus between a random variable with a known distribution and the decision variable. It is the integer analogue of the simple (continuous) recourse function in two-stage stochastic linear programming. Structural properties and approximations of SIR functions have been extensively studied in the seminal works of van der Vlerk and coauthors. We study a distributionally robust SIR function (DR-SIR) that considers the worst-case expectation over a given family of distributions. Under the assumption that the distribution family is specified by its mean and support, we derive a closed form analytical expression for the DR-SIR function. We also show that this nonconvex DR-SIR function can be represented using a mixed-integer second-order conic program.

Suggested Citation

  • Weijun Xie & Shabbir Ahmed, 2018. "Distributionally robust simple integer recourse," Computational Management Science, Springer, vol. 15(3), pages 351-367, October.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:3:d:10.1007_s10287-018-0313-1
    DOI: 10.1007/s10287-018-0313-1
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    References listed on IDEAS

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    1. Ward Romeijnders & David P. Morton & Maarten H. van der Vlerk, 2017. "Assessing the Quality of Convex Approximations for Two-Stage Totally Unimodular Integer Recourse Models," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 211-231, May.
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    8. Postek, Krzysztof & Ben-Tal, A. & den Hertog, Dick & Melenberg, Bertrand, 2015. "Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information," Discussion Paper 2015-030, Tilburg University, Center for Economic Research.
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    Cited by:

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    3. Liu, Ming & Liu, Xin & Chu, Feng & Zheng, Feifeng & Chu, Chengbin, 2019. "Distributionally robust inventory routing problem to maximize the service level under limited budget," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 190-211.

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