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Technical Note—Minimax Procedure for a Class of Linear Programs under Uncertainty

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  • R. Jagannathan

    (University of Iowa, Iowa City, Iowa)

Abstract

We consider a linear programming problem with random a ij and b i elements that have known (finite) mean and variance, but whose distribution functions are otherwise unspecified. A minimax solution of the stochastic programming model is obtained by solving an equivalent deterministic convex programming problem. We derive these deterministic equivalents under different assumptions regarding the stochastic nature of the random parameters.

Suggested Citation

  • R. Jagannathan, 1977. "Technical Note—Minimax Procedure for a Class of Linear Programs under Uncertainty," Operations Research, INFORMS, vol. 25(1), pages 173-177, February.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:1:p:173-177
    DOI: 10.1287/opre.25.1.173
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    Cited by:

    1. Yuanying Guan & Zhanyi Jiao & Ruodu Wang, 2022. "A reverse ES (CVaR) optimization formula," Papers 2203.02599, arXiv.org, revised May 2023.
    2. Woonghee Tim Huh & Paat Rusmevichientong, 2014. "Online Sequential Optimization with Biased Gradients: Theory and Applications to Censored Demand," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 150-159, February.
    3. 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.
    4. Kyungchul Park & Kyungsik Lee, 2016. "Distribution-robust single-period inventory control problem with multiple unreliable suppliers," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 949-966, October.
    5. Liu, Haiyan & Mao, Tiantian, 2022. "Distributionally robust reinsurance with Value-at-Risk and Conditional Value-at-Risk," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 393-417.
    6. Woonghee Tim Huh & Paat Rusmevichientong, 2009. "A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 103-123, February.
    7. Jun Cai & Zhanyi Jiao & Tiantian Mao, 2024. "Worst-case values of target semi-variances with applications to robust portfolio selection," Papers 2410.01732, arXiv.org, revised Oct 2024.
    8. Ch. Pflug, Georg & Timonina-Farkas, Anna & Hochrainer-Stigler, Stefan, 2017. "Incorporating model uncertainty into optimal insurance contract design," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 68-74.
    9. Ioana Popescu, 2007. "Robust Mean-Covariance Solutions for Stochastic Optimization," Operations Research, INFORMS, vol. 55(1), pages 98-112, February.

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