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Models and formulations for multivariate dominance-constrained stochastic programs

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  • Benjamin Armbruster
  • James Luedtke

Abstract

The use of a stochastic dominance constraint to specify risk preferences in a stochastic program has been recently proposed in the literature. Such a constraint requires the random outcome resulting from one’s decision to stochastically dominate a given random comparator. These ideas have been extended to problems with multiple random outcomes, using the notion of positive linear stochastic dominance. This article proposes a constraint using a different version of multivariate stochastic dominance. This version is natural due to its connection to expected utility maximization theory and relatively tractable. In particular, it is shown that such a constraint can be formulated with linear constraints for the second-order dominance relation and with mixed-integer constraints for the first-order relation. This is in contrast with a constraint on second-order positive linear dominance, for which no efficient algorithms are known. The proposed formulations are tested in the context of two applications: budget allocation in a setting with multiple objectives and finding radiation treatment plans in the presence of organ motion.

Suggested Citation

  • Benjamin Armbruster & James Luedtke, 2015. "Models and formulations for multivariate dominance-constrained stochastic programs," IISE Transactions, Taylor & Francis Journals, vol. 47(1), pages 1-14, January.
    • Handle: RePEc:taf:uiiexx:v:47:y:2015:i:1:p:1-14
    DOI: 10.1080/0740817X.2014.889336
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    Cited by:

    1. Barbora Petrová, 2019. "Multistage portfolio optimization with multivariate dominance constraints," Computational Management Science, Springer, vol. 16(1), pages 17-46, February.
    2. Yu Mei & Zhiping Chen & Jia Liu & Bingbing Ji, 2022. "Multi-stage portfolio selection problem with dynamic stochastic dominance constraints," Journal of Global Optimization, Springer, vol. 83(3), pages 585-613, July.
    3. Darinka Dentcheva & Gabriela Martinez & Eli Wolfhagen, 2016. "Augmented Lagrangian Methods for Solving Optimization Problems with Stochastic-Order Constraints," Operations Research, INFORMS, vol. 64(6), pages 1451-1465, December.
    4. Jamshidi, Movahed & Kebriaei, Hamed & Sheikh-El-Eslami, Mohammad-Kazem, 2018. "An interval-based stochastic dominance approach for decision making in forward contracts of electricity market," Energy, Elsevier, vol. 158(C), pages 383-395.
    5. William B. Haskell & J. George Shanthikumar & Z. Max Shen, 2017. "Aspects of optimization with stochastic dominance," Annals of Operations Research, Springer, vol. 253(1), pages 247-273, June.

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