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Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse

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  • Dentcheva, Darinka
  • Martinez, Gabriela

Abstract

We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. Two new characterizations of the increasing convex order relation are provided. They are based on conditional expectations and on integrated quantile functions: a counterpart of the Lorenz function. We propose two decomposition methods to solve the problems and prove their convergence. Our methods exploit the decomposition structure of the risk-neutral two-stage problems and construct successive approximations of the stochastic ordering constraints. Numerical results confirm the efficiency of the methods.

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  • Dentcheva, Darinka & Martinez, Gabriela, 2012. "Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse," European Journal of Operational Research, Elsevier, vol. 219(1), pages 1-8.
    • Handle: RePEc:eee:ejores:v:219:y:2012:i:1:p:1-8
    DOI: 10.1016/j.ejor.2011.11.044
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    References listed on IDEAS

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    1. Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, University Library of Munich, Germany.
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    Cited by:

    1. Walter Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    2. Wang, S. & Huang, G.H., 2014. "An integrated approach for water resources decision making under interactive and compound uncertainties," Omega, Elsevier, vol. 44(C), pages 32-40.
    3. Walter J. Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    4. 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.
    5. 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.
    6. Escudero Bueno, Laureano F. & Garín Martín, María Araceli & Merino Maestre, María & Pérez Sainz de Rozas, Gloria, 2015. "Some experiments on solving multistage stochastic mixed 0-1 programs with time stochastic dominance constraints," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    7. İ. Esra Büyüktahtakın, 2022. "Stage-t scenario dominance for risk-averse multi-stage stochastic mixed-integer programs," Annals of Operations Research, Springer, vol. 309(1), pages 1-35, February.
    8. Darinka Dentcheva & Eli Wolfhagen, 2016. "Two-Stage Optimization Problems with Multivariate Stochastic Order Constraints," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 1-22, February.
    9. Zhao, Kena & Ng, Tsan Sheng & Tan, Chin Hon & Pang, Chee Khiang, 2021. "An almost robust model for minimizing disruption exposures in supply systems," European Journal of Operational Research, Elsevier, vol. 295(2), pages 547-559.
    10. Alonso-Ayuso, Antonio & Carvallo, Felipe & Escudero, Laureano F. & Guignard, Monique & Pi, Jiaxing & Puranmalka, Raghav & Weintraub, Andrés, 2014. "Medium range optimization of copper extraction planning under uncertainty in future copper prices," European Journal of Operational Research, Elsevier, vol. 233(3), pages 711-726.
    11. Escudero, Laureano F. & Garín, M. Araceli & Monge, Juan F. & Unzueta, Aitziber, 2020. "Some matheuristic algorithms for multistage stochastic optimization models with endogenous uncertainty and risk management," European Journal of Operational Research, Elsevier, vol. 285(3), pages 988-1001.
    12. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.
    13. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
    14. Baptista, Susana & Barbosa-Póvoa, Ana Paula & Escudero, Laureano F. & Gomes, Maria Isabel & Pizarro, Celeste, 2019. "On risk management of a two-stage stochastic mixed 0–1 model for the closed-loop supply chain design problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 91-107.

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