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On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs

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  • Escudero, Laureano F.
  • Garín, María Araceli
  • Merino, María
  • Pérez, Gloria

Abstract

We propose in this work a new multistage risk averse strategy based on Time Stochastic Dominance (TSD) along a given horizon. It can be considered as a mixture of the two risk averse measures based on first- and second-order stochastic dominance constraints induced by mixed integer-linear recourse, respectively. Given the dimensions of medium-sized problems augmented by the new variables and constraints required by this new risk measure, it is unrealistic to solve the problem up to optimality by plain use of MIP solvers in a reasonable computing time, at least. Instead of it, decomposition algorithms of some type should be used. We present an extension of our Branch-and-Fix Coordination algorithm, so named BFC-TSD, where a special treatment is given to cross scenario group constraints that link variables from different scenario groups. A broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies. The performance of the new version of the BFC algorithm versus the plain use of a state-of-the-art MIP solver is also reported.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:249:y:2016:i:1:p:164-176
    DOI: 10.1016/j.ejor.2015.03.050
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Maram Alwohaibi & Diana Roman, 2018. "ALM models based on second order stochastic dominance," Computational Management Science, Springer, vol. 15(2), pages 187-211, June.
    2. Laureano F. Escudero & María Araceli Garín & Celeste Pizarro & Aitziber Unzueta, 2018. "On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems," Computational Optimization and Applications, Springer, vol. 70(3), pages 865-888, July.
    3. Miloš Kopa & Vittorio Moriggia & Sebastiano Vitali, 2018. "Individual optimal pension allocation under stochastic dominance constraints," Annals of Operations Research, Springer, vol. 260(1), pages 255-291, January.
    4. Laureano F. Escudero & Juan F. Monge, 2018. "On capacity expansion planning under strategic and operational uncertainties based on stochastic dominance risk averse management," Computational Management Science, Springer, vol. 15(3), pages 479-500, October.
    5. 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.
    6. Eguía Ribero, María Isabel & Garín Martín, María Araceli & Unzueta Inchaurbe, Aitziber, 2018. "Generating cluster submodels from two-stage stochastic mixed integer optimization models," BILTOKI Biltoki;DT-2018-01, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    7. 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.
    8. 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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