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A Risk-Aversion Approach for the Multiobjective Stochastic Programming Problem

Author

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  • Javier León

    (HUM-LOG Research Group, Instituto de Matemática Interdisciplinar (IMI), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040 Madrid, Spain)

  • Justo Puerto

    (Mathematical Research Institute (IMUS), University of Seville, 41004 Sevilla, Spain)

  • Begoña Vitoriano

    (HUM-LOG Research Group, Instituto de Matemática Interdisciplinar (IMI), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040 Madrid, Spain)

Abstract

Multiobjective stochastic programming is a field that is well suited to tackling problems that arise in many fields: energy, financial, emergencies, among others; given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in this work, which is especially designed for risk-averse solutions. The proposed concept combines the notions of conditional value-at-risk and ordered weighted averaging operator to find solutions protected against risks due to uncertainty and under-achievement of criteria. A small example is presented in order to illustrate the concept in small discrete feasible spaces. A linear programming model is also introduced to obtain the solution in continuous spaces. Finally, computational experiments are performed by applying the obtained linear programming model to the multiobjective stochastic knapsack problem, gaining insight into the behaviour of the new solution concept.

Suggested Citation

  • Javier León & Justo Puerto & Begoña Vitoriano, 2020. "A Risk-Aversion Approach for the Multiobjective Stochastic Programming Problem," Mathematics, MDPI, vol. 8(11), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2026-:d:444879
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    1. Francisco Salas-Molina & Juan A. Rodriguez-Aguilar & David Pla-Santamaria, 2020. "A stochastic goal programming model to derive stable cash management policies," Journal of Global Optimization, Springer, vol. 76(2), pages 333-346, February.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. Ben Abdelaziz, Fouad & Masri, Hatem, 2010. "A compromise solution for the multiobjective stochastic linear programming under partial uncertainty," European Journal of Operational Research, Elsevier, vol. 202(1), pages 55-59, April.
    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    5. Ferrer, José M. & Martín-Campo, F. Javier & Ortuño, M. Teresa & Pedraza-Martínez, Alfonso J. & Tirado, Gregorio & Vitoriano, Begoña, 2018. "Multi-criteria optimization for last mile distribution of disaster relief aid: Test cases and applications," European Journal of Operational Research, Elsevier, vol. 269(2), pages 501-515.
    6. Gutjahr, Walter J. & Nolz, Pamela C., 2016. "Multicriteria optimization in humanitarian aid," European Journal of Operational Research, Elsevier, vol. 252(2), pages 351-366.
    7. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    8. Xin Chen & Melvyn Sim & Peng Sun, 2007. "A Robust Optimization Perspective on Stochastic Programming," Operations Research, INFORMS, vol. 55(6), pages 1058-1071, December.
    9. Vijaya Dixit & Manoj Kumar Tiwari, 2020. "Project portfolio selection and scheduling optimization based on risk measure: a conditional value at risk approach," Annals of Operations Research, Springer, vol. 285(1), pages 9-33, February.
    10. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    11. Angilella, Silvia & Mazzù, Sebastiano, 2015. "The financing of innovative SMEs: A multicriteria credit rating model," European Journal of Operational Research, Elsevier, vol. 244(2), pages 540-554.
    12. Caballero, Rafael & Cerda, Emilio & del Mar Munoz, Maria & Rey, Lourdes, 2004. "Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 158(3), pages 633-648, November.
    13. Aouni, Belaid & Ben Abdelaziz, Foued & Martel, Jean-Marc, 2005. "Decision-maker's preferences modeling in the stochastic goal programming," European Journal of Operational Research, Elsevier, vol. 162(3), pages 610-618, May.
    14. Leclercq, J. -P., 1982. "Stochastic programming: An interactive multicriteria approach," European Journal of Operational Research, Elsevier, vol. 10(1), pages 33-41, May.
    15. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    16. Álvarez-Miranda, Eduardo & Garcia-Gonzalo, Jordi & Ulloa-Fierro, Felipe & Weintraub, Andrés & Barreiro, Susana, 2018. "A multicriteria optimization model for sustainable forest management under climate change uncertainty: An application in Portugal," European Journal of Operational Research, Elsevier, vol. 269(1), pages 79-98.
    17. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms," Computational Optimization and Applications, Springer, vol. 58(3), pages 563-595, July.
    18. Abdelaziz, Fouad Ben & Aouni, Belaid & Fayedh, Rimeh El, 2007. "Multi-objective stochastic programming for portfolio selection," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1811-1823, March.
    19. Xiao Liu & Simge Küçükyavuz & Nilay Noyan, 2017. "Robust multicriteria risk-averse stochastic programming models," Annals of Operations Research, Springer, vol. 259(1), pages 259-294, December.
    20. Teghem, J. & Dufrane, D. & Thauvoye, M. & Kunsch, P., 1986. "Strange: An interactive method for multi-objective linear programming under uncertainty," European Journal of Operational Research, Elsevier, vol. 26(1), pages 65-82, July.
    21. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    22. Klamroth, Kathrin & Köbis, Elisabeth & Schöbel, Anita & Tammer, Christiane, 2017. "A unified approach to uncertain optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 403-420.
    23. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
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