IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p2026-d444879.html
   My bibliography  Save this article

A Risk-Aversion Approach for the Multiobjective Stochastic Programming Problem

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/2026/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/11/2026/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Gutjahr, Walter J. & Nolz, Pamela C., 2016. "Multicriteria optimization in humanitarian aid," European Journal of Operational Research, Elsevier, vol. 252(2), pages 351-366.
    5. 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.
    6. Xin Chen & Melvyn Sim & Peng Sun, 2007. "A Robust Optimization Perspective on Stochastic Programming," Operations Research, INFORMS, vol. 55(6), pages 1058-1071, December.
    7. 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.
    8. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    9. 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.
    10. 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.
    11. 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.
    12. Leclercq, J. -P., 1982. "Stochastic programming: An interactive multicriteria approach," European Journal of Operational Research, Elsevier, vol. 10(1), pages 33-41, May.
    13. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
    2. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    3. Selçuklu, Saltuk Buğra & Coit, David W. & Felder, Frank A., 2020. "Pareto uncertainty index for evaluating and comparing solutions for stochastic multiple objective problems," European Journal of Operational Research, Elsevier, vol. 284(2), pages 644-659.
    4. Benati, S. & Conde, E., 2022. "A relative robust approach on expected returns with bounded CVaR for portfolio selection," European Journal of Operational Research, Elsevier, vol. 296(1), pages 332-352.
    5. Hatem Masri, 2017. "A multiple stochastic goal programming approach for the agent portfolio selection problem," Annals of Operations Research, Springer, vol. 251(1), pages 179-192, April.
    6. Junna Bi & Jun Cai & Yan Zeng, 2021. "Equilibrium reinsurance-investment strategies with partial information and common shock dependence," Annals of Operations Research, Springer, vol. 307(1), pages 1-24, December.
    7. 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.
    8. 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.
    9. Mingfa Zheng & Yuan Yi & Zutong Wang & Tianjun Liao, 2017. "Relations among efficient solutions in uncertain multiobjective programming," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 329-357, September.
    10. Belaid AOUNI & Cinzia COLAPINTO & Davide LA TORRE, 2008. "Solving stochastic multi-objective programming through the GP model," Departmental Working Papers 2008-18, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    11. Fatima Bellahcene, 2019. "Decision maker's preferences modeling for multiple objective stochastic linear programming problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(3), pages 5-16.
    12. Alireza Azimian & Belaid Aouni, 2025. "Multi-item order quantity optimization through stochastic goal programing," Annals of Operations Research, Springer, vol. 346(2), pages 751-779, March.
    13. Mercier, Quentin & Poirion, Fabrice & Désidéri, Jean-Antoine, 2018. "A stochastic multiple gradient descent algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 808-817.
    14. Meryem Masmoudi & Fouad Ben Abdelaziz, 2018. "Portfolio selection problem: a review of deterministic and stochastic multiple objective programming models," Annals of Operations Research, Springer, vol. 267(1), pages 335-352, August.
    15. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    16. Baker, Erin & Bosetti, Valentina & Salo, Ahti, 2016. "Finding Common Ground when Experts Disagree: Belief Dominance over Portfolios of Alternatives," MITP: Mitigation, Innovation and Transformation Pathways 243147, Fondazione Eni Enrico Mattei (FEEM).
    17. Jang Ho Kim & Yongjae Lee & Woo Chang Kim & Frank J. Fabozzi, 2022. "Goal-based investing based on multi-stage robust portfolio optimization," Annals of Operations Research, Springer, vol. 313(2), pages 1141-1158, June.
    18. Murat Köksalan & Ceren Tuncer Şakar, 2016. "An interactive approach to stochastic programming-based portfolio optimization," Annals of Operations Research, Springer, vol. 245(1), pages 47-66, October.
    19. Li Zhu & Yeming Gong & Yishui Xu & Jun Gu, 2019. "Emergency Relief Routing Models for Injured Victims Considering Equity and Priority," Post-Print hal-02879681, HAL.
    20. Amy Givler Chapman & John E. Mitchell, 2018. "A fair division approach to humanitarian logistics inspired by conditional value-at-risk," Annals of Operations Research, Springer, vol. 262(1), pages 133-151, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2026-:d:444879. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.