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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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