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A compromise solution method for the multiobjective minimum risk problem

Author

Listed:
  • Fatima Bellahcene

    (Mouloud Mammeri University)

  • Philippe Marthon

    (ENSEEIHT Informatique)

Abstract

We develop an approach which enables the decision maker to search for a compromise solution to a multiobjective stochastic linear programming (MOSLP) problem where the objective functions depend on parameters which are continuous random variables with normal multivariate distributions. The minimum-risk criterion is used to transform the MOSLP problem into its corresponding deterministic equivalent which in turn is reduced to a Chebyshev problem. An algorithm based on the combined use of the bisection method and the probabilities of achieving goals is developed to obtain the optimal or epsilon optimal solution of this specific problem. An illustrated example is included in this paper to clarify the developed theory.

Suggested Citation

  • Fatima Bellahcene & Philippe Marthon, 2021. "A compromise solution method for the multiobjective minimum risk problem," Operational Research, Springer, vol. 21(3), pages 1913-1926, September.
    • Handle: RePEc:spr:operea:v:21:y:2021:i:3:d:10.1007_s12351-019-00493-1
    DOI: 10.1007/s12351-019-00493-1
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    References listed on IDEAS

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