A compromise solution method for the multiobjective minimum risk problem

  • Fatima BellahceneEmail author
  • Philippe Marthon
Original paper


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.


Multiobjective programming Stochastic programming Nonlinear programming Minimum-risk criterion 



We thank the anonymous referees for their useful comments that improved the content and presentation of the paper.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LAROMAD Laboratory, Faculty of SciencesMouloud Mammeri UniversityTizi-OuzouAlgeria
  2. 2.ENSEEIHT InformatiqueToulouse Cedex 7France

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