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A compromise solution method for the multiobjective minimum risk problem

Fatima Bellahcene () and Philippe Marthon ()
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Fatima Bellahcene: Mouloud Mammeri University
Philippe Marthon: ENSEEIHT Informatique

Operational Research, 2021, vol. 21, issue 3, No 19, 1913-1926

Abstract: 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.

Keywords: Multiobjective programming; Stochastic programming; Nonlinear programming; Minimum-risk criterion (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s12351-019-00493-1

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