A compromise solution method for the multiobjective minimum risk problem

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-r...

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Bibliographic Details
Published in:Operational research Vol. 21; no. 3; pp. 1913 - 1926
Main Authors: Bellahcene, Fatima, Marthon, Philippe
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021
Springer Nature B.V
Springer
Subjects:
Algorithms
Business and Management
Chebyshev approximation
Computational Intelligence
Computer Science
Continuity (mathematics)
Decision making
Linear programming
Management Science
Mathematical analysis
Multiple objective analysis
Operations Research
Operations Research/Decision Theory
Original Paper
Random variables
Nonlinear programming
Minimum-risk criterion
Multiobjective programming
Stochastic programming
Nonlnear programming
ISSN:1109-2858, 1866-1505
Online Access:Get full text
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Summary: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.
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ISSN:1109-2858
1866-1505
DOI:10.1007/s12351-019-00493-1