Decision makers preferences modeling for multiple objective stochastic linear programming problems

A method has been suggested which solves a multiobjective stochastic linear programming problem with normal multivariate distributions in accordance with the minimum-risk criterion. The approach to the problem uses the concept of satisfaction functions for the explicit integration of the preferences of the decision-maker for different achievement level of each objective. Thereafter, a nonlinear deterministic equivalent problem is formulated and solved by the bisection method. Numerical examples with two and three objectives are given for illustration. The solutions obtained by this method are compared with the solutions given by other approaches.