Satisfactory solution concepts and their relations for Stochastic Multiobjective Programming problems

This work deals with the concept of satisfactory solution for Stochastic Multiobjective Programming (SMP) problems. Based on previous literature, we will introduce different concepts of satisfactory solutions for SMP problems, define a new concept of solution (where the decision maker (DM) sets his/her preferences in terms of two aspiration levels for the stochastic objective and two probabilities to reach those levels), and establish some relationship between these concepts. The results will aim at featuring these concepts and determine the differences between them. Moreover, the paper proposes a new step by step procedure to exchange information between the analyst and DM prior to solving the problem. Thus, the DM will be able to choose the transformation criterion for each stochastic objective and the aspiration level.