Dominance and Efficiency in Multiobjective Stochastic Linear Programming

Several concepts of distributional efficiency are proposed for the Multiobjective Stochastic Linear Programming (MSLP) problem, in contexts where the probability distribution of random parameters is known and the decision maker (DM) has an unknown multi-attribute utility function belonging to a given glass U. We present a general efficient set, the U-admissible solutions, and two subsets, the U-unanimous and U-advocated solutions, the latter being particularly relevant to the case of a single DM. We show how advocated solutions can be generated and/or tested when U is the class of non-decreasing additive concave functions.