Hierarchical Multiobjective Stochastic Linear Programming Problems Considering Both Probability Maximization and Fractile Optimization

In this paper, we focus on hierarchical multiobjective stochastic linear programming problems (HMOP) where multiple decision makers in a hierarchical organization have their own multiple objective linear functions together with common linear constraints. In order to deal with HMOP, a probability maximization model and a fractile optimization model are applied. By considering the conflict between permissible objective levels and permissible probability levels in such two models, it is assumed that each of the decision makers has fuzzy goals for permissible objective levels and permissible probability levels, and such fuzzy goals can be quantified by eliciting the membership functions. Through the fuzzy decision, such membership functions are integrated. In the integrated membership space, Pareto optimality concept is introduced. The interactive algorithm to obtain a satisfactory solution from among a Pareto optimal solution set is proposed on the basis of linear programming technique, in which the hierarchical decision structure is reflected by the decision power and the proper balance between permissible objective levels and the corresponding probability function is attained.