Stackelberg solutions to multiobjective two-level linear programming problems with random variable coefficients

In this paper, to cope with multiobjective hierarchical decision making problems under uncertainty, we formulate a multiobjective two-level linear programming problem with random variable coefficients and reduce the problem into a deterministic problem by using the expectation and the variance models. Moreover, because the lower level decision maker has multiple objective functions, we must take into account multiple or an infinite number of rational responses of the lower level decision maker. Incorporating anticipation of the upper level decision maker to manage a multiplicity of the rational responses, we present computational methods for obtaining the Stackelberg solutions to the multiobjective two-level linear programming problem with random variable coefficients. An illustrative numerical example is provided to understand the geometrical properties of the solutions.