Stackelberg solutions to stochastic two-level linear programming problems

Abstract

This paper considers a two-level linear programming problem involving random variable coefficients to cope with hierarchical decision making problems under uncertainty. Two decision making models are provided to optimize the mean of the objective function value or to minimize the variance. It is shown that the original problem is transformed into a deterministic problem. The computational methods are constructed to obtain the Stackelberg solution to the two-level programming problems. An illustrative numerical example is provided to understand the geometrical properties of the solutions