Interactive fuzzy programming for stochastic two-level linear programming problems through probability maximization

This paper considers two-level linear programming problems involving random variable coefficients both in objective functions and constraints. Using the concept of chance constraints, under some appropriate assumptions for distribution functions, the original stochastic two-level linear programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, in order to derive a satisfactory solution considering satisfactory balance between both levels, an interactive fuzzy programming method is proposed. The proposed method has an advantage that candidates for a satisfactory solution can be easily obtained through the combined use of the bisection method and the phase one of the simplex method. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.