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

Abstract

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