Interactive fuzzy programming based on a probability maximization model using genetic algorithms for two-level integer programming problems involving random variable coefficients

In this paper, we focus on two-level integer programming problems with random variable coefficients in objective functions and/or constraints. Using chance constrained programming approaches in stochastic programming, the stochastic two-level integer programming problems are transformed into deterministic two-level integer programming problems. After introducing fuzzy goals for objective functions, we consider the application of the interactive fuzzy programming technique to derive a satisfactory solution for decision makers. Since several integer programming problems have to be solved in the interactive fuzzy programming technique, we incorporate a genetic algorithm designed for integer programming problems into it. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.