Fuzzy bi-level multi-objective programming for supply chain

For a two-echelon supply chain consisted of multi-plants and multi-warehouses, with multi-productions, this paper develops a bi-level programming model aims to minimize the total cost. The problem includes two sub-problems: the higher-level problem and the lower-level problem respectively decided by plants and warehouses. Built in dynamic environments the model has fuzzy parameters in constraints. The way to convert fuzzy constraints to their crisp equivalents is discussed. To simplify the solution, membership function of fuzzy theory is applied to transform the bi-level programming to single-level problem. Then Genetic Algorithm is proposed for generating Pareto optimal solutions. Finally, the model and algorithm are illustrated with a numerical example.