This paper considers a real-world industrial problem in order to minimize the (weighted) number of tardy jobs. This problem occurs in a company where due dates are associated with parts, and penalties incur when the parts are completed after the due dates, whatever the magnitude of the tardiness. Therefore, the objective function can be modelled as minimization of the (weighted) number of tardy jobs. The system studied is a hybrid flow shop with re entrance (or recirculation). In order to deal with large size problems arising in real life, a Genetic Algorithm (GA) is implemented. A coding system, adapted to the considered problem, is designed, and existing crossover and mutation operators are adapted to this coding. To evaluate the effectiveness of the proposed method, it is tested against a commercial software package. The results show that the proposed GA performs well on the scheduling part for a given resource allocation, but it still requires an effective resource allocation procedure.