This paper deals with an efficient scheduling method for job shop scheduling with alternative machines with the objective to minimize mean tardiness. The method uses a genetic algorithm incorporating heuristic rules for job sequencing and machine selection. Effective heuristic rules for this method have been proposed so far. However due-date related information has not been included in the heuristic rule for machine selection even though the objective is to minimize mean tardiness. This paper examines the effectiveness of due-date related information for machine selection in this method through numerical experiments.