This study is concerned with the scheduling problems in flexible manufacturing systems(FMSs). The scheduling problem in FMSs is a complex one when the number of machines and jobs are increased. Thus, a heuristic method is recommended in order to gain near-optimal solutions in a practically acceptable time. The purpose of this study is to develope a machine and AGV dispatching algorithm. The proposed dispatching algorithm is a on-line scheduling algorithm considering the due date of parts and the status of the system in the scheduling process. In the new machine and AGV dispatching algorithm, a job priority is determined by LPT/LQS rules considering job tardiness. The proposed heuristic dispatching algorithm is evaluated by comparison with the existing dispatching rules such as LPT/LQS, SPT/LQS, EDD/LQS and MOD/LQS. The new dispatching algorithm is predominant to existing dispatching rules in 100 cases out of 100 for the mean tardiness and 89 cases out of 100 for the number of tardy jobs.