This study presents the new dispatching rules of job shop scheduling with auxiliary resource constraint to improve the schedule performance measures related to completion time and due dates. The proposed dispatching rules consider the information of total work remaining and machine utilization to decrease mean flowtime and mean tardiness. The results of computer experiments show that those schedule performances are significantly improved by using the new dispatching rules. The results provide guidance for the researchers and practitioners of auxiliary resource constrained job shop scheduling to decrease mean flowtime and mean tardiness.