In this paper, we deal with a single machine scheduling problems integrating with step deterioration effect and a rate-modifying activity (RMA). The scheduling problem assumes that the machine may have a single RMA and each job has the processing time of a job with deterioration is a step function of the gap between recent RMA and starting time of the job and a deteriorating date that is individual to all jobs. Based on the two scheduling phenomena, we simultaneously determine the schedule of step deteriorating jobs and the position of the RMA to minimize the makespan. To solve the problem, we propose a hybrid typed genetic algorithm compared with conventional GAs.