We study the scheduling problem of simple linear deteriorating jobs with rate-modifying activities on identical parallel machines. Our goal is to minimize the makespan. We show that our problem with fixed number of RMAs and on a single machine can be reduced to the k-ways partitioning problem, which is known to be NP-hard by Graham (1966). Therefore we generalize the optimality conditions for a single machine to multiple identical machines and propose three heuristics. We also identify a lower bound of the optimal makespan by job preemption and workload balance. Finally, we implement numerical studies to verify the performance of our heuristics. The results show that our heuristics are steady. The mean relative errors of our heuristic are not impacted by the number of jobs and the number of machines.