The single-machine scheduling problem with multi-rate-modifying activities(multi-RMAs) and due date assignment is considered under the case of processing time deteriorating. The object is to minimize earliness and tardiness penalties. In the processing of jobs, several rate-modifying activities are allowed to insert before processing a job in order to decrease deterioration phenomenon and recover the capability of a single machine. The aim is to minimize the total earliness and tardiness penalties through finding jointly the optimal scheduling sequence, the optimal common slack time and the optimal inserting positions of multi-RMAs. According to the characteristics of the problem, several propositions and theorem are proposed, and the optimal slack time is given by proof. Finally, it is proved that the problem is solvable in polynominal time.