In many production systems a time period is scheduled for machine maintenance, during which the machine is idle. After the maintenance activity is completed the production rate may be affected. The decisions under consideration are (i) when to schedule this rate-modifying activity, and (ii) how to sequence the jobs. We study three single machine scheduling problems with a rate-modifying activity: minimum makespan with precedence constraints, minimum makespan with a learning effect and minimum number of tardy jobs. We introduce a polynomial time solution for each of the three problems.