A single-machine production scheduling problem is addressed for jobs with outsourcing and machine with deteriorating maintenance activity. We consider the learning effect and the deteriorating effect. The actual processing time of a job is a function on its position. In order to improve the productivity of the machine, each machine has at most one deteriorating maintenance activity throughout the scheduling horizon, where the impact of performing deteriorating maintenance activities is reflected in the reduction of job processing time. The duration of the maintenance activity increases linearly with its starting time. The objective is to find the position of the maintenance activity and the most available processing order of the task such that the sum of the maximum, the total completion time, the total weighted completion time and the cost to be paid for outsourcing is minimized. When the scheduling measures are the makespan, total completion time, we provide polynomial time algorithms to solve these problems, respectively. When the scheduling measures is the total weighted completion time, we introduce pseudo-polynomial time algorithms to solve this NP-hard problem.