This paper studies a two-stage production-service inventory system which is composed of a  production center and a distribution center. A new production strategy, $(rQ+m,KQ)$ production strategy, is proposed for the production center. The distribution center adopts $(s,Q)$ inventory replenishment strategy. Customers arrive according to a Poisson process, and the lead time, the service time and the production time are assumed to be exponentially distributed. Firstly, the continuous-time Markov model is established, and the steady-state condition of the system is obtained by using the theory of quasi-birth-and-death process. Secondly, by solving the steady-state probability distribution of the modified system model, some steady-state probability distribution of the system is obtained. Then formula of computing of the steady-state performance indexes of the system are given. Finally, by using genetic algorithm, the optimal inventory strategies and average cost of the system that aim to minimize the average cost of the system are calculated. The four production inventory strategies of the system are compared by numerical examples. The results show that under certain conditions, the average cost of the system is the lowest when the production center adopts the $(m,KQ)$ strategy.