The production service inventory system with server's vacation by combining the server's vacation and the production-service inventory is examined in the paper. Demands (customers) arrive according to a Poisson process, and the service time of each customer and the production time of each product are all assumed to be exponentially distributed. When the inventory is depleted, the server goes to a random time of a vacation. It is assumed that the vacation time follows an exponential distribution. Firstly, the steady state condition of the system is obtained by using the quasi-birth-and-death process. Then, the steady-state analysis is established for the case of the system model with negligible service time and the explicit expressions of the steady state probabilities is obtained of this special case. Furthermore, it is proved that the steady-state probability distribution of the system has a structure of product form solution. On this basis, some performance indexes and cost function are calculated. Finally, the optimal $( {s, S})$ inventory strategy of the model is numerically obtained. The numerical analysis is performed to study the influence of some system parameters on performance indexes, the optimal inventory strategy and the optimal cost.