In this paper we study the allocation of production services (e.g., maintenance) to machining centers in a job shop when there is a limited amount of resources for such services. Different classes of jobs go through the shop. A job class is characterized by its route, its processing requirements, and its priority. The problem we address is how to optimally allocate production services (the resources) to machining centers so as to minimize the total Work-In-Process in the entire system. In order to analyze this problem we model the job shop as an open queueing network. Assuming certain relationships between performances of machining centers (i.e., speeds) and the amounts of resources allocated, we present methods for allocating the resources to the individual machining centers optimally.