Closed-loop production systems are used in many factories, e.g., machining, adhesive manufacturing, plastic forming and assembly factories. In these systems, many pallets, jigs or molds circulate and are used repeatedly, and the number affects the system production rate. In this paper, we analyze the effect of a number of pallets and system parameters on the production rate, and present the existence of the optimum number of pallets which yields the maximum production rate. Next, we propose an approximation method for estimating the optimum number of pallets, for which the estimation error is very small and the estimated number gives almost the same production rate as that yielded by the optimum number of pallets.