In this paper, a multiple-identical-machine manufacturing system with random breakdowns, repairs and preventive maintenance activities is considered. The objective of the control problem is to find the production and the preventive maintenance rates of the machines so as to minimize the total cost of inventory/backlog. By combining analytical formalism and simulation based statistical tools such as experimental design and response surface methodology (RSM), an approximation of the optimal control policy is obtained. A numerical example is presented to illustrate the usefulness of the proposed approach. It is found that the complexity of the experimental design problem remains constant (3³ factorial design) when the number of machines increases. Based on the obtained results, the extension of the proposed approach to more complex manufacturing systems is discussed.