We calculate optimal safety stock in a periodic review (T,S) Assemble-to-Order system having multiple components and multiple finished goods. Customer orders for finished goods arrive according to independent Poisson processes, and cannot be neither backlogged nor lost. In case of potential component stock-out, the studied system uses rush deliveries from suppliers. For this setting, approximate expressions of the optimal safety stock that minimize the sum of inventory holding and rush ordering costs are developed. Exact optimal safety stocks are calculated using discrete event simulation, and compared numerically to the approximate expressions. The model is applied to a first-tier automotive supplier and yields to a significant reduction in terms of inventory holding and rush ordering costs. A sensitivity analysis on relevant system parameters such as components demand, assembly coefficients and unit rush ordering cost is conducted.