We consider a perishable inventory system that operates under stochastic demand, constant lifetime and a constant lead time. The system employs a continuous review ðr; Q Þ inventory control policy where unfilled demands are lost. We investigate the properties of the cost function and present an approximation procedure to find the parameters r and Q that minimize the total cost. We then conduct a numerical analysis to examine the performance of the proposed model and study the sensitivity to changes in the system parameters. We demonstrate the suitability of the proposed approximations compared to optimal ðr; Q Þ parameters obtained by simulation and show that our proposal outperforms another approximation procedure from the literature, in particular for increasing ordering cost and demand variability. The proposed model contributes to the literature by providing a simple and efficient algorithm to compute the best (r, Q) parameters that minimize the total cost. Besides, it can be used in automated store ordering systems. &