This paper comprises a one warehouse multiple retailer (OWMR) inventory model operating under a continuous-review (R, Q) policy. Customer demand at each retailer is modeled as a compound Poisson process with stochastic lead times while the warehouse has a fixed lead time. Solution Procedure together with convexity analysis of the total cost function has been carried out. An algorithm is given to obtain optimal decision variables. Sensitivity analysis is performed to investigate the effects of key system parameters on the inventory policy and total system cost. The results demonstrate that the proposed policy is robust to variations in warehouse ordering, holding, and shortage costs, whereas the demand size distribution and retailer lead time have the greatest influence on the optimal inventory decisions and total system cost.