Abstract: A continuous-review inventory system with compound Poisson demand, exponential lead time and lost sale are considered in this paper. Assuming that the durations of the available and unavailable periods at both the supplier and the retailer follow independently exponential distributions, the stationary distribution of the retailer's inventory level is derived by utilizing level crossing method. This distribution is then used to formulate the long-run average cost rate model and the cross-entropy approach is adopted to determine the optimal inventory control policy. Numerical results are provided to illustrate the effects of disruption intensity and system parameters on the optimal inventory policy and the average cost rate.