This paper considers a
continuous-review inventory system with compound Poisson demand,
exponential lead times and lost sales. Under the assumption that
both the supplier's states and the occurrence rate for Poisson
demand are subject to independently and randomly fluctuating
environmental conditions, the stationary distribution of the
retailer's inventory level is derived by utilizing level-crossing
approach. Then the distribution is used to establish the long-run
average cost rate minimization model with a service level
constraint, and the cross-entropy method is applied to determine the
optimal $(r,Q)$ inventory control policy. Numerical results show the effect of environmental fluctuation on
the optimal inventory and the average cost rate.