A replenishment model for the supply-uncertainty problem

We consider a continuous-review inventory system with compound Poisson demand, hyperexponentially distributed lead time, and lost sales where the supply process may be randomly interrupted depending on the availability of a supplier. It is assumed that the supplier's availability can be modeled as an alternating renewal process in which the on and off periods are independent random variables following general and hyperexponential distributions, respectively. We present an exact formulation of the long-run average cost rate function based on deriving the stationary distribution of the on-hand inventory, and provide some numerical results.