An inventory model with non-resuming randomly interruptible lead time

We assume that an unreliable supplier in a single-item stochastic inventory system alternates randomly between two possible states (i.e., available and unavailable), following a two-state continuous-time homogeneous Markov chain. For a compound Poisson stream of demands and Erlang lead times, our model considers the scenario where the processing of the outstanding order (if any) is interrupted at every supplier's transition epoch from the available to the unavailable state, and is restarted from the outset upon the supplier's regaining its available state. We derive the stationary distribution of the on-hand inventory under a continuous-review policy and provide some numerical results.