When supplier's availability affects the replenishment lead time – An extension of the supply-interruption problem

This paper presents an exact treatment of a continuous-review inventory system with compound Poisson demand, Erlang-distributed lead times and random supply interruptions. In contrast with the existing models in the literature, we take into account the supplier's availability in characterizing the lead time of a replenishment order. Assuming that the supplier's availability can be described by a continuous-time homogeneous Markov chain with two states (on and off) and that stockouts are lost, we derive the stationary distribution of the inventory level (stock-on-hand) under an (s, Q)-type control policy. This probability distribution is then used to formulate an exact expression for the long-run average cost per unit time of operating the inventory system. Some numerical results are also provided.