Supply interruptions in a lost–sales inventory system with random lead time

This paper presents an analytical model for computing the stationary distribution of the on-hand inventory in a continuous-review inventory system with compound Poisson demand, Erlang distributed lead time, and lost sales, where the supplier can assume one of the two ‘available’ and ‘unavailable’ states at any point in time according to a continuous-time Markov chain. Exact analytical expressions are derived for the special case where demand sizes are exponentially distributed, and some cost minimization numerical results are presented.