On the (S-1,S) model for renewal demand processes: Poisson's poison

In the standard (S - 1,S) stock model, demand follows a Poisson process. It has appeared to many stock analysts that this model causes an abundance of stock in reality. In case demand is caused by failure or is derived from another process, demand typically does not follow a Poisson process. In this paper, we discuss the (S - 1,S) stock model where demand follows a renewal process and the lead time is deterministic. Morover, we will extend this to compound renewal demand and multi-echelon inventory systems. Our goal is to show the severe influence of taking the Poisson process for granted.