A Continous-Review (s, S) Inventory System with Arbitrary Interarrival Distribution between Unit Demand

For a continuous-review inventory system where demand is defined by a discrete-valued process with units withdrawn from stock one at a time and where the interarrival times between successive demands are independently and identically distributed, the transient and steady-state distribution for the position inventory are derived when operating under an (s, S) policy. This paper shows that the limiting distribution of the position inventory is uniform over the set (s + 1, …, S) and is independent of the distribution of the interarrival times. When instantaneous delivery of orders is allowed, the problem is equivalent to an independent stand-by system consisting of Q = S − s operating elements subject to failure, where, following the failure of the last operating element, all Q failed elements are immediately repaired or replaced by Q new identical elements.