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

Abstract

For a continuous-review inventory system where demand is defined by a discrete-valued process with units withdrawn from stock one at a time and where the interarrival times between successive demands are independently and identically distributed, the transient and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.