On the Probability Distribution for Inventory Position in Two Echelon Continuous Review Systems.

摘要

This paper derives the stationary probability distribution for the inventory position at each location in a two echelon inventory system. The inventory system consists of a depot and a set of bases. All system demands are assumed to originate at a base in the second echelon. Bases are resupplied as necessary by the depot, the first echelon; the depot is resupplied by an external supplier. Each location is assumed to follow a continuous review (S,s) policy. All excess demand is assumed backordered. Furthermore, the process generating demand at each base is assumed to be a Poisson process. A simple queuing analysis is used to obtain the probability distribution for inventory position. In the case where all bases have identical arrival rates and follow the same (S,s) policy, it is shown that the random variables describing the inventory position at each location are uniformly distributed and are independent.