Stationary Properties of a Two-Echelon Inventory Model for Low Demand Items

This paper considers a two-echelon inventory model for consumable or repairable parts in which the first-echelon facilities use one-for-one replenishment policies and the second-echelon facility uses a continuous-review (s, S) policy. Repair may be accomplished at all facilities. Repair and transportation times are assumed to be deterministic, and the failure processes that generate demands are assumed to be Poisson. The paper derives exact expressions for the stationary distributions of stock on hand, stock in repair, and backlogged demand at each facility, and indicates how these expressions may be utilized for optimization purposes.