A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment

The problem that we address is to determine the inventory stockage levels in a multi-echelon inventory system for a repairable item. In its simplest form the multi-echelon system consists of a set of operating sites supported by a centrally-located repair depot. Each operating site requires a set of working items and maintains an inventory of spare items. The repair depot also holds an inventory of spare items. Item failures are infrequent and are replaced on a one-for-one basis. In this paper we present an exact model for finding the steady-state distribution of the net inventory level at each site. This model assumes that the failures are generated by a compound Poisson process and that the shipment time from the repair depot to each site is deterministic. No assumptions are made with regard to the repair cycle at the depot. We contrast this model with existing models for these systems. Based on the exact model we present an approximation for the steady-state distribution for the case with ample servers at the repair depot. We show that this approximation is very accurate on a set of test problems.