Capacitated Two-Echelon Inventory Models for Repairable Item Systems

In this paper, we consider two-echelon maintenance systems with repair facilities both at a number of local service centers (called bases) and at a central location. Each repair facility may be considered to be a job shop and is modeled as a (limited capacity) open queuing network, while any transport from the central facility to the bases (and vice versa) is modeled as an ample server. At all bases as well as at the central repair facility, ready-for-use spare parts are kept in stock. Once an item in the field fails, it is returned to one of the bases and replaced by a ready-for-use item from the spare parts stock, if available. The returned failed item is either repaired at the base or shipped to and repaired at the central facility. In the case of local repair, the item is added to the local spare parts stock as a ready-for-use item after repair. If a repair at the central facility is needed, the base orders an item from the central spare parts stock to replenish its local stock, while the failed item is added to the central stock after repair. Orders are satisfied on a first-come-first-serve basis while any requirement that cannot be satisfied immediately either at the bases or at the central facility is backlogged.We assume that failed items are returned to the bases according to a Poisson process, and that each repair shop (at the bases as well as at the central facility) can be modeled as a Jackson network. Under these conditions, we propose a special near-product-form solution that provides an excellent approximation for the steady-state distribution of a slightly aggregated system, that permits us to calculate all relevant performance measures (such as fill rates and stockout probabilities) at the bases as well as at the central facility, as a function of target inventory levels at each location. Errors of these performance measures are generally less than one percent, when compared with simulation results. Finally, we show how these approximations can be used to determine optimal inventory levels at both the central and local facilities.