A new approximate evaluation method for two-echelon inventory systems with emergency shipments

We consider the inventory control of repairable spare parts in a network consisting of a central warehouse, a central repair facility, and multiple local warehouses. Demands for spare parts occur at the local warehouses. If a local warehouse is out of stock, then an arriving demand is satisfied by an emergency shipment from the central warehouse or the central repair facility. Such emergency shipments are common practice for networks that support technical systems with high downtime costs. We develop a new evaluation method that provides accurate approximations for the key performance measures like fractions of demands supplied by the local warehouses or emergency shipments. The method can be easily incorporated in existing (greedy) heuristic optimization methods. Our method outperforms the approximate evaluation method of Muckstadt and Thomas (Manag. Sci. 26:483–494, 1980 ), as we show via a numerical analysis. Finally, we show that the performance of the system is virtually insensitive to the leadtime distribution of repairs at the central repair facility.