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

We consider the 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 delivery 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, and it is important to take them into account when the inventory is optimized. Our main contribution consists of the development of a new approximate evaluation method. This method gives accurate approximations for the key performance measures, as we show via numerical analysis. The method is also fast and thus can easily be incorporated in existing (greedy) heuristic optimization methods. Our method outperforms the approximate evaluation method of Muckstadt and Thomas (1980), as we also show via the numerical analysis. Finally, we show that the performance of the system is rather insensitive to the leadtime distribution of the repairs at the central repair facility, which implies that our method works well for generally distributed repair leadtimes.