We consider a single-item, two-echelon spare parts inventory model for repairable parts for capital goods with high downtime costs. The inventory system consists of multiple local warehouses, a central warehouse, and a central repair facility. When a part at a customer fails, if possible his request for a ready-for-use part is fulfilled by his local warehouse. Also, the failed part is sent to the central repair facility for repair. If the local warehouse is out of stock, then, via an emergency shipment, a ready-for-use part is sent from the central warehouse if it has a part in stock. Otherwise, it is sent via a lateral transshipment from another local warehouse, or via an emergency shipment from the external supplier. We assume Poisson demand processes, generally distributed leadtimes for replenishments, repairs, and emergency shipments, and a basestock policy for the inventory control.
Our inventory system is too complex to solve for a steady-state distribution in closed form. We approximate it by a network of Erlang loss queues with hierarchical jump-over blocking. We show that this network has a product-form steady-state distribution. This enables an efficient heuristic for the optimization of basestock levels, resulting in good approximations of the optimal costs.