TY - BOOK
T1 - A two-echelon spare parts network with lateral and emergency shipments
T2 - A product-form approximation
AU - Boucherie, Richard J.
AU - van Houtum, Geert-Jan
AU - Timmer, Judith B.
AU - van Ommeren, Jan C.W.
N1 - eemcs-eprint-26712
PY - 2016/1/26
Y1 - 2016/1/26
N2 - We consider a single-item, two-echelon spare parts inventory model for repairable parts for capital goods with high down time costs. The inventory system consists of a central warehouse and multiple local warehouses, from where customers are served, and a central repair facility at an external supplier. When a part fails at a customer, his request for a ready-for-use part is immediately fullled by his local warehouse if it has a part on stock. At the same time, 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 on stock. Otherwise, it is sent via a lateral transshipment from another local warehouse or the external supplier. We assume Poisson demand processes, generally distributed leadtimes for replenishments, repairs, and emergency shipments, and a base-stock policy for the inventory control.
Because 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 so-called hierarchical jump-over blocking. We show that this network has a steady-state distribution in product-form. Further, this steady-state distribution and several relevant performance measures only depend on the distributions for the repair and replenishment lead times via their means (i.e., they are insensitive for the underlying probability distributions). The steady-state distribution in product-form enables an ecient heuristic for the optimization of base-stock levels, resulting in good approximations of the optimal costs.
AB - We consider a single-item, two-echelon spare parts inventory model for repairable parts for capital goods with high down time costs. The inventory system consists of a central warehouse and multiple local warehouses, from where customers are served, and a central repair facility at an external supplier. When a part fails at a customer, his request for a ready-for-use part is immediately fullled by his local warehouse if it has a part on stock. At the same time, 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 on stock. Otherwise, it is sent via a lateral transshipment from another local warehouse or the external supplier. We assume Poisson demand processes, generally distributed leadtimes for replenishments, repairs, and emergency shipments, and a base-stock policy for the inventory control.
Because 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 so-called hierarchical jump-over blocking. We show that this network has a steady-state distribution in product-form. Further, this steady-state distribution and several relevant performance measures only depend on the distributions for the repair and replenishment lead times via their means (i.e., they are insensitive for the underlying probability distributions). The steady-state distribution in product-form enables an ecient heuristic for the optimization of base-stock levels, resulting in good approximations of the optimal costs.
KW - Emergency shipments
KW - Spare parts inventory control
KW - Product form solution
KW - Multi-echelon
M3 - Report
T3 - Memorandum
BT - A two-echelon spare parts network with lateral and emergency shipments
PB - University of Twente
CY - Enschede
ER -