A two-echelon spare parts network with lateral and emergency shipments: A product-form approximation

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Abstract

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.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages26
Publication statusPublished - 26 Jan 2016

Publication series

NameMemorandum
PublisherUniversity of Twente, Department of Applied Mathematics
No.2053
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • IR-99176
  • METIS-315536
  • Emergency shipments
  • EWI-26712
  • Spare parts inventory control
  • Product form solution
  • Multi-echelon

Cite this

Boucherie, R. J., van Houtum, G-J., Timmer, J. B., & van Ommeren, J. C. W. (2016). A two-echelon spare parts network with lateral and emergency shipments: A product-form approximation. (Memorandum; No. 2053). Enschede: University of Twente, Department of Applied Mathematics.
Boucherie, Richardus J. ; van Houtum, Geert-Jan ; Timmer, Judith B. ; van Ommeren, Jan C.W. / A two-echelon spare parts network with lateral and emergency shipments: A product-form approximation. Enschede : University of Twente, Department of Applied Mathematics, 2016. 26 p. (Memorandum; 2053).
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Boucherie, RJ, van Houtum, G-J, Timmer, JB & van Ommeren, JCW 2016, A two-echelon spare parts network with lateral and emergency shipments: A product-form approximation. Memorandum, no. 2053, University of Twente, Department of Applied Mathematics, Enschede.

A two-echelon spare parts network with lateral and emergency shipments: A product-form approximation. / Boucherie, Richardus J.; van Houtum, Geert-Jan; Timmer, Judith B.; van Ommeren, Jan C.W.

Enschede : University of Twente, Department of Applied Mathematics, 2016. 26 p. (Memorandum; No. 2053).

Research output: Book/ReportReportOther research output

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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.

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KW - EWI-26712

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: A product-form approximation

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Boucherie RJ, van Houtum G-J, Timmer JB, van Ommeren JCW. A two-echelon spare parts network with lateral and emergency shipments: A product-form approximation. Enschede: University of Twente, Department of Applied Mathematics, 2016. 26 p. (Memorandum; 2053).