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Stationary Properties of a Two-Echelon Inventory Model for Low Demand Items

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  • R. M. Simon

    (National Institutes of Health, Bethesda, Maryland)

Abstract

This paper considers a two-echelon inventory model for consumable or repairable parts in which the first-echelon facilities use one-for-one replenishment policies and the second-echelon facility uses a continuous-review ( s , S ) policy. Repair may be accomplished at all facilities. Repair and transportation times are assumed to be deterministic, and the failure processes that generate demands are assumed to be Poisson. The paper derives exact expressions for the stationary distributions of stock on hand, stock in repair, and backlogged demand at each facility, and indicates how these expressions may be utilized for optimization purposes.

Suggested Citation

  • R. M. Simon, 1971. "Stationary Properties of a Two-Echelon Inventory Model for Low Demand Items," Operations Research, INFORMS, vol. 19(3), pages 761-773, June.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:3:p:761-773
    DOI: 10.1287/opre.19.3.761
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    Cited by:

    1. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    2. Rezaei Somarin, Aghil & Chen, Songlin & Asian, Sobhan & Wang, David Z.W., 2017. "A heuristic stock allocation rule for repairable service parts," International Journal of Production Economics, Elsevier, vol. 184(C), pages 131-140.
    3. Sven Axsäter, 1995. "Approximate evaluation of batch‐ordering policies for a one‐warehouse, N non‐identical retailer system under compound poisson demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 807-819, August.
    4. Jovan Grahovac & Amiya Chakravarty, 2001. "Sharing and Lateral Transshipment of Inventory in a Supply Chain with Expensive Low-Demand Items," Management Science, INFORMS, vol. 47(4), pages 579-594, April.
    5. Yunzeng Wang & Morris A. Cohen & Yu-Sheng Zheng, 2000. "A Two-Echelon Repairable Inventory System with Stocking-Center-Dependent Depot Replenishment Lead Times," Management Science, INFORMS, vol. 46(11), pages 1441-1453, November.
    6. Chew, E. P. & Johnson, L. A., 1996. "Service level approximations for multiechelon inventory systems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 440-455, June.
    7. Olsson, Ralph J. & Hill, Roger M., 2007. "A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon," European Journal of Operational Research, Elsevier, vol. 177(1), pages 310-324, February.
    8. Paul Zipkin, 1991. "Evaluation of base‐stock policies in multiechelon inventory systems with compound‐poisson demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 397-412, June.
    9. Guide, V. Daniel R. & Srivastava, Rajesh, 1997. "Repairable inventory theory: Models and applications," European Journal of Operational Research, Elsevier, vol. 102(1), pages 1-20, October.
    10. Mustafa K. Doğru & Ulaş Özen, 2015. "Tactical Inventory Planning at Alcatel-Lucent’s Repair and Exchange Services," Interfaces, INFORMS, vol. 45(3), pages 228-242, June.
    11. Huaxiao Shen & Tian Tian & Han Zhu, 2019. "A Two-Echelon Inventory System with a Minimum Order Quantity Requirement," Sustainability, MDPI, vol. 11(18), pages 1-22, September.
    12. Guillermo Gallego & Özalp Özer & Paul Zipkin, 2007. "Bounds, Heuristics, and Approximations for Distribution Systems," Operations Research, INFORMS, vol. 55(3), pages 503-517, June.
    13. Graves, Stephen C., 1989. "A multi-echelon inventory model with fixed reorder intervals," Working papers 3045-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    14. Izack Cohen & Morris A. Cohen & Elad Landau, 2017. "On sourcing and stocking policies in a two-echelon, multiple location, repairable parts supply chain," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 617-629, June.
    15. Olof Stenius & Ayşe Gönül Karaarslan & Johan Marklund & A. G. de Kok, 2016. "Exact Analysis of Divergent Inventory Systems with Time-Based Shipment Consolidation and Compound Poisson Demand," Operations Research, INFORMS, vol. 64(4), pages 906-921, August.
    16. Vinayak Deshpande & Morris A. Cohen & Karen Donohue, 2003. "An Empirical Study of Service Differentiation for Weapon System Service Parts," Operations Research, INFORMS, vol. 51(4), pages 518-530, August.
    17. Rustenburg, W. D. & van Houtum, G. J. & Zijm, W. H. M., 2001. "Spare parts management at complex technology-based organizations: An agenda for research," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 177-193, May.
    18. Andersson, Jonas & Malmberg, Filip & Marklund, Johan, 2023. "Exact analysis of One-Warehouse-Multiple-Retailer inventory systems with quantity restricted deliveries," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1161-1172.
    19. Sven Axsäter & Wen‐Fa Zhang, 1996. "Recursive evaluation of order‐up‐to‐S policies for two‐echelon inventory systems with compound Poisson demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(1), pages 151-157, February.
    20. Vinayak Deshpande & Ananth V. Iyer & Richard Cho, 2006. "Efficient Supply Chain Management at the U.S. Coast Guard Using Part-Age Dependent Supply Replenishment Policies," Operations Research, INFORMS, vol. 54(6), pages 1028-1040, December.
    21. Basten, R.J.I. & van der Heijden, M.C. & Schutten, J.M.J., 2012. "Joint optimization of level of repair analysis and spare parts stocks," European Journal of Operational Research, Elsevier, vol. 222(3), pages 474-483.
    22. Stenius, Olof & Marklund, Johan & Axsäter, Sven, 2018. "Sustainable multi-echelon inventory control with shipment consolidation and volume dependent freight costs," European Journal of Operational Research, Elsevier, vol. 267(3), pages 904-916.

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