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Optimal Position-Based Warehouse Ordering in Divergent Two-Echelon Inventory Systems

Author

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  • Sven Axsäter

    (Department of Industrial Management and Logistics, Lund University, 221 00 Lund, Sweden)

  • Johan Marklund

    (Department of Industrial Management and Logistics, Lund University, 221 00 Lund, Sweden)

Abstract

A continuous-review two-echelon inventory system with one central warehouse and a number of nonidentical retailers is considered. The retailers face independent Poisson demand and apply standard ( R, Q ) policies. The retailer order quantities are fixed integer multiples of a certain batch size, representing the smallest pallet or container size transported in the system. A warehouse order may consist of one or several such batches. We derive a new policy for warehouse ordering, which is optimal in the broad class of position-based policies relying on complete information about the retailer inventory positions, transportation times, cost structures, and demand distributions at all facilities. The exact analysis of the new policy includes a method for determining the expected total inventory holding and backorder costs for the entire system. The class of position-based policies encompasses both the traditional installation-stock and echelon-stock ( R, Q ) policies, as well as the more sophisticated policies recently analyzed in the literature. The value of more carefully incorporating a richer information structure into the warehouse ordering policy is illustrated in a numerical study.

Suggested Citation

  • Sven Axsäter & Johan Marklund, 2008. "Optimal Position-Based Warehouse Ordering in Divergent Two-Echelon Inventory Systems," Operations Research, INFORMS, vol. 56(4), pages 976-991, August.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:4:p:976-991
    DOI: 10.1287/opre.1080.0560
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    1. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    2. Hau L. Lee & Kut C. So & Christopher S. Tang, 2000. "The Value of Information Sharing in a Two-Level Supply Chain," Management Science, INFORMS, vol. 46(5), pages 626-643, May.
    3. Axsater, Sven & Juntti, Lars, 1996. "Comparison of echelon stock and installation stock policies for two-level inventory systems," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 303-310, August.
    4. Sven Axsäter & Kaj Rosling, 1993. "Notes: Installation vs. Echelon Stock Policies for Multilevel Inventory Control," Management Science, INFORMS, vol. 39(10), pages 1274-1280, October.
    5. Fangruo Chen, 1998. "Echelon Reorder Points, Installation Reorder Points, and the Value of Centralized Demand Information," Management Science, INFORMS, vol. 44(12-Part-2), pages 221-234, December.
    6. Gérard P. Cachon & Marshall Fisher, 2000. "Supply Chain Inventory Management and the Value of Shared Information," Management Science, INFORMS, vol. 46(8), pages 1032-1048, August.
    7. Kamran Moinzadeh, 2002. "A Multi-Echelon Inventory System with Information Exchange," Management Science, INFORMS, vol. 48(3), pages 414-426, March.
    8. Srinagesh Gavirneni & Roman Kapuscinski & Sridhar Tayur, 1999. "Value of Information in Capacitated Supply Chains," Management Science, INFORMS, vol. 45(1), pages 16-24, January.
    9. Forsberg, Rolf, 1997. "Exact evaluation of (R, Q)-policies for two-level inventory systems with Poisson demand," European Journal of Operational Research, Elsevier, vol. 96(1), pages 130-138, January.
    10. Fangruo Chen & Yu-Sheng Zheng, 1997. "One-Warehouse Multiretailer Systems with Centralized Stock Information," Operations Research, INFORMS, vol. 45(2), pages 275-287, April.
    11. Ki Ling Cheung & Hau L. Lee, 2002. "The Inventory Benefit of Shipment Coordination and Stock Rebalancing in a Supply Chain," Management Science, INFORMS, vol. 48(2), pages 300-306, February.
    12. Sven Axsäter & Johan Marklund & Edward A. Silver, 2002. "Heuristic Methods for Centralized Control of One-Warehouse, N-Retailer Inventory Systems," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 75-97, October.
    13. Srinagesh Gavirneni, 2002. "Information Flows in Capacitated Supply Chains with Fixed Ordering Costs," Management Science, INFORMS, vol. 48(5), pages 644-651, May.
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    Cited by:

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    9. Amir Hosein Afshar Sedigh & Rasoul Haji & Seyed Mehdi Sajadifar, 2023. "The Cost Function of a Two-Level Inventory System with identical retailers benefitting from Information Sharing," Papers 2312.03898, arXiv.org.
    10. Han Zhu, 2022. "A simple heuristic policy for stochastic inventory systems with both minimum and maximum order quantity requirements," Annals of Operations Research, Springer, vol. 309(1), pages 347-363, February.
    11. Darmawan, Agus & Wong, Hartanto & Thorstenson, Anders, 2021. "Supply chain network design with coordinated inventory control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    12. 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.
    13. Karzan Mahdi Ghafour & Nerda ZuraZaibidi, 2014. "A Simulation Approach to Determine the Probability of Demand during Lead-Time When Demand Distributed Normal and Lead-Time Distributed Gamma," Journal of Economics and Behavioral Studies, AMH International, vol. 6(11), pages 840-847.
    14. Wang, Qinan & Wan, Guangyu, 2023. "Fixed-interval order-up-to policies and myopic optimal warehouse stock allocation for one-warehouse multiple-retailer systems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1112-1124.
    15. Johan Marklund, 2011. "Inventory control in divergent supply chains with time‐based dispatching and shipment consolidation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(1), pages 59-71, February.
    16. 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.
    17. Johan Marklund & Kaj Rosling, 2012. "Lower Bounds and Heuristics for Supply Chain Stock Allocation," Operations Research, INFORMS, vol. 60(1), pages 92-105, February.
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    19. 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.
    20. Christian Howard & Johan Marklund & Tarkan Tan & Ingrid Reijnen, 2015. "Inventory Control in a Spare Parts Distribution System with Emergency Stocks and Pipeline Information," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 142-156, May.

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