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Exact Analysis of Divergent Inventory Systems with Time-Based Shipment Consolidation and Compound Poisson Demand

Author

Listed:
  • Olof Stenius

    (Department of Industrial Management and Logistics, Lund University, 22100 Lund, Sweden)

  • Ayşe Gönül Karaarslan

    (Department of Econometrics, Erasmus University Rotterdam, 3000DR Rotterdam, Netherlands)

  • Johan Marklund

    (Department of Industrial Management and Logistics, Lund University, 22100 Lund, Sweden)

  • A. G. de Kok

    (Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, 5600MB Eindhoven, Netherlands)

Abstract

Sustainable and efficient management of a distribution system requires coordination between transportation planning and inventory control decisions. In this context, we consider a one warehouse multi-retailer inventory system with a time-based shipment consolidation policy at the warehouse. This means that there are fixed costs associated with each shipment, and retailer orders are consolidated and shipped periodically to groups of retailers sharing the same delivery routes. Customer demand is compound Poisson distributed and unsatisfied demand at each stock point is backordered and allocated on a first-come first-served basis. The system is centralized and inventory levels are reviewed continuously. The warehouse has access to real-time inventory information from the retailers, and uses a ( R , nQ ) policy to replenish from an outside supplier/manufacturer. We derive the exact probability distributions for the inventory levels at the retailers, and use these to obtain exact expressions for the system’s expected shipment, holding and backorder costs, its average inventory levels, and fill rates. Based on the analytical properties of the objective function, we construct an optimization procedure by deriving bounds on the optimal reorder levels and shipment intervals both for single-item and multi-item systems.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:oropre:v:64:y:2016:i:4:p:906-921
    DOI: 10.1287/opre.2016.1510
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    References listed on IDEAS

    as
    1. Craig C. Sherbrooke, 1968. "Metric: A Multi-Echelon Technique for Recoverable Item Control," Operations Research, INFORMS, vol. 16(1), pages 122-141, February.
    2. Kevin H. Shang & Zhijie Tao & Sean X. Zhou, 2015. "Optimizing Reorder Intervals for Two-Echelon Distribution Systems with Stochastic Demand," Operations Research, INFORMS, vol. 63(2), pages 458-475, April.
    3. Howard, Christian & Marklund, Johan, 2011. "Evaluation of stock allocation policies in a divergent inventory system with shipment consolidation," European Journal of Operational Research, Elsevier, vol. 211(2), pages 298-309, June.
    4. Johan Marklund & Kaj Rosling, 2012. "Lower Bounds and Heuristics for Supply Chain Stock Allocation," Operations Research, INFORMS, vol. 60(1), pages 92-105, February.
    5. Özalp Özer, 2003. "Replenishment Strategies for Distribution Systems Under Advance Demand Information," Management Science, INFORMS, vol. 49(3), pages 255-272, March.
    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. 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.
    9. Diks, E. B. & de Kok, A. G., 1999. "Computational results for the control of a divergent N-echelon inventory system," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 327-336, March.
    10. van der Heijden, M. C. & Diks, E. B. & de Kok, A. G., 1997. "Stock allocation in general multi-echelon distribution systems with (R, S) order-up-to-policies," International Journal of Production Economics, Elsevier, vol. 49(2), pages 157-174, April.
    11. Stephen C. Graves, 1985. "A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment," Management Science, INFORMS, vol. 31(10), pages 1247-1256, October.
    12. Stephen C. Graves, 1996. "A Multiechelon Inventory Model with Fixed Replenishment Intervals," Management Science, INFORMS, vol. 42(1), pages 1-18, January.
    13. Awi Federgruen & Paul Zipkin, 1984. "Approximations of Dynamic, Multilocation Production and Inventory Problems," Management Science, INFORMS, vol. 30(1), pages 69-84, January.
    14. Johan Marklund, 2006. "Controlling Inventories in Divergent Supply Chains with Advance-Order Information," Operations Research, INFORMS, vol. 54(5), pages 988-1010, October.
    15. 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.
    16. Lengu, D. & Syntetos, A.A. & Babai, M.Z., 2014. "Spare parts management: Linking distributional assumptions to demand classification," European Journal of Operational Research, Elsevier, vol. 235(3), pages 624-635.
    17. Diks, E. B. & de Kok, A. G., 1998. "Optimal control of a divergent multi-echelon inventory system," European Journal of Operational Research, Elsevier, vol. 111(1), pages 75-97, November.
    18. Johan Marklund, 2002. "Centralized inventory control in a two‐level distribution system with Poisson demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(8), pages 798-822, December.
    19. Sila Çetinkaya & Chung-Yee Lee, 2000. "Stock Replenishment and Shipment Scheduling for Vendor-Managed Inventory Systems," Management Science, INFORMS, vol. 46(2), pages 217-232, February.
    20. 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.
    21. Roman Kapuscinski & Rachel Q. Zhang & Paul Carbonneau & Robert Moore & Bill Reeves, 2004. "Inventory Decisions in Dell's Supply Chain," Interfaces, INFORMS, vol. 34(3), pages 191-205, June.
    22. Craig C. Sherbrooke, 1986. "VARI-METRIC : Improved Approximations for Multi-Indenture, Multi-Echelon Availability Models," Operations Research, INFORMS, vol. 34(2), pages 311-319, April.
    23. Fangruo Chen & Yu-Sheng Zheng, 1997. "One-Warehouse Multiretailer Systems with Centralized Stock Information," Operations Research, INFORMS, vol. 45(2), pages 275-287, April.
    24. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    25. van Houtum, G. J. & Inderfurth, K. & Zijm, W. H. M., 1996. "Materials coordination in stochastic multi-echelon systems," European Journal of Operational Research, Elsevier, vol. 95(1), pages 1-23, November.
    26. Andersson, Jonas & Marklund, Johan, 2000. "Decentralized inventory control in a two-level distribution system," European Journal of Operational Research, Elsevier, vol. 127(3), pages 483-506, December.
    27. 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.
    28. Mustafa Çagri Gürbüz & Kamran Moinzadeh & Yong-Pin Zhou, 2007. "Coordinated Replenishment Strategies in Inventory/Distribution Systems," Management Science, INFORMS, vol. 53(2), pages 293-307, February.
    29. Berling, Peter & Marklund, Johan, 2013. "A model for heuristic coordination of real life distribution inventory systems with lumpy demand," European Journal of Operational Research, Elsevier, vol. 230(3), pages 515-526.
    30. Fatih Mutlu & Sila Çetinkaya & James Bookbinder, 2010. "An analytical model for computing the optimal time-and-quantity-based policy for consolidated shipments," IISE Transactions, Taylor & Francis Journals, vol. 42(5), pages 367-377.
    31. Forsberg, Rolf, 1995. "Optimization of order-up-to-S policies for two-level inventory systems with compound Poisson demand," European Journal of Operational Research, Elsevier, vol. 81(1), pages 143-153, February.
    32. Leon Yang Chu & Zuo-Jun Max Shen, 2010. "A Power-of-Two Ordering Policy for One-Warehouse Multiretailer Systems with Stochastic Demand," Operations Research, INFORMS, vol. 58(2), pages 492-502, April.
    33. Vishal Gaur & Marshall L. Fisher, 2004. "A Periodic Inventory Routing Problem at a Supermarket Chain," Operations Research, INFORMS, vol. 52(6), pages 813-822, December.
    34. 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.
    35. Çetinkaya, SIla & Bookbinder, James H., 2003. "Stochastic models for the dispatch of consolidated shipments," Transportation Research Part B: Methodological, Elsevier, vol. 37(8), pages 747-768, September.
    36. Peter L. Jackson, 1988. "Stock Allocation in a Two-Echelon Distribution System Or "What to Do Until Your Ship Comes In"," Management Science, INFORMS, vol. 34(7), pages 880-895, July.
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    6. Zhang, Yuankai & Lin, Wei-Hua & Huang, Minfang & Hu, Xiangpei, 2021. "Multi-warehouse package consolidation for split orders in online retailing," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1040-1055.
    7. Cook, Robert A. & Lodree, Emmett J., 2017. "Dispatching policies for last-mile distribution with stochastic supply and demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 353-371.
    8. Ke, Ginger Y. & Bookbinder, James H., 2018. "Coordinating the discount policies for retailer, wholesaler, and less-than-truckload carrier under price-sensitive demand: A tri-level optimization approach," International Journal of Production Economics, Elsevier, vol. 196(C), pages 82-100.
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    13. 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.
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    16. Sonntag, Danja R. & Schrotenboer, Albert H. & Kiesmüller, Gudrun P., 2023. "Stochastic inventory routing with time-based shipment consolidation," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1186-1201.

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