IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v309y2023i3p1161-1172.html
   My bibliography  Save this article

Exact analysis of One-Warehouse-Multiple-Retailer inventory systems with quantity restricted deliveries

Author

Listed:
  • Andersson, Jonas
  • Malmberg, Filip
  • Marklund, Johan

Abstract

Joint consideration and coordination of inventory and shipment decisions is an important challenge in the quest for sustainable distribution systems. This paper addresses this issue by presenting a method for exact analysis of the inventory level distributions in a centralized One-Warehouse-Multiple-Retailer (OWMR) inventory system with quantity restricted deliveries from the warehouse. The system is characterized by continuous review (R,nQ) policies, complete backordering, and compound Poisson demand. The class of quantity restricted delivery policies we consider is motivated by a common desire in practice to ship full load carriers. It generalizes the assumption of unrestricted partial deliveries often used in the literature, and allows the warehouse to only ship retailer specific delivery batch quantities to the different retailers. The delivery batches typically represent package or pallet sizes, containers, or full truckloads. An attractive feature of our approach is that it does not add to the computational effort of analyzing the special case of unrestricted partial deliveries available in the existing literature. A numerical study shows that accounting for quantitative delivery restrictions used in transportation and handling operations when optimizing the reorder points in multi-echelon systems can be very important. Failure to do so can lead to high backorder costs and inadequate customer service.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:309:y:2023:i:3:p:1161-1172
    DOI: 10.1016/j.ejor.2023.02.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723001583
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.02.026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Johan Marklund, 2006. "Controlling Inventories in Divergent Supply Chains with Advance-Order Information," Operations Research, INFORMS, vol. 54(5), pages 988-1010, October.
    6. Cetinkaya, Sila & Mutlu, Fatih & Lee, Chung-Yee, 2006. "A comparison of outbound dispatch policies for integrated inventory and transportation decisions," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1094-1112, June.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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. 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.
    13. 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.
    14. 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.
    15. Shoshana Anily & Michal Tzur, 2005. "Shipping Multiple Items by Capacitated Vehicles: An Optimal Dynamic Programming Approach," Transportation Science, INFORMS, vol. 39(2), pages 233-248, May.
    16. Satır, Benhür & Erenay, Fatih Safa & Bookbinder, James H., 2018. "Shipment consolidation with two demand classes: Rationing the dispatch capacity," European Journal of Operational Research, Elsevier, vol. 270(1), pages 171-184.
    17. Dekker, Rommert & Bloemhof, Jacqueline & Mallidis, Ioannis, 2012. "Operations Research for green logistics – An overview of aspects, issues, contributions and challenges," European Journal of Operational Research, Elsevier, vol. 219(3), pages 671-679.
    18. 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.
    19. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    20. 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.
    21. Kamran Moinzadeh, 2002. "A Multi-Echelon Inventory System with Information Exchange," Management Science, INFORMS, vol. 48(3), pages 414-426, March.
    22. Gerard Cachon, 2001. "Managing a Retailer's Shelf Space, Inventory, and Transportation," Manufacturing & Service Operations Management, INFORMS, vol. 3(3), pages 211-229, July.
    23. Stephen C. Graves, 1996. "A Multiechelon Inventory Model with Fixed Replenishment Intervals," Management Science, INFORMS, vol. 42(1), pages 1-18, January.
    24. 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.
    25. Fangruo Chen & Yu-Sheng Zheng, 1997. "One-Warehouse Multiretailer Systems with Centralized Stock Information," Operations Research, INFORMS, vol. 45(2), pages 275-287, April.
    26. Chung-Yee Lee & Sila Çetinkaya & Wikrom Jaruphongsa, 2003. "A Dynamic Model for Inventory Lot Sizing and Outbound Shipment Scheduling at a Third-Party Warehouse," Operations Research, INFORMS, vol. 51(5), pages 735-747, October.
    27. 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.
    28. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Wei, Bo & Çetinkaya, Sıla & Cline, Daren B.H., 2023. "Inbound replenishment and outbound dispatch decisions under hybrid shipment consolidation policies: An analytical model and comparison," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).
    6. 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.
    7. Jana Ralfs & Gudrun P. Kiesmüller, 2022. "Inventory management with advance demand information and flexible shipment consolidation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1009-1044, December.
    8. 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.
    9. 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.
    10. Sancak, Emre & Salman, F. Sibel, 2011. "Multi-item dynamic lot-sizing with delayed transportation policy," International Journal of Production Economics, Elsevier, vol. 131(2), pages 595-603, 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. Dinçer Konur & Joseph Geunes, 2019. "Integrated districting, fleet composition, and inventory planning for a multi-retailer distribution system," Annals of Operations Research, Springer, vol. 273(1), pages 527-559, February.
    13. 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.
    14. 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.
    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. Chen, Jing & Dong, Ming & Xu, Lei, 2018. "A perishable product shipment consolidation model considering freshness-keeping effort," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 56-86.
    17. Romero-Silva, Rodrigo & Mujica Mota, Miguel, 2022. "Trade-offs in the landside operations of air cargo hubs: Horizontal cooperation and shipment consolidation policies considering capacitated nodes," Journal of Air Transport Management, Elsevier, vol. 103(C).
    18. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    19. Kyunghoon Kang & Ki-sung Hong & Ki Hong Kim & Chulung Lee, 2017. "Shipment Consolidation Policy under Uncertainty of Customer Order for Sustainable Supply Chain Management," Sustainability, MDPI, vol. 9(9), pages 1-17, September.
    20. Berling, Peter & Eng-Larsson, Fredrik, 2016. "Pricing and timing of consolidated deliveries in the presence of an express alternative: Financial and environmental analysis," European Journal of Operational Research, Elsevier, vol. 250(2), pages 590-601.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:309:y:2023:i:3:p:1161-1172. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.