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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

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    5. El Bhilat, El Mehdi & El Jaouhari, Asmae & Hamidi, L. Saadia, 2024. "Assessing the influence of artificial intelligence on agri-food supply chain performance: the mediating effect of distribution network efficiency," Technological Forecasting and Social Change, Elsevier, vol. 200(C).
    6. 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.
    7. 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).
    8. 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.
    9. Kaynov, Illya & van Knippenberg, Marijn & Menkovski, Vlado & van Breemen, Albert & van Jaarsveld, Willem, 2024. "Deep Reinforcement Learning for One-Warehouse Multi-Retailer inventory management," International Journal of Production Economics, Elsevier, vol. 267(C).
    10. Zhang, Yuankai & Sun, Lijun & Hu, Xiangpei & Zhao, Chen, 2019. "Order consolidation for the last-mile split delivery in online retailing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 309-327.
    11. Chen, Yan & Huang, Zhenhua & Ai, Hongshan & Guo, Xingkun & Luo, Fan, 2021. "The Impact of GIS/GPS Network Information Systems on the Logistics Distribution Cost of Tobacco Enterprises," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    12. 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.
    13. Dimitrova, Dimitrina S. & Ignatov, Zvetan G. & Kaishev, Vladimir K. & Tan, Senren, 2020. "On double-boundary non-crossing probability for a class of compound processes with applications," European Journal of Operational Research, Elsevier, vol. 282(2), pages 602-613.
    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. 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.
    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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