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Markovian Decision Processes in Shipment Consolidation

Author

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  • James K. Higginson

    (School of Business and Economics, Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5)

  • James H. Bookbinder

    (Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1)

Abstract

Shipment consolidation is a logistics strategy that combines two or more orders or shipments so that a larger quantity can be dispatched on the same vehicle. This paper discusses a discrete-time Markovian decision process (MDP) approach for determining when to release consolidated loads. We assume that the shipper controls the timing of each load dispatch. Thus, whenever a customer places an order, a choice must be made between dispatching this order (plus all others waiting) immediately, or continuing to consolidate until at least the arrival of the next order. Our MDP models of shipment consolidation consider movement by for-hire transportation (common carriage) or by a firm's own vehicles (private fleet). Small but realistic numerical examples illustrate the application of these models and the data-aggregation issues that must be resolved. Two minimization criteria are considered: cost per unit time, or cost per hundredweight per unit time. For private carriage, the optimal policy is of the control-limit type; for common carriage, it may not be. These potential differences in form of the optimal policy are true for either objective function. The possibly contrasting optimal policies are interpreted in light of the costs encountered by an industrial firm's private fleet compared to the freight charges of a public trucking company.

Suggested Citation

  • James K. Higginson & James H. Bookbinder, 1995. "Markovian Decision Processes in Shipment Consolidation," Transportation Science, INFORMS, vol. 29(3), pages 242-255, August.
    • Handle: RePEc:inm:ortrsc:v:29:y:1995:i:3:p:242-255
    DOI: 10.1287/trsc.29.3.242
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    Citations

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    Cited by:

    1. 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.
    2. Sara Martins & Pedro Amorim & Bernardo Almada-Lobo, 2018. "Delivery mode planning for distribution to brick-and-mortar retail stores: discussion and literature review," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 785-812, December.
    3. Sıla Çetinkaya & Chung‐Yee Lee, 2002. "Optimal outbound dispatch policies: Modeling inventory and cargo capacity," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 531-556, September.
    4. 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.
    5. 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.
    6. 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).
    7. Ülkü, M. Ali & Bookbinder, James H., 2012. "Optimal quoting of delivery time by a third party logistics provider: The impact of shipment consolidation and temporal pricing schemes," European Journal of Operational Research, Elsevier, vol. 221(1), pages 110-117.
    8. 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.
    9. 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.
    10. Qi‐Ming He & James H. Bookbinder & Qishu Cai, 2020. "Optimal policies for stochastic clearing systems with time‐dependent delay penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 487-502, October.
    11. 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.
    12. 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.
    13. Kang, Jae-Hun & Kim, Yeong-Dae, 2010. "Coordination of inventory and transportation managements in a two-level supply chain," International Journal of Production Economics, Elsevier, vol. 123(1), pages 137-145, January.
    14. Nguyen, Christine & Dessouky, Maged & Toriello, Alejandro, 2014. "Consolidation strategies for the delivery of perishable products," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 69(C), pages 108-121.
    15. 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.
    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.

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