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An analytical model for computing the optimal time-and-quantity-based policy for consolidated shipments

Author

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  • Fatih Mutlu
  • Sila Çetinkaya
  • James Bookbinder

Abstract

The logistics literature reports that three different types of shipment consolidation policies are popular in current practice. These are time-based, quantity-based and Time-and-Quantity (TQ)-based consolidation policies. Although time-based and quantity-based policies have been studied via analytical modeling, to the best of the authors knowledge, there is no exact analytical model for computing the optimal TQ-based policy parameters. Considering the case of stochastic demand/order arrivals, an analytical model for computing the expected long-run average cost of a consolidation system implementing a TQ-based policy is developed. The cost expression is used to analyze the optimal TQ-based policy parameters. The presented analytical results prove that: (i) the optimal TQ-based policy outperforms the optimal time-based policy; and (ii) the optimal quantity-based policy is superior to the other two (i.e., optimal time-based and TQ-based) policies in terms of cost. Considering the expected maximum waiting time as a measure of timely delivery performance, however, it is numerically demonstrated that the TQ-based policies improve on the quantity-based policies significantly with only a slight increase in the cost.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:uiiexx:v:42:y:2010:i:5:p:367-377
    DOI: 10.1080/07408170903462368
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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. 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.
    3. Hong, Ki-sung & Lee, Chulung, 2013. "Optimal time-based consolidation policy with price sensitive demand," International Journal of Production Economics, Elsevier, vol. 143(2), pages 275-284.
    4. 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.
    5. Özen, Ulaş & Doğru, Mustafa K. & Armagan Tarim, S., 2012. "Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem," Omega, Elsevier, vol. 40(3), pages 348-357.
    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. Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
    8. 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.
    9. Huseyin Tunc & Onur A. Kilic & S. Armagan Tarim & Roberto Rossi, 2018. "An Extended Mixed-Integer Programming Formulation and Dynamic Cut Generation Approach for the Stochastic Lot-Sizing Problem," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 492-506, August.
    10. Kilic, Onur A. & Tunc, Huseyin & Tarim, S. Armagan, 2018. "Heuristic policies for the stochastic economic lot sizing problem with remanufacturing under service level constraints," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1102-1109.
    11. E. Ursavas & Stuart X. Zhu, 2018. "Integrated Passenger and Freight Train Planning on Shared-Use Corridors," Service Science, INFORMS, vol. 52(6), pages 1376-1390, December.
    12. Christine Nguyen & Alejandro Toriello & Maged Dessouky & James E. Moore, 2013. "Evaluation of Transportation Practices in the California Cut Flower Industry," Interfaces, INFORMS, vol. 43(2), pages 182-193, April.
    13. 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).
    14. 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.
    15. 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.
    16. Dural-Selcuk, Gozdem & Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2020. "The benefit of receding horizon control: Near-optimal policies for stochastic inventory control," Omega, Elsevier, vol. 97(C).
    17. Fan, Yun & Behdani, Behzad & Bloemhof-Ruwaard, Jacqueline & Zuidwijk, Rob, 2019. "Flow consolidation in hinterland container transport: An analysis for perishable and dry cargo," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 130(C), pages 128-160.
    18. 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.
    19. 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.
    20. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.
    21. 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.

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