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Managing stochastic inventory systems with free shipping option

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  • Zhou, Bin
  • Katehakis, Michael N.
  • Zhao, Yao

Abstract

In many industries, customers are offered free shipping whenever an order placed exceeds a minimum quantity specified by suppliers. This allows the suppliers to achieve economies of scale in terms of production and distribution by encouraging customers to place large orders. In this paper, we consider the optimal policy of a retailer who operates a single-product inventory system under periodic review. The ordering cost of the retailer is a linear function of the ordering quantity, and the shipping cost is a fixed constant K whenever the order size is less than a given quantity - the free shipping quantity (FSQ), and it is zero whenever the order size is at least as much as the FSQ. Demands in different time periods are i.i.d. random variables. We provide the optimal inventory control policy and characterize its structural properties for the single-period model. For multi-period inventory systems, we propose and analyze a heuristic policy that has a simple structure, the (s, t, S) policy. Optimal parameters of the proposed heuristic policy are then computed. Through an extensive numerical study, we demonstrate that the heuristic policy is sufficiently accurate and close to optimal.

Suggested Citation

  • Zhou, Bin & Katehakis, Michael N. & Zhao, Yao, 2009. "Managing stochastic inventory systems with free shipping option," European Journal of Operational Research, Elsevier, vol. 196(1), pages 186-197, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:1:p:186-197
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    References listed on IDEAS

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    Cited by:

    1. Hua, Guowei & Wang, Shouyang & Cheng, T.C.E., 2012. "Optimal order lot sizing and pricing with free shipping," European Journal of Operational Research, Elsevier, vol. 218(2), pages 435-441.
    2. Hayya, Jack C. & Harrison, Terry P. & He, X. James, 2011. "The impact of stochastic lead time reduction on inventory cost under order crossover," European Journal of Operational Research, Elsevier, vol. 211(2), pages 274-281, June.
    3. Bin Zhou, 2016. "Lean principles, practices, and impacts: a study on small and medium-sized enterprises (SMEs)," Annals of Operations Research, Springer, vol. 241(1), pages 457-474, June.
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    5. Becerril-Arreola, Rafael & Leng, Mingming & Parlar, Mahmut, 2013. "Online retailers’ promotional pricing, free-shipping threshold, and inventory decisions: A simulation-based analysis," European Journal of Operational Research, Elsevier, vol. 230(2), pages 272-283.
    6. Alain Bensoussan & Lama Moussawi-Haidar & Metin Çakanyıldırım, 2010. "Inventory control with an order-time constraint: optimality, uniqueness and significance," Annals of Operations Research, Springer, vol. 181(1), pages 603-640, December.
    7. Qing-chun Meng & Xiao-le Wan & Xiao-xia Rong, 2015. "A Robust Ordering Strategy for Retailers Facing a Free Shipping Option," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-14, May.
    8. Kartikeya Puranam & David C. Novak & Marilyn Lucas, 2022. "Extending the newsvendor model to account for uncontrolled inventory transfers," Annals of Operations Research, Springer, vol. 317(1), pages 213-226, October.
    9. T. M. Rofin & Biswajit Mahanty, 2021. "Fulfillment mode selection for Indian online sellers under free and flat rate shipping policies," Electronic Commerce Research, Springer, vol. 21(2), pages 263-296, June.
    10. Shao, Xiao-Feng, 2017. "Free or calculated shipping: Impact of delivery cost on supply chains moving to online retailing," International Journal of Production Economics, Elsevier, vol. 191(C), pages 267-277.
    11. F. Kleintje-Ell & G. Kiesmüller, 2015. "Cost minimising order schedules for a capacitated inventory system," Annals of Operations Research, Springer, vol. 229(1), pages 501-520, June.
    12. Xiaxia Ma & Wenliang Bian & Xiqing Yang & Shengnan Niu & Yongming Cai & Jie Guan & Wenbin Wang, 2022. "Online Retailer’s Contingent Free-Shipping Decisions under Large-Scale Promotions Considering Delayed Delivery," Sustainability, MDPI, vol. 14(17), pages 1-22, August.
    13. Zhu, Han & Liu, Xing & Chen, Youhua (Frank), 2015. "Effective inventory control policies with a minimum order quantity and batch ordering," International Journal of Production Economics, Elsevier, vol. 168(C), pages 21-30.
    14. Hua, Guowei & Wang, Shouyang & Cheng, T.C.E., 2012. "Optimal pricing and order quantity for the newsvendor problem with free shipping," International Journal of Production Economics, Elsevier, vol. 135(1), pages 162-169.
    15. Kwon, Kysang & Cheong, Taesu, 2014. "A minimax distribution-free procedure for a newsvendor problem with free shipping," European Journal of Operational Research, Elsevier, vol. 232(1), pages 234-240.
    16. Shuangchi He & Dacheng Yao & Hanqin Zhang, 2017. "Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 979-1006, November.
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    18. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Characterizing order processes of continuous review (s,S) and (r,nQ) policies," European Journal of Operational Research, Elsevier, vol. 236(2), pages 534-547.

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