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A minimax distribution-free procedure for a newsvendor problem with free shipping

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  • Kwon, Kysang
  • Cheong, Taesu

Abstract

In this paper, we study the optimal policies of retailers who operate their inventory with a single period model (i.e., newsvendor model) under a free shipping offer where a fixed shipping fee is exempted if an order quantity is greater than or equal to a given minimum quantity. Zhou et al. (2009) have explored this model, and we further investigate their analysis for the optimal ordering policies which they did not sufficiently develop. Based on the investigation, we extend the base model in order to deal with the practically important aspect of inventory management when the exact distribution function of demand is not available. We incorporate the aspect into the base model and present the optimal policies for the extended model with a numerical example. Finally, we conduct extensive numerical experiments to evaluate the performance of the extended model and analyze the impacts of minimum free shipping quantity and the fixed shipping fee on the performance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:1:p:234-240
    DOI: 10.1016/j.ejor.2013.07.004
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Guo, Peijun & Ma, Xiuyan, 2014. "Newsvendor models for innovative products with one-shot decision theory," European Journal of Operational Research, Elsevier, vol. 239(2), pages 523-536.
    2. Qiu, Ruozhen & Sun, Minghe & Lim, Yun Fong, 2017. "Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches," European Journal of Operational Research, Elsevier, vol. 261(3), pages 880-892.
    3. Kamburowski, Jerzy, 2014. "The distribution-free newsboy problem under the worst-case and best-case scenarios," European Journal of Operational Research, Elsevier, vol. 237(1), pages 106-112.
    4. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    5. Irfanullah Khan & Biswajit Sarkar, 2021. "Transfer of Risk in Supply Chain Management with Joint Pricing and Inventory Decision Considering Shortages," Mathematics, MDPI, vol. 9(6), pages 1-20, March.
    6. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    7. Raza, Syed Asif & Rathinam, Sivakumar, 2017. "A risk tolerance analysis for a joint price differentiation and inventory decisions problem with demand leakage effect," International Journal of Production Economics, Elsevier, vol. 183(PA), pages 129-145.
    8. 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.
    9. 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.
    10. Ata Allah Taleizadeh & Mahsa Noori-daryan & Kannan Govindan, 2016. "Pricing and ordering decisions of two competing supply chains with different composite policies: a Stackelberg game-theoretic approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(9), pages 2807-2836, May.
    11. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    12. Bai, Qingguo & Xu, Jianteng & Gong, Yeming & Chauhan, Satyaveer S., 2022. "Robust decisions for regulated sustainable manufacturing with partial demand information: Mandatory emission capacity versus emission tax," European Journal of Operational Research, Elsevier, vol. 298(3), pages 874-893.
    13. Qingguo Bai & Jianteng Xu & Yuzhong Zhang, 2022. "The distributionally robust optimization model for a remanufacturing system under cap-and-trade policy: a newsvendor approach," Annals of Operations Research, Springer, vol. 309(2), pages 731-760, February.

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