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Solving a Distribution-Free Multi-Period Newsvendor Problem With Advance Purchase Discount via an Online Ordering Solution

Author

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  • Rui Wang
  • Xiao Yan
  • Chuanjin Zhu

Abstract

In this paper, we study a distribution-free multi-period newsvendor problem with advance purchase discount (APD). In addition to the regular-order placed at the beginning of each period, a decision-maker (DM) can also commit to an advance-order from the upstream supplier and receive discounts. The goal of the DM is to maximize total profits, and in this problem, the DM only has access to past demand data. To solve this problem, we apply an online method based on the theory of prediction and learning with expert advice to propose an explicit online ordering solution by using the fixed-stock policy as expert advice. With the properties of the gain function, we derive a theoretical result that guarantees, for any given advance-order quantity, the newsvendor’s cumulative gains achieved by the proposed online ordering solution converge to those from the best expert advice in hindsight for a sufficient large horizon. In addition, we extend the problem to the discrete case and obtain the corresponding explicit strategy and performance guarantee. Finally, numerical studies illustrate the effectiveness of the proposed solution, and the newsvendor’s total profits are comparable to the best expert advice. Sensitivity analysis also shows the robustness of the proposed solution.

Suggested Citation

  • Rui Wang & Xiao Yan & Chuanjin Zhu, 2023. "Solving a Distribution-Free Multi-Period Newsvendor Problem With Advance Purchase Discount via an Online Ordering Solution," SAGE Open, , vol. 13(2), pages 21582440231, June.
    • Handle: RePEc:sae:sagope:v:13:y:2023:i:2:p:21582440231181101
    DOI: 10.1177/21582440231181101
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    References listed on IDEAS

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    1. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    2. Yong Zhang & Xingyu Yang & Weiguo Zhang & Weiwei Chen, 2020. "Online ordering rules for the multi-period newsvendor problem with quantity discounts," Annals of Operations Research, Springer, vol. 288(1), pages 495-524, May.
    3. Chen, Jen-Yi & Dada, Maqbool & Hu, Qiaohai (Joice), 2017. "Flexible procurement contracts for competing retailers," European Journal of Operational Research, Elsevier, vol. 259(1), pages 130-142.
    4. Qin, Yan & Wang, Ruoxuan & Vakharia, Asoo J. & Chen, Yuwen & Seref, Michelle M.H., 2011. "The newsvendor problem: Review and directions for future research," European Journal of Operational Research, Elsevier, vol. 213(2), pages 361-374, September.
    5. Yong Zhang & Vladimir Vovk & Weiguo Zhang, 2014. "Probability-free solutions to the non-stationary newsvendor problem," Annals of Operations Research, Springer, vol. 223(1), pages 433-449, December.
    6. Retsef Levi & Georgia Perakis & Joline Uichanco, 2015. "The Data-Driven Newsvendor Problem: New Bounds and Insights," Operations Research, INFORMS, vol. 63(6), pages 1294-1306, December.
    7. Khouja, Moutaz J., 2000. "Optimal ordering, discounting, and pricing in the single-period problem," International Journal of Production Economics, Elsevier, vol. 65(2), pages 201-216, April.
    8. Volodya Vovk, 2001. "Competitive On‐line Statistics," International Statistical Review, International Statistical Institute, vol. 69(2), pages 213-248, August.
    9. Wenjie Tang & Karan Girotra, 2017. "Using Advance Purchase Discount Contracts under Uncertain Information Acquisition Cost," Production and Operations Management, Production and Operations Management Society, vol. 26(8), pages 1553-1567, August.
    10. Boxiao Chen & Xiuli Chao & Hyun-Soo Ahn, 2019. "Coordinating Pricing and Inventory Replenishment with Nonparametric Demand Learning," Operations Research, INFORMS, vol. 67(4), pages 1035-1052, July.
    11. Gah-Yi Ban & Cynthia Rudin, 2019. "The Big Data Newsvendor: Practical Insights from Machine Learning," Operations Research, INFORMS, vol. 67(1), pages 90-108, January.
    12. Katy S. Azoury, 1985. "Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution," Management Science, INFORMS, vol. 31(9), pages 1150-1160, September.
    13. Gan, Xianghua & Sethi, Suresh P. & Xu, Liang, 2019. "Simultaneous Optimization of Contingent and Advance Purchase Orders with Fixed Ordering Costs," Omega, Elsevier, vol. 89(C), pages 227-241.
    14. Alfares, Hesham K. & Elmorra, Hassan H., 2005. "The distribution-free newsboy problem: Extensions to the shortage penalty case," International Journal of Production Economics, Elsevier, vol. 93(1), pages 465-477, January.
    15. Gérard P. Cachon, 2004. "The Allocation of Inventory Risk in a Supply Chain: Push, Pull, and Advance-Purchase Discount Contracts," Management Science, INFORMS, vol. 50(2), pages 222-238, February.
    16. Jinjin Zhang & Xin Li & Yong-Hong Kuo & Yan Chen, 2021. "Coordinating Supply Chain Financing for E-commerce Companies Through a Loan Contract," SAGE Open, , vol. 11(4), pages 21582440211, December.
    17. Zhang, Guoqing, 2010. "The multi-product newsboy problem with supplier quantity discounts and a budget constraint," European Journal of Operational Research, Elsevier, vol. 206(2), pages 350-360, October.
    18. Cvsa, Viswanath & Gilbert, Stephen M., 2002. "Strategic commitment versus postponement in a two-tier supply chain," European Journal of Operational Research, Elsevier, vol. 141(3), pages 526-543, September.
    19. Woonghee Tim Huh & Retsef Levi & Paat Rusmevichientong & James B. Orlin, 2011. "Adaptive Data-Driven Inventory Control with Censored Demand Based on Kaplan-Meier Estimator," Operations Research, INFORMS, vol. 59(4), pages 929-941, August.
    20. Biswajit Sarkar & Chong Zhang & Arunava Majumder & Mitali Sarkar & Yong Won Seo, 2018. "A distribution free newsvendor model with consignment policy and retailer’s royalty reduction," International Journal of Production Research, Taylor & Francis Journals, vol. 56(15), pages 5025-5044, August.
    21. Lingxiu Dong & Kaijie Zhu, 2007. "Two-Wholesale-Price Contracts: Push, Pull, and Advance-Purchase Discount Contracts," Manufacturing & Service Operations Management, INFORMS, vol. 9(3), pages 291-311, January.
    22. Ana Bravo-Moreno, 2019. "Deconstructing “Single†Mothers by Choice: Transcending Blood, Genes, and the Biological Nuclear Family?," SAGE Open, , vol. 9(4), pages 21582440198, December.
    23. Woonghee Tim Huh & Paat Rusmevichientong, 2009. "A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 103-123, February.
    24. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2007. "Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 821-839, November.
    25. Soo-Haeng Cho & Christopher S. Tang, 2013. "Advance Selling in a Supply Chain Under Uncertain Supply and Demand," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 305-319, May.
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