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Online ordering rules for the multi-period newsvendor problem with quantity discounts

Author

Listed:
  • Yong Zhang

    (Guangdong University of Technology)

  • Xingyu Yang

    (Guangdong University of Technology)

  • Weiguo Zhang

    (South China University of Technology)

  • Weiwei Chen

    (Rutgers University)

Abstract

In this paper, we study the multi-period newsvendor problem with quantity discounts and stationary demand, where order quantities need to be decided sequentially over a finite or infinite horizon without making statistical assumption on demands. The Weak Aggregating Algorithm (WAA), which is an online learning method of prediction with expert advice, is applied to the problem. We first consider the all-unit discount case, in which the reduced unit cost is applied to all units in an order. We present explicit online ordering rules by using the fixed-stock strategy as expert advice during the application of WAA. A modified gain function implying convoluted contracts between the newsvendor and his supplier is defined to obtain some theoretical guarantees, which ensure that the newsvendor’s average gains are almost as large as those from the best expert advice for a sufficiently large horizon. Further, we generalize the results to the multi-level incremental discount case, in which there are different unit costs for different quantity ranges. We also extend the results to cases where order quantities are integer-valued, and provide correspondingly online ordering rules and theoretical guarantees. Finally, numerical experiments are performed and show that the average gains obtained by the proposed online ordering rules are comparable to those offered by the best experts in hindsight. The results also indicate that the cumulative gains achieved by the ordering rules for the problem with all-unit discount are larger than those achieved by the ordering rules for the problem with incremental discount; and order quantities increase with the discount level for the all-unit discount while decrease for the incremental discount. The results obtained in this paper can provide competitive online ordering rules for industry managers who need to place long-term continuous orders for perishable products when the demand distribution is unknown.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:288:y:2020:i:1:d:10.1007_s10479-020-03551-6
    DOI: 10.1007/s10479-020-03551-6
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    1. 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.
    2. 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.
    3. Lin, Chen-Sin & Kroll, Dennis E., 1997. "The single-item newsboy problem with dual performance measures and quantity discounts," European Journal of Operational Research, Elsevier, vol. 100(3), pages 562-565, August.
    4. Arpita Roy & Shib Sankar Sana & Kripasindhu Chaudhuri, 2018. "Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model," Annals of Operations Research, Springer, vol. 260(1), pages 481-500, January.
    5. Michael Katehakis & Laurens Smit, 2012. "On computing optimal (Q,r) replenishment policies under quantity discounts," Annals of Operations Research, Springer, vol. 200(1), pages 279-298, November.
    6. Shi, Jianmai & Zhang, Guoqing, 2010. "Multi-product budget-constrained acquisition and pricing with uncertain demand and supplier quantity discounts," International Journal of Production Economics, Elsevier, vol. 128(1), pages 322-331, November.
    7. Parvaneh Samouei & Amir Kheirkhah & Parviz Fattahi, 2015. "A network approach modeling of multi-echelon spare-part inventory system with backorders and quantity discount," Annals of Operations Research, Springer, vol. 226(1), pages 551-563, March.
    8. 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.
    9. 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.
    10. Moon, Ilkyeong & Choi, Sangjin, 1997. "Distribution free procedures for make-to-order (MTO), make-in-advance (MIA), and composite policies," International Journal of Production Economics, Elsevier, vol. 48(1), pages 21-28, January.
    11. James V. Jucker & Meir J. Rosenblatt, 1985. "Single‐period inventory models with demand uncertainty and quantity discounts: Behavioral implications and a new solution procedure," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(4), pages 537-550, November.
    12. 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.
    13. Arunava Majumder & Rekha Guchhait & Biswajit Sarkar, 2017. "Manufacturing quality improvement and setup cost reduction in a vendor-buyer supply chain model," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 11(5), pages 588-612.
    14. Khouja, Moutaz, 1995. "The newsboy problem under progressive multiple discounts," European Journal of Operational Research, Elsevier, vol. 84(2), pages 458-466, July.
    15. 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.
    16. Sarkar, Biswajit & Moon, Ilkyeong, 2014. "Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process," International Journal of Production Economics, Elsevier, vol. 155(C), pages 204-213.
    17. 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.
    18. 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.
    19. Andreas Thorsen & Tao Yao, 2017. "Robust inventory control under demand and lead time uncertainty," Annals of Operations Research, Springer, vol. 257(1), pages 207-236, October.
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    4. Shuangsheng Wu & Qi Li, 2021. "Emergency Quantity Discount Contract with Suppliers Risk Aversion under Stochastic Price," Mathematics, MDPI, vol. 9(15), pages 1-12, July.

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