IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v46y2023i2d10.1007_s10878-023-01079-6.html
   My bibliography  Save this article

An improved online replenishment policy and its competitive ratio analysis for a purchase-to-order seller

Author

Listed:
  • Guanqun Ni

    (Shandong University of Technology)

Abstract

For a purchase-to-order seller, there is no inventory and the seller has to purchase goods to fulfill orders already placed. For each purchase, there is a constant ordering cost. For each order, delay cost will be incurred if it is not fulfilled timely. Consequently, there is a tradeoff between the ordering cost and the delay cost for the seller to make replenishment decisions minimizing the total cost. In practice it is impossible or difficult for the seller to know demand information about future orders in advance, and thus this decision-making problem is of an online fashion. In the previous work, this online problem is classified into three cases according to capacity limit and demand quantity, and a 10-competitive online policy is proposed for the general case. In the present paper, an improved 4-competitive online policy is proposed. Besides, an asymptotic lower bound of 2 is derived for this online decision-making problem.

Suggested Citation

  • Guanqun Ni, 2023. "An improved online replenishment policy and its competitive ratio analysis for a purchase-to-order seller," Journal of Combinatorial Optimization, Springer, vol. 46(2), pages 1-14, September.
    • Handle: RePEc:spr:jcomop:v:46:y:2023:i:2:d:10.1007_s10878-023-01079-6
    DOI: 10.1007/s10878-023-01079-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-023-01079-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-023-01079-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wilco Van den Heuvel & Albert P. M. Wagelmans, 2010. "Worst-Case Analysis for a General Class of Online Lot-Sizing Heuristics," Operations Research, INFORMS, vol. 58(1), pages 59-67, February.
    2. Tempelmeier, Horst & Herpers, Sascha, 2011. "Dynamic uncapacitated lot sizing with random demand under a fillrate constraint," European Journal of Operational Research, Elsevier, vol. 212(3), pages 497-507, August.
    3. Dimitris Bertsimas & Aurélie Thiele, 2006. "A Robust Optimization Approach to Inventory Theory," Operations Research, INFORMS, vol. 54(1), pages 150-168, February.
    4. Michael R. Wagner, 2010. "Fully Distribution-Free Profit Maximization: The Inventory Management Case," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 728-741, November.
    5. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    6. Guanqun Ni, 2020. "Replenishment policy for a purchase-to-order seller: a tradeoff between ordering cost and delay cost," International Journal of Production Research, Taylor & Francis Journals, vol. 58(4), pages 1239-1254, February.
    7. Chuen-Teck See & Melvyn Sim, 2010. "Robust Approximation to Multiperiod Inventory Management," Operations Research, INFORMS, vol. 58(3), pages 583-594, June.
    8. Matthieu Godichaud & Lionel Amodeo, 2019. "EOQ inventory models for disassembly systems with disposal and lost sales," International Journal of Production Research, Taylor & Francis Journals, vol. 57(18), pages 5685-5704, September.
    9. Larsen, Kim S. & Wøhlk, Sanne, 2010. "Competitive analysis of the online inventory problem," European Journal of Operational Research, Elsevier, vol. 207(2), pages 685-696, December.
    10. Niels De Smet & El-Houssaine Aghezzaf & Bram Desmet, 2019. "Optimising installation (R,Q) policies in distribution networks with stochastic lead times: a comparative analysis of guaranteed- and stochastic service models," International Journal of Production Research, Taylor & Francis Journals, vol. 57(13), pages 4148-4165, July.
    11. Niv Buchbinder & Tracy Kimbrel & Retsef Levi & Konstantin Makarychev & Maxim Sviridenko, 2013. "Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms," Operations Research, INFORMS, vol. 61(4), pages 1014-1029, August.
    12. Mervegül Kırcı & Işık Biçer & Ralf W. Seifert, 2019. "Optimal replenishment cycle for perishable items facing demand uncertainty in a two-echelon inventory system," International Journal of Production Research, Taylor & Francis Journals, vol. 57(4), pages 1250-1264, February.
    13. Ju‐Liang Zhang & Jian Chen & Chung‐Yee Lee, 2012. "Coordinated pricing and inventory control problems with capacity constraints and fixed ordering cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 376-383, August.
    14. Paolo Priore & Borja Ponte & Rafael Rosillo & David de la Fuente, 2019. "Applying machine learning to the dynamic selection of replenishment policies in fast-changing supply chain environments," International Journal of Production Research, Taylor & Francis Journals, vol. 57(11), pages 3663-3677, June.
    15. Lina Johansson & Fredrik Olsson, 2017. "Quantifying sustainable control of inventory systems with non-linear backorder costs," Annals of Operations Research, Springer, vol. 259(1), pages 217-239, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hamed Mamani & Shima Nassiri & Michael R. Wagner, 2017. "Closed-Form Solutions for Robust Inventory Management," Management Science, INFORMS, vol. 63(5), pages 1625-1643, May.
    2. Wenqiang Dai & Meng Zheng & Xu Chen & Zhuolin Yang, 0. "Online economic ordering problem for deteriorating items with limited price information," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    3. Wenqiang Dai & Meng Zheng & Xu Chen & Zhuolin Yang, 2022. "Online economic ordering problem for deteriorating items with limited price information," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2246-2268, November.
    4. 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.
    5. Xie, Chen & Wang, Liangquan & Yang, Chaolin, 2021. "Robust inventory management with multiple supply sources," European Journal of Operational Research, Elsevier, vol. 295(2), pages 463-474.
    6. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    7. Xin, Linwei & Goldberg, David A., 2021. "Time (in)consistency of multistage distributionally robust inventory models with moment constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1127-1141.
    8. Adam N. Elmachtoub & Retsef Levi, 2016. "Supply Chain Management with Online Customer Selection," Operations Research, INFORMS, vol. 64(2), pages 458-473, April.
    9. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    10. Michael R. Wagner, 2010. "Fully Distribution-Free Profit Maximization: The Inventory Management Case," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 728-741, November.
    11. Qiu, Ruozhen & Shang, Jennifer & Huang, Xiaoyuan, 2014. "Robust inventory decision under distribution uncertainty: A CVaR-based optimization approach," International Journal of Production Economics, Elsevier, vol. 153(C), pages 13-23.
    12. Meng Qi & Ying Cao & Zuo-Jun (Max) Shen, 2022. "Distributionally Robust Conditional Quantile Prediction with Fixed Design," Management Science, INFORMS, vol. 68(3), pages 1639-1658, March.
    13. Wang, Wei & Lan, Yingjie, 2022. "Robust one-way trading with limited number of transactions and heuristics for fixed transaction costs," International Journal of Production Economics, Elsevier, vol. 247(C).
    14. Ben-Tal, A. & den Hertog, D. & De Waegenaere, A.M.B. & Melenberg, B. & Rennen, G., 2011. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Other publications TiSEM 4d43dc51-86d9-4804-8563-9, Tilburg University, School of Economics and Management.
    15. Thevenin, Simon & Ben-Ammar, Oussama & Brahimi, Nadjib, 2022. "Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1199-1215.
    16. Oğuz Solyalı & Jean-François Cordeau & Gilbert Laporte, 2016. "The Impact of Modeling on Robust Inventory Management Under Demand Uncertainty," Management Science, INFORMS, vol. 62(4), pages 1188-1201, April.
    17. Zhi Chen & Melvyn Sim & Peng Xiong, 2020. "Robust Stochastic Optimization Made Easy with RSOME," Management Science, INFORMS, vol. 66(8), pages 3329-3339, August.
    18. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    19. Yingjie Lan & Michael O. Ball & Itir Z. Karaesmen, 2011. "Regret in Overbooking and Fare-Class Allocation for Single Leg," Manufacturing & Service Operations Management, INFORMS, vol. 13(2), pages 194-208, December.
    20. Jiankun Sun & Jan A. Van Mieghem, 2019. "Robust Dual Sourcing Inventory Management: Optimality of Capped Dual Index Policies and Smoothing," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 912-931, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:46:y:2023:i:2:d:10.1007_s10878-023-01079-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.