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Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms

Author

Listed:
  • Niv Buchbinder

    (Statistics and Operations Research Department, Tel Aviv University, Ramat Aviv 6997801, Israel)

  • Tracy Kimbrel

    (National Science Foundation, Arlington, Virginia 22230)

  • Retsef Levi

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139)

  • Konstantin Makarychev

    (Microsoft Research, Redmond, Washington 98052)

  • Maxim Sviridenko

    (Department of Computer Science, University of Warwick, Coventry CV4 7AL, United Kingdom)

Abstract

In this paper, we study an online make-to-order variant of the classical joint replenishment problem (JRP) that has been studied extensively over the years and plays a fundamental role in broader planning issues, such as the management of supply chains. In contrast to the traditional approaches of the stochastic inventory theory, we study the problem using competitive analysis against a worst-case adversary.Our main result is a 3-competitive deterministic algorithm for the online version of the JRP. We also prove a lower bound of approximately 2.64 on the competitiveness of any deterministic online algorithm for the problem. Our algorithm is based on a novel primal-dual approach using a new linear programming relaxation of the offline JRP model. The primal-dual approach that we propose departs from previous primal-dual and online algorithms in rather significant ways. We believe that this approach can extend the range of problems to which online and primal-dual algorithms can be applied and analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:4:p:1014-1029
    DOI: 10.1287/opre.2013.1188
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    References listed on IDEAS

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    Cited by:

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    3. Péter Györgyi & Tamás Kis & Tímea Tamási, 2023. "An online joint replenishment problem combined with single machine scheduling," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-20, July.
    4. 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.
    5. He-Yau Kang & Amy H.I. Lee & Chien-Wei Wu & Cheng-Han Lee, 2017. "An efficient method for dynamic-demand joint replenishment problem with multiple suppliers and multiple vehicles," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1065-1084, February.
    6. Esmaeil Keyvanshokooh & Cong Shi & Mark P. Van Oyen, 2021. "Online Advance Scheduling with Overtime: A Primal-Dual Approach," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 246-266, 1-2.
    7. Péter Györgyi & Tamás Kis & Tímea Tamási & József Békési, 2023. "Joint replenishment meets scheduling," Journal of Scheduling, Springer, vol. 26(1), pages 77-94, February.
    8. Xinshang Wang & Van-Anh Truong, 2018. "Multi-Priority Online Scheduling with Cancellations," Operations Research, INFORMS, vol. 66(1), pages 104-122, January.

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