IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v45y2023i5d10.1007_s10878-023-01064-z.html
   My bibliography  Save this article

An online joint replenishment problem combined with single machine scheduling

Author

Listed:
  • Péter Györgyi

    (ELKH Institute for Computer Science and Control)

  • Tamás Kis

    (ELKH Institute for Computer Science and Control)

  • Tímea Tamási

    (ELKH Institute for Computer Science and Control
    ELTE Eötvös Loránd University)

Abstract

This paper considers a combination of the joint replenishment problem with single machine scheduling. There is a single resource, which is required by all the unit-time jobs, and a job can be started at time point t on the machine if and only if the machine does not process another job at t, and the resource is replenished between its release date and t. Each replenishment has a cost, which is independent of the amount replenished. The objective is to minimize the total replenishment cost plus the maximum flow time of the jobs. We consider the online variant of the problem, where the jobs are released over time, and once a job is inserted into the schedule, its starting time cannot be changed. We propose a deterministic 2-competitive online algorithm for the general input. Moreover, we show that for a certain class of inputs (so-called p-bounded input), the competitive ratio of the algorithm tends to $$\sqrt{2}$$ 2 as the number of jobs tends to infinity. We also derive several lower bounds for the best competitive ratio of any deterministic online algorithm under various assumptions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:5:d:10.1007_s10878-023-01064-z
    DOI: 10.1007/s10878-023-01064-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-023-01064-z
    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/s10878-023-01064-z?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. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2006. "Primal-Dual Algorithms for Deterministic Inventory Problems," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 267-284, May.
    2. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    3. 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.
    4. Péter Györgyi & Tamás Kis & Tímea Tamási & József Békési, 2023. "Joint replenishment meets scheduling," Journal of Scheduling, Springer, vol. 26(1), pages 77-94, February.
    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. Péter Györgyi & Tamás Kis & Tímea Tamási & József Békési, 2023. "Joint replenishment meets scheduling," Journal of Scheduling, Springer, vol. 26(1), pages 77-94, February.
    2. Gautier Stauffer, 2018. "Approximation algorithms for k-echelon extensions of the one warehouse multi-retailer problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 445-473, December.
    3. 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.
    4. Jean-Philippe Gayon & Guillaume Massonnet & Christophe Rapine & Gautier Stauffer, 2017. "Fast Approximation Algorithms for the One-Warehouse Multi-Retailer Problem Under General Cost Structures and Capacity Constraints," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 854-875, August.
    5. Stefanny Ramirez & Laurence H. Brandenburg & Dario Bauso, 2023. "Coordinated Replenishment Game and Learning Under Time Dependency and Uncertainty of the Parameters," Dynamic Games and Applications, Springer, vol. 13(1), pages 326-352, March.
    6. Tamar Cohen-Hillel & Liron Yedidsion, 2018. "The Periodic Joint Replenishment Problem Is Strongly 𝒩𝒫-Hard," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1269-1289, November.
    7. 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.
    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. 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.
    10. Padilla Tinoco, Silvia Valeria & Creemers, Stefan & Boute, Robert N., 2017. "Collaborative shipping under different cost-sharing agreements," European Journal of Operational Research, Elsevier, vol. 263(3), pages 827-837.
    11. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2016. "A coordinated multi-item inventory system for perishables with random lifetime," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 226-237.
    12. Bo Dai & Fenfen Li, 2021. "Joint Inventory Replenishment Planning of an E-Commerce Distribution System with Distribution Centers at Producers’ Locations," Logistics, MDPI, vol. 5(3), pages 1-14, July.
    13. Wang, Lin & He, Jing & Wu, Desheng & Zeng, Yu-Rong, 2012. "A novel differential evolution algorithm for joint replenishment problem under interdependence and its application," International Journal of Production Economics, Elsevier, vol. 135(1), pages 190-198.
    14. Evren Körpeoğlu & Alper Şen & Kemal Güler, 2012. "A private contributions game for joint replenishment," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 67-82, February.
    15. Narayanan, Arunachalam & Robinson, Powell, 2010. "Evaluation of joint replenishment lot-sizing procedures in rolling horizon planning systems," International Journal of Production Economics, Elsevier, vol. 127(1), pages 85-94, September.
    16. Xuefei Shi & Haiyan Wang, 2022. "Design of the cost allocation rule for joint replenishment to an overseas warehouse with a piecewise linear holding cost rate," Operational Research, Springer, vol. 22(5), pages 4905-4929, November.
    17. Pundoor, Guruprasad & Chen, Zhi-Long, 2009. "Joint cyclic production and delivery scheduling in a two-stage supply chain," International Journal of Production Economics, Elsevier, vol. 119(1), pages 55-74, May.
    18. Nguyen, Christine & Dessouky, Maged & Toriello, Alejandro, 2014. "Consolidation strategies for the delivery of perishable products," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 69(C), pages 108-121.
    19. Marcello Braglia & Davide Castellano & Marco Frosolini, 2016. "Joint-replenishment problem under stochastic demands with backorders-lost sales mixtures, controllable lead times, and investment to reduce the major ordering cost," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1108-1120, August.
    20. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2015. "Optimal Replenishment Order Placement in a Finite Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1078-1089, March.

    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:45:y:2023:i:5:d:10.1007_s10878-023-01064-z. 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.