IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v324y2025i1p40-48.html
   My bibliography  Save this article

Single-machine scheduling with fixed energy recharging times to minimize the number of late jobs and the number of just-in-time jobs: A parameterized complexity analysis

Author

Listed:
  • Yu, Renjie
  • Oron, Daniel

Abstract

We study single-machine scheduling problems where processing each job requires both processing time and rechargeable energy. Subject to a predefined energy capacity, energy can be recharged after each job during a fixed recharging period. Our focus is on two due date-related scheduling criteria: minimizing the number of late jobs and maximizing the weighted number of jobs completed exactly at their due dates. This study aims to analyze the parameterized tractability of the two problems and develop fixed-parameter algorithms with respect to three natural parameters: the number of different due dates vd, the number of different processing times vp, and the number of different energy consumptions ve. Following the proofs of NP-hardness across several contexts, we demonstrate that both problems remain intractable when parameterized by vd and vp. To complement our results, we show that both problems become fixed-parameter tractable (FPT) when parameterized by ve and vd, and are solvable in polynomial time when both ve and vp are constant.

Suggested Citation

  • Yu, Renjie & Oron, Daniel, 2025. "Single-machine scheduling with fixed energy recharging times to minimize the number of late jobs and the number of just-in-time jobs: A parameterized complexity analysis," European Journal of Operational Research, Elsevier, vol. 324(1), pages 40-48.
    • Handle: RePEc:eee:ejores:v:324:y:2025:i:1:p:40-48
    DOI: 10.1016/j.ejor.2025.01.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221725000323
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2025.01.007?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.

    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:eee:ejores:v:324:y:2025:i:1:p:40-48. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.