IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v129y2004i1p21-3210.1023-banor.0000030679.25466.02.html
   My bibliography  Save this article

Maximization Problems in Single Machine Scheduling

Author

Listed:
  • Mohamed Aloulou
  • Mikhail Kovalyov
  • Marie-Claude Portmann

Abstract

Problems of scheduling n jobs on a single machine to maximize regular objective functions are studied. Precedence constraints may be given on the set of jobs and the jobs may have different release times. Schedules of interest are only those for which the jobs cannot be shifted to start earlier without changing job sequence or violating release times or precedence constraints. Solutions to the maximization problems provide an information about how poorly such schedules can perform. The most general problem of maximizing maximum cost is shown to be reducible to n similar problems of scheduling n−1 jobs available at the same time. It is solved in O(mn+n 2 ) time, where m is the number of arcs in the precedence graph. When all release times are equal to zero, the problem of maximizing the total weighted completion time or the weighted number of late jobs is equivalent to its minimization counterpart with precedence constraints reversed with respect to the original ones. If there are no precedence constraints, the problem of maximizing arbitrary regular function reduces to n similar problems of scheduling n−1 jobs available at the same time. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Mohamed Aloulou & Mikhail Kovalyov & Marie-Claude Portmann, 2004. "Maximization Problems in Single Machine Scheduling," Annals of Operations Research, Springer, vol. 129(1), pages 21-32, July.
    • Handle: RePEc:spr:annopr:v:129:y:2004:i:1:p:21-32:10.1023/b:anor.0000030679.25466.02
    DOI: 10.1023/B:ANOR.0000030679.25466.02
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/B:ANOR.0000030679.25466.02
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/B:ANOR.0000030679.25466.02?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2013. "Single machine total tardiness maximization problems: complexity and algorithms," Annals of Operations Research, Springer, vol. 207(1), pages 121-136, August.
    2. Xin Chen & Sergey Kovalev & Małgorzata Sterna & Jacek Błażewicz, 2021. "Mirror scheduling problems with early work and late work criteria," Journal of Scheduling, Springer, vol. 24(5), pages 483-487, October.
    3. Sergey Kovalev, 2015. "Maximizing total tardiness on a single machine in $$O(n^2)$$ O ( n 2 ) time via a reduction to half-product minimization," Annals of Operations Research, Springer, vol. 235(1), pages 815-819, December.
    4. Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2012. "Transforming a pseudo-polynomial algorithm for the single machine total tardiness maximization problem into a polynomial one," Annals of Operations Research, Springer, vol. 196(1), pages 247-261, July.

    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:annopr:v:129:y:2004:i:1:p:21-32:10.1023/b:anor.0000030679.25466.02. 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: 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.