IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v83y1998i0p23-4010.1023-a1018912114491.html
   My bibliography  Save this article

Batch scheduling with deadlines on parallel machines

Author

Listed:
  • Peter Brucker
  • Mikhail Kovalyov
  • Yakov Shafransky
  • Frank Werner

Abstract

The problem of scheduling G groups of jobs on m parallel machines is considered. Each group consists of several identical jobs. We have to find splittings of groups into batches (i.e. sets of jobs to be processed contiguously) and to schedule the batches on the machines. It is possible for different batches of the same group to be processed concurrently on different machines. However, at any time, a batch can be processed on at most one machine. A sequence-independent machine set-up time is required immediately before a batch of a group is processed. A deadline is associated with each group. The objective is to find a schedule which is feasible with respect to deadlines. The problem is shown to be NP-hard even for the case of two identical machines, unit processing times, unit set-up times and a common deadline. It is strongly NP-hard if machines are uniform, the number of jobs in each group is equal and processing times, set-up times and deadlines are unit. Special cases which are polynomially solvable are discussed. For the general problem, a family {DP ɛ } of approximation algorithms is constructed. A new dynamic rounding technique is used to develop DP ɛ . For any ɛ > 0, DP ɛ delivers a schedule in which the completion time of each group is at most (1 + ɛ) times the value of its deadline if there exists a schedule which is feasible with respect to the deadlines. The time complexity of DP ɛ is O(G 2m+1 /ɛ 2m ). Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Peter Brucker & Mikhail Kovalyov & Yakov Shafransky & Frank Werner, 1998. "Batch scheduling with deadlines on parallel machines," Annals of Operations Research, Springer, vol. 83(0), pages 23-40, October.
    • Handle: RePEc:spr:annopr:v:83:y:1998:i:0:p:23-40:10.1023/a:1018912114491
    DOI: 10.1023/A:1018912114491
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1018912114491
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1018912114491?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. Edwin Cheng, T. C. & Kovalyov, Mikhail Y., 1998. "An exact algorithm for batching and scheduling two part types in a mixed shop: A technical note," International Journal of Production Economics, Elsevier, vol. 55(1), pages 53-56, June.
    2. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    3. Cheng, T.C.E. & Shafransky, Y. & Ng, C.T., 2016. "An alternative approach for proving the NP-hardness of optimization problems," European Journal of Operational Research, Elsevier, vol. 248(1), pages 52-58.
    4. Alexandre Dolgui & Mikhail Y. Kovalyov & Alain Quilliot, 2018. "Simple paths with exact and forbidden lengths," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 78-85, February.

    More about this item

    Statistics

    Access and download statistics

    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:83:y:1998:i:0:p:23-40:10.1023/a:1018912114491. 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.