IDEAS home Printed from
   My bibliography  Save this article

Johnson's rule, composite jobs and the relocation problem


  • Cheng, T.C.E.
  • Lin, B.M.T.


Two-machine flowshop scheduling to minimize makespan is one of the most well-known classical scheduling problems. Johnson's rule for solving this problem has been widely cited in the literature. We introduce in this paper the concept of composite job, which is an artificially constructed job with processing times such that it will incur the same amount of idle time on the second machine as that incurred by a chain of jobs in a given processing sequence. This concept due to Kurisu first appeared in 1976 to deal with the two-machine flowshop scheduling problem involving precedence constraints among the jobs. We show that this concept can be applied to reduce the computational time to solve some related scheduling problems. We also establish a link between solving the two-machine flowshop makespan minimization problem using Johnson's rule and the relocation problem introduced by Kaplan. We present an intuitive interpretation of Johnson's rule in the context of the relocation problem.

Suggested Citation

  • Cheng, T.C.E. & Lin, B.M.T., 2009. "Johnson's rule, composite jobs and the relocation problem," European Journal of Operational Research, Elsevier, vol. 192(3), pages 1008-1013, February.
  • Handle: RePEc:eee:ejores:v:192:y:2009:i:3:p:1008-1013

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. E H Kaplan, 1986. "Relocation models for public housing redevelopment programs," Environment and Planning B: Planning and Design, Pion Ltd, London, vol. 13(1), pages 5-19, January.
    2. Kamburowski, J., 1997. "The nature of simplicity of Johnson's algorithm," Omega, Elsevier, vol. 25(5), pages 581-584, October.
    3. Kaplan, Edward H. & Amir, Amihood, 1988. "A fast feasibility test for relocation problems," European Journal of Operational Research, Elsevier, vol. 35(2), pages 201-206, May.
    Full references (including those not matched with items on IDEAS)


    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:192:y:2009:i:3:p:1008-1013. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.