IDEAS home Printed from
   My bibliography  Save this article

A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times


  • Edward Sewell


  • Jason Sauppe


  • David Morrison


  • Sheldon Jacobson


  • Gio Kao



This paper presents a Branch, Bound, and Remember (BB&R) exact algorithm using the Cyclic Best First Search (CBFS) exploration strategy for solving the $${1|ST_{sd}|\sum T_{i}}$$ scheduling problem, a single machine scheduling problem with sequence dependent setup times where the objective is to find a schedule with minimum total tardiness. The BB&R algorithm incorporates memory-based dominance rules to reduce the solution search space. The algorithm creates schedules in the reverse direction for problems where fewer than half the jobs are expected to be tardy. In addition, a branch and bound algorithm is used to efficiently compute tighter lower bounds for the problem. This paper also presents a counterexample for a previously reported exact algorithm in Luo and Chu (Appl Math Comput 183(1):575–588, 2006 ) and Luo et al. (Int J Prod Res 44(17):3367–3378, 2006 ). Computational experiments demonstrate that the algorithm is two orders of magnitude faster than the fastest exact algorithm that has appeared in the literature. Computational experiments on two sets of benchmark problems demonstrate that the CBFS search exploration strategy can be used as an effective heuristic on problems that are too large to solve to optimality. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Edward Sewell & Jason Sauppe & David Morrison & Sheldon Jacobson & Gio Kao, 2012. "A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times," Journal of Global Optimization, Springer, vol. 54(4), pages 791-812, December.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:4:p:791-812
    DOI: 10.1007/s10898-011-9793-z

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    1. Tan, K. C. & Narasimhan, R., 1997. "Minimizing tardiness on a single processor with sequence-dependent setup times: a simulated annealing approach," Omega, Elsevier, vol. 25(6), pages 619-634, December.
    2. Gupta, Skylab R. & Smith, Jeffrey S., 2006. "Algorithms for single machine total tardiness scheduling with sequence dependent setups," European Journal of Operational Research, Elsevier, vol. 175(2), pages 722-739, December.
    3. Luo, Xiaochuan & Chu, Chengbin, 2007. "A branch-and-bound algorithm of the single machine schedule with sequence-dependent setup times for minimizing maximum tardiness," European Journal of Operational Research, Elsevier, vol. 180(1), pages 68-81, July.
    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:spr:jglopt:v:54:y:2012:i:4:p:791-812. 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: (Sonal Shukla) or (Rebekah McClure). 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.