IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v54y2012i4p791-812.html
   My bibliography  Save this article

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

Author

Listed:
  • Edward Sewell
  • Jason Sauppe
  • David Morrison
  • Sheldon Jacobson
  • Gio Kao

Abstract

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-011-9793-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-011-9793-z?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.

    References listed on IDEAS

    as
    1. Thomas L. Morin & Roy E. Marsten, 1976. "Branch-and-Bound Strategies for Dynamic Programming," Operations Research, INFORMS, vol. 24(4), pages 611-627, August.
    2. C Gagné & M Gravel & W L Price, 2005. "Using metaheuristic compromise programming for the solution of multiple-objective scheduling problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 687-698, June.
    3. C Gagné & W L Price & M Gravel, 2002. "Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(8), pages 895-906, August.
    4. 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.
    5. 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.
    6. 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)

    Citations

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


    Cited by:

    1. Wenda Zhang & Jason J. Sauppe & Sheldon H. Jacobson, 2023. "Results for the close-enough traveling salesman problem with a branch-and-bound algorithm," Computational Optimization and Applications, Springer, vol. 85(2), pages 369-407, June.
    2. David R. Morrison & Edward C. Sewell & Sheldon H. Jacobson, 2016. "Solving the Pricing Problem in a Branch-and-Price Algorithm for Graph Coloring Using Zero-Suppressed Binary Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 67-82, February.
    3. David R. Morrison & Jason J. Sauppe & Edward C. Sewell & Sheldon H. Jacobson, 2014. "A Wide Branching Strategy for the Graph Coloring Problem," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 704-717, November.
    4. Yolmeh, Abdolmajid & Baykal-Gürsoy, Melike, 2021. "Weighted network search games with multiple hidden objects and multiple search teams," European Journal of Operational Research, Elsevier, vol. 289(1), pages 338-349.
    5. David R. Morrison & Jason J. Sauppe & Wenda Zhang & Sheldon H. Jacobson & Edward C. Sewell, 2017. "Cyclic best first search: Using contours to guide branch‐and‐bound algorithms," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 64-82, February.
    6. Geert De Maere & Jason A. D. Atkin & Edmund K. Burke, 2018. "Pruning Rules for Optimal Runway Sequencing," Transportation Science, INFORMS, vol. 52(4), pages 898-916, August.
    7. Morrison, David R. & Sewell, Edward C. & Jacobson, Sheldon H., 2014. "An application of the branch, bound, and remember algorithm to a new simple assembly line balancing dataset," European Journal of Operational Research, Elsevier, vol. 236(2), pages 403-409.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hanen Akrout & Bassem Jarboui & Patrick Siarry & Abdelwaheb Rebaï, 2012. "A GRASP based on DE to solve single machine scheduling problem with SDST," Computational Optimization and Applications, Springer, vol. 51(1), pages 411-435, January.
    2. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    3. S-W Lin & K-C Ying, 2008. "A hybrid approach for single-machine tardiness problems with sequence-dependent setup times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(8), pages 1109-1119, August.
    4. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    5. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    6. C Gagné & M Gravel & W L Price, 2005. "Using metaheuristic compromise programming for the solution of multiple-objective scheduling problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 687-698, June.
    7. 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.
    8. Anzanello, Michel J. & Fogliatto, Flavio S. & Santos, Luana, 2014. "Learning dependent job scheduling in mass customized scenarios considering ergonomic factors," International Journal of Production Economics, Elsevier, vol. 154(C), pages 136-145.
    9. Og[breve]uz, Ceyda & Sibel Salman, F. & Bilgintürk YalçIn, Zehra, 2010. "Order acceptance and scheduling decisions in make-to-order systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 200-211, May.
    10. Lubbecke, Marco E., 2005. "Dual variable based fathoming in dynamic programs for column generation," European Journal of Operational Research, Elsevier, vol. 162(1), pages 122-125, April.
    11. Ferretti, Ivan & Zanoni, Simone & Zavanella, Lucio, 2006. "Production-inventory scheduling using Ant System metaheuristic," International Journal of Production Economics, Elsevier, vol. 104(2), pages 317-326, December.
    12. N Nekoiemehr & G Moslehi, 2011. "Minimizing the sum of maximum earliness and maximum tardiness in the single-machine scheduling problem with sequence-dependent setup time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1403-1412, July.
    13. Yolmeh, Abdolmajid & Baykal-Gürsoy, Melike, 2021. "Weighted network search games with multiple hidden objects and multiple search teams," European Journal of Operational Research, Elsevier, vol. 289(1), pages 338-349.
    14. Miguel A. González & Juan José Palacios & Camino R. Vela & Alejandro Hernández-Arauzo, 2017. "Scatter search for minimizing weighted tardiness in a single machine scheduling with setups," Journal of Heuristics, Springer, vol. 23(2), pages 81-110, June.
    15. Jayaraman, Vaidyanathan & Ross, Anthony, 2003. "A simulated annealing methodology to distribution network design and management," European Journal of Operational Research, Elsevier, vol. 144(3), pages 629-645, February.
    16. E. C. Sewell & S. H. Jacobson, 2012. "A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 433-442, August.
    17. Herr, Oliver & Goel, Asvin, 2016. "Minimising total tardiness for a single machine scheduling problem with family setups and resource constraints," European Journal of Operational Research, Elsevier, vol. 248(1), pages 123-135.
    18. Franca, Paulo M. & Mendes, Alexandre & Moscato, Pablo, 2001. "A memetic algorithm for the total tardiness single machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 132(1), pages 224-242, July.
    19. Khachai, Daniil & Sadykov, Ruslan & Battaia, Olga & Khachay, Michael, 2023. "Precedence constrained generalized traveling salesman problem: Polyhedral study, formulations, and branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 309(2), pages 488-505.
    20. Allahverdi, Ali, 2015. "The third comprehensive survey on scheduling problems with setup times/costs," European Journal of Operational Research, Elsevier, vol. 246(2), pages 345-378.

    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:jglopt:v:54:y:2012:i:4:p:791-812. 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.

    If CitEc recognized a bibliographic 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.

    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.