IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v36y2024i3p836-848.html
   My bibliography  Save this article

Minimizing the Weighted Number of Tardy Jobs via (max,+)-Convolutions

Author

Listed:
  • Danny Hermelin

    (Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel)

  • Hendrik Molter

    (Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel)

  • Dvir Shabtay

    (Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel)

Abstract

In this paper we consider the fundamental scheduling problem of minimizing the weighted number of tardy jobs on a single machine. We present a simple pseudo polynomial-time algorithm for this problem that improves upon the classical Lawler and Moore algorithm from the late 60’s under certain scenarios and parameter settings. Our algorithm uses (max,+)-convolutions as its main tool, exploiting recent improved algorithms for computing such convolutions, and obtains several different running times depending on the specific improvement used. We also provide a related lower bound for the problem under a variant of the well-known Strong Exponential Time Hypothesis (SETH).

Suggested Citation

  • Danny Hermelin & Hendrik Molter & Dvir Shabtay, 2024. "Minimizing the Weighted Number of Tardy Jobs via (max,+)-Convolutions," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 836-848, May.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:3:p:836-848
    DOI: 10.1287/ijoc.2022.0307
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2022.0307
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2022.0307?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
    ---><---

    References listed on IDEAS

    as
    1. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    2. Danny Hermelin & Shlomo Karhi & Michael Pinedo & Dvir Shabtay, 2021. "New algorithms for minimizing the weighted number of tardy jobs on a single machine," Annals of Operations Research, Springer, vol. 298(1), pages 271-287, March.
    3. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    4. M'Hallah, Rym & Bulfin, R. L., 2003. "Minimizing the weighted number of tardy jobs on a single machine," European Journal of Operational Research, Elsevier, vol. 145(1), pages 45-56, February.
    Full references (including those not matched with items on IDEAS)

    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. Hejl, Lukáš & Šůcha, Přemysl & Novák, Antonín & Hanzálek, Zdeněk, 2022. "Minimizing the weighted number of tardy jobs on a single machine: Strongly correlated instances," European Journal of Operational Research, Elsevier, vol. 298(2), pages 413-424.
    2. M'Hallah, Rym & Bulfin, R.L., 2007. "Minimizing the weighted number of tardy jobs on a single machine with release dates," European Journal of Operational Research, Elsevier, vol. 176(2), pages 727-744, January.
    3. Danny Hermelin & Shlomo Karhi & Michael Pinedo & Dvir Shabtay, 2021. "New algorithms for minimizing the weighted number of tardy jobs on a single machine," Annals of Operations Research, Springer, vol. 298(1), pages 271-287, March.
    4. Chen, Ke & Cheng, T.C.E. & Huang, Hailiang & Ji, Min & Yao, Danli, 2023. "Single-machine scheduling with autonomous and induced learning to minimize total weighted number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 309(1), pages 24-34.
    5. Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    6. Shabtay, Dvir & Steiner, George & Zhang, Rui, 2016. "Optimal coordination of resource allocation, due date assignment and scheduling decisions," Omega, Elsevier, vol. 65(C), pages 41-54.
    7. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 325-332, June.
    8. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1994. "Due‐date assignment and early/tardy scheduling on identical parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 17-32, February.
    9. Iida, Hiroshi, 2011. "How to solve the collapsing subset-sum problem revisited," ビジネス創造センターディスカッション・ペーパー (Discussion papers of the Center for Business Creation) 10252/4432, Otaru University of Commerce.
    10. Vairaktarakis, George L., 2000. "Robust multi-item newsboy models with a budget constraint," International Journal of Production Economics, Elsevier, vol. 66(3), pages 213-226, July.
    11. Glover, Fred, 2013. "Advanced greedy algorithms and surrogate constraint methods for linear and quadratic knapsack and covering problems," European Journal of Operational Research, Elsevier, vol. 230(2), pages 212-225.
    12. Marc Goerigk, 2014. "A note on upper bounds to the robust knapsack problem with discrete scenarios," Annals of Operations Research, Springer, vol. 223(1), pages 461-469, December.
    13. Willem E. de Paepe & Jan Karel Lenstra & Jiri Sgall & René A. Sitters & Leen Stougie, 2004. "Computer-Aided Complexity Classification of Dial-a-Ride Problems," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 120-132, May.
    14. Rasti-Barzoki, Morteza & Hejazi, Seyed Reza, 2013. "Minimizing the weighted number of tardy jobs with due date assignment and capacity-constrained deliveries for multiple customers in supply chains," European Journal of Operational Research, Elsevier, vol. 228(2), pages 345-357.
    15. Viet Anh Nguyen & Fan Zhang & Shanshan Wang & Jose Blanchet & Erick Delage & Yinyu Ye, 2021. "Robustifying Conditional Portfolio Decisions via Optimal Transport," Papers 2103.16451, arXiv.org, revised Apr 2024.
    16. Jooken, Jorik & Leyman, Pieter & De Causmaecker, Patrick, 2022. "A new class of hard problem instances for the 0–1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 841-854.
    17. Dunstall, Simon & Wirth, Andrew, 2005. "A comparison of branch-and-bound algorithms for a family scheduling problem with identical parallel machines," European Journal of Operational Research, Elsevier, vol. 167(2), pages 283-296, December.
    18. M Hifi & M Michrafy & A Sbihi, 2004. "Heuristic algorithms for the multiple-choice multidimensional knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1323-1332, December.
    19. 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.
    20. Herweg, Fabian & Müller, Daniel, 2008. "The Optimality of Simple Contracts: Moral Hazard and Loss Aversion," Bonn Econ Discussion Papers 17/2008, University of Bonn, Bonn Graduate School of Economics (BGSE).

    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:inm:orijoc:v:36:y:2024:i:3:p:836-848. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.