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

Author

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  • 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
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    References listed on IDEAS

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    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)

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