Minimizing the weighted number of tardy jobs via (max,+)-convolutions

Danny Hermelin, Hendrik Molter, Dvir Shabtay

Research output: Contribution to journalArticlepeer-review


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).
Original languageAmerican English
JournalINFORMS Journal on Computing
StatePublished Online - 21 Dec 2023


  • weighted number of tardy jobs
  • Single machine scheduling
  • pseudo-polynomial algorithms
  • Conditional lower bounds


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