On the tractability of hard scheduling problems with generalized due-dates with respect to the number of different due-dates

Gur Mosheiov, Daniel Oron*, Dvir Shabtay

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study two NP-hard single-machine scheduling problems with generalized due-dates. In such problems, due-dates are associated with positions in the job sequence rather than with jobs. Accordingly, the job that is assigned to position j in the job processing order (job sequence), is assigned with a predefined due-date, δj. In the first problem, the objective consists of finding a job schedule that minimizes the maximal absolute lateness, while in the second problem, we aim to maximize the weighted number of jobs completed exactly at their due-date. Both problems are known to be strongly NP-hard when the instance includes an arbitrary number of different due-dates. Our objective is to study the tractability of both problems with respect to the number of different due-dates in the instance, νd. We show that both problems remain NP-hard even when νd= 2 , and are solvable in pseudo-polynomial time when the value of νd is upper bounded by a constant. To complement our results, we show that both problems are fixed parameterized tractable (FPT) when we combine the two parameters of number of different due-dates (νd) and number of different processing times (νp).

Original languageAmerican English
Pages (from-to)577-587
Number of pages11
JournalJournal of Scheduling
Volume25
Issue number5
DOIs
StatePublished - Oct 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).

Keywords

  • Generalized due-dates
  • NP-hard
  • Parameterized complexity
  • Pseudo-polynomial time algorithm
  • Scheduling
  • Single machine

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