Single machine scheduling with non-availability interval and optional job rejection

Baruch Mor, Dana Shapira

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This paper studies the single machine scheduling problem with availability constraints and optional job rejection. We consider the non-resumable and resumable variants, and show that the problems remain ordinary NP-hard, even with the rejection possibility extension, by presenting pseudo-polynomial dynamic-programming (DP) solutions. We also present an enhanced running time implementation of the algorithm of Kellerer and Strusevich (Algorithmica 57(4):769–795, 2010) for the resumable scenario without job rejection. This solution is adapted to efficiently solve the machine non-availability problem with a floating interval and the problem of two competing agents on a single machine, with and without optional job rejection. Numerical experiments support the efficiency of our DP implementation.

Original languageEnglish
Pages (from-to)480-497
Number of pages18
JournalJournal of Combinatorial Optimization
Issue number1
StatePublished - Aug 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Dynamic programming
  • Job rejection
  • NP-hard
  • Non-availability interval


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