The single machine CON problem with unavailability period

Enrique Gerstl*, Gur Mosheiov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The classical CON problem focuses on scheduling jobs on a single machine sharing a common due-date. We study the CON problem with a given unavailability period. The basic problem (assuming linear job-independent costs and no idle times prior to or after the unavailability period) is easily shown to be NP-hard, and an efficient pseudo-polynomial dynamic programming algorithm is introduced. Extensions of the algorithm to general monotonic job-independent costs, and to linear job-dependent costs are studied as well. All algorithms are tested numerically, and are shown to produce optimal schedules in reasonable time. Then we allow idle times, verify that this case is NP-hard in the ordinary sense as well, and introduce a greedy-type heuristic. Numerical tests are performed, and the results indicate that the heuristic performs extremely well.

Original languageAmerican English
Pages (from-to)824-838
Number of pages15
JournalInternational Journal of Production Research
Issue number3
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.


  • Scheduling
  • dynamic programming
  • heuristics
  • single machine
  • unavailability period


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