Single machine scheduling to maximize the number of on-time jobs with generalized due-dates

Enrique Gerstl, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In scheduling problems with generalized due dates (gdd), the due dates are specified according to their position in the sequence, and the j-th due date is assigned to the job in the j-th position. We study a single-machine problem with generalized due dates, where the objective is maximizing the number of jobs completed exactly on time. We prove that the problem is NP-hard in the strong sense. To our knowledge, this is the only example of a scheduling problem where the job-specific version has a polynomial-time solution, and the gdd version is strongly NP-hard. A branch-and-bound (B&B) algorithm, an integer programming (IP)-based procedure, and an efficient heuristic are introduced and tested. Both the B&B algorithm and the IP-based solution procedure can solve most medium-sized problems in a reasonable computational effort. The heuristic serves as the initial step of the B&B algorithm and in itself obtains the optimum in most cases. We also study two special cases: max-on-time for a given job sequence and max-on-time with unit-execution-time jobs. For both cases, polynomial-time dynamic programming algorithms are introduced, and large-sized problems are easily solved.

Original languageAmerican English
Pages (from-to)289-299
Number of pages11
JournalJournal of Scheduling
Issue number3
StatePublished - 1 Jun 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.


  • Branch-and-bound algorithm
  • Generalized due dates
  • Heuristic
  • NP-hardness
  • Scheduling
  • Single machine


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