Minsum scheduling with acceptable lead-times and optional job rejection

Baruch Mor, Dana Shapira

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In our current fast-paced era, customers are often willing to pay extra premium for shorter lead times, which motivates further research on the scheduling problem with due-date assignment and customer-specified lead times. As part of this effort, we extend the classic minsum ‘DIF’ scheduling model to allow optional job-rejection, thus adding an important component of real-life applications, namely, the possibility that the scheduler decides to process only a subset of the jobs and outsource the disjoint set. The scheduler is penalised for rejecting certain jobs by setting job-dependent rejection costs, and he is limited by a given upper bound on the total rejection cost. The most general version of the minsum DIF problem includes job-dependent cost parameters and lead-times, and it is strongly NP-hard. Therefore, we study six variants of the problem, where either only the cost parameters or the lead-times are job dependent. All alternatives are extended by optional job-rejection that possibly bounds the constraints or the underlying cost functions. We establish that all studied problems are NP-hard in the ordinary sense and present pseudo-polynomial dynamic programming algorithms and extensive numerical studies for most solutions.

Original languageEnglish
Pages (from-to)1073-1091
Number of pages19
JournalOptimization Letters
Issue number3
StatePublished - Apr 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • Due-date assignment
  • Dynamic programming
  • Job-rejection
  • Minsum
  • Single-machine scheduling


Dive into the research topics of 'Minsum scheduling with acceptable lead-times and optional job rejection'. Together they form a unique fingerprint.

Cite this