Scheduling on a proportionate flowshop to minimise total late work

Enrique Gerstl, Baruch Mor, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We study a scheduling problem to minimise total late work, i.e. each job is penalised according to the duration of its parts scheduled after its due-date. The machine setting is an m-machine proportionate flow shop. Two versions of the problem are studied: (i) the case that total late work refers to the last operation of the job (i.e. the operation performed on the last machine of the flow shop); (ii) the case that total late work refers to all the operations (on all machines). Both versions are known to be NP-hard. We prove a crucial property of an optimal schedule, and consequently introduce efficient pseudo-polynomial dynamic programming algorithms for the two versions. The dynamic programming algorithms are tested numerically and proved to perform well on large size instances.

Original languageAmerican English
Pages (from-to)531-543
Number of pages13
JournalInternational Journal of Production Research
Issue number2
StatePublished - 17 Jan 2019

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.


  • combinatorial optimization
  • dynamic programming
  • flow shop
  • scheduling
  • sequencing
  • total late work


Dive into the research topics of 'Scheduling on a proportionate flowshop to minimise total late work'. Together they form a unique fingerprint.

Cite this