A note on the single machine CON and CONW problems with lot scheduling

Baruch Mor, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We study extensions of the classical single machine common due-date (CON) and common due-window (CONW) assignment problems to the setting of lot scheduling. In the CON problem, all the jobs share a common due-date, and jobs completed prior to or after the due-date are penalized according to their earliness/tardiness. In CONW, there exists a time interval, such that jobs completed within this interval are not penalized. In both cases the due-date/due-window are decision variables. In lot scheduling, a number of customer orders of different sizes may be processed in the same lot. We allow order splitting between consecutive lots. The objective is to find the order allocation to lots, such that the total cost of earliness, tardiness and due-date/due-window is minimized. Given n orders, and under the very realistic assumption that the lot capacity is of the order of n, we introduce polynomial time dynamic programming algorithms for both extensions. Our numerical tests indicate that both algorithms can easily solve medium-size problems.

Original languageAmerican English
Pages (from-to)327-338
Number of pages12
JournalJournal of Combinatorial Optimization
Issue number2
StatePublished - Aug 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.


  • Common due-date
  • Common due-window
  • Dynamic programming
  • Lot scheduling
  • Single machine


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