Scheduling with a due-window for acceptable lead-times

Enrique Gerstl, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Due-dates are often determined during sales negotiations in two stages: (i) in the pre-sale stage, the customer provides a time interval (due-window) of his acceptable due-dates, (ii) in the second stage, the parties agree on the delivery penalties. Thus, the contract reflects penalties of both parts of the sales negotiations: earliness/tardiness penalties of the due-dates (as a function of the deviation from the agreed upon due-window), and earliness/tardiness penalties of the actual delivery times (as a function of the deviation from the due-dates). We model this setting of a two-stage negotiation on a single machine, and reduce the problem to a well-known setting of minimizing the weighted earliness/tardiness with a given (fixed) due-window. We adopt (and correct) a pseudo-polynomial dynamic programming algorithm for this NP-hard problem. The algorithm is extended to a setting of parallel identical machines, verifying that this case remains NP-hard in the ordinary sense. Moreover, an efficient greedy heuristic and a tight lower bound are introduced and tested. Extremely small optimality gaps are obtained in our numerical tests.

Original languageAmerican English
Pages (from-to)1578-1588
Number of pages11
JournalJournal of the Operational Research Society
Issue number9
StatePublished - 1 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015 Operational Research Society Ltd.


  • due-window assignment
  • earliness/tardiness
  • lead-time
  • scheduling
  • single machine


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