Minimizing maximum earliness on parallel identical machines

Micha Mandel, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper addresses the scheduling problem of minimizing maximum earliness (or more generally - maximizing minimum lateness) on parallel identical machines. We prove that the two-machine case is NP-hard in the ordinary sense, and introduce a pseudo-polynomial dynamic programming algorithm for this case. When the number of machines is arbitrary, the problem is shown to be NP-hard in the strong sense. Then we introduce an efficient heuristic and two simple upper bounds on the optimal minimum lateness value. Finally we provide an extensive numerical study which indicates that the heuristic performs well in various job and machine settings. Scope and purpose In recent years many researchers have focused on minimizing both earliness and tardiness costs. Only a few studies have considered problems with (maximum or total) earliness as the sole performance measure. We believe that the earliness measure is appropriate for many real-life settings, where the main cost component is the earliness (inventory) cost, and the tardiness (positive lateness) cost component is negligible. Our paper studies the scheduling problem of minmax earliness on parallel identical machines: we analyze the complexity of the problem, and introduce an efficient heuristic and simple bounds on the optimal cost.

Original languageAmerican English
Pages (from-to)317-327
Number of pages11
JournalComputers and Operations Research
Issue number4
StatePublished - Apr 2001

Bibliographical note

Funding Information:
The authors are grateful to an anonymous referee for very helpful comments which improved both the content and presentation of the paper. This research was supported in part by the Recanati Fund of The School of Business, The Hebrew University, Jerusalem, Israel.


  • Earliness
  • Heuristics
  • Lateness
  • Parallel machines
  • Scheduling


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