Scheduling job classes on uniform machines

Enrique Gerstl, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study a scheduling problem with job classes on parallel uniform machines. All the jobs of a given class share a common due-date. General, non-decreasing and class-dependent earliness and tardiness cost functions are assumed. Two objectives are considered: (i) minmax, where the scheduler is required to minimize the maximum earliness/tardiness cost among all the jobs and (ii) minmax-minsum, where the scheduler minimizes the sum of the maximum earliness/tardiness cost in all job classes. The problem is easily shown to be NP-hard, and we focus here on the introduction of simple heuristics. We introduce LPT (Largest Processing Time first)-based heuristics for the allocation of jobs to machines within each class, followed by a solution of an appropriate non-linear program, which produces for this job allocation an optimal schedule of the classes. We also propose a lower bound, based on balancing the load on the machines. Our numerical tests indicate that the heuristics result in very small optimality gaps.

Original languageAmerican English
Pages (from-to)1927-1932
Number of pages6
JournalComputers and Operations Research
Issue number9
StatePublished - Sep 2012

Bibliographical note

Funding Information:
This paper was supported in part by The Recanati Fund of The School of Business Administration, and by The Charles Rosen Chair of Management, The Hebrew University, Jerusalem, Israel.


  • Earlinesstardiness
  • Heuristics
  • Minmax
  • Scheduling
  • Uniform machines


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