Minmax earliness-tardiness costs with unit processing time jobs

Gur Mosheiov, Michal Shadmon

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


The problem addressed in this paper is defined by M parallel identical machines, N jobs with identical (unit) processing time, job-dependent weights, and a common due-date for all jobs. The objective is of a minmax type, i.e. we are interested in minimizing the cost of the worst scheduled job. In the case of a non-restrictive (i.e., sufficiently large) common due-date, the problem is shown to have a solution that is polynomial in the number of jobs. The solution in the case of a restrictive due-date remains polynomial in the number of jobs, but is exponential in the number of machines. We introduce a lower bound on the optimal cost and an efficient heuristic. We show that the worst case relative error of the heuristic is bounded by 2 and that this bound is tight. We also prove that the heuristic is asymptotically optimal under very general assumptions. Finally, we provide an extensive numerical study demonstrating that in most cases the heuristic performs extremely well.

Original languageAmerican English
Pages (from-to)638-652
Number of pages15
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - 1 May 2001


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