A polynomial-time algorithm for a special case of minimizing the lateness on a single machine

Authors:
Nodari Vakhania
Affiliations:
State University Morelos, Science Faculty, Cuernavaca, Morelos, Mexico and Institute of Computational Mathematics, Georgian Academy of Sciences, Tbilisi, Georgia
Venue:
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
Year:
2010

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Abstract

We study the problem of scheduling jobs with release times and due-dates on a single machine with the objective to minimize the maximal job lateness. This problem is strongly NP-hard, however it is known to be polynomially solvable for the case when the processing times of some jobs are restricted to either p or 2p, for some integer p. We present a polynomial-time algorithm when job processing times are less restricted; in particular, when they are mutually divisible. Our algorithm works for the case when for any pair of jobs, if one is longer than another then the due-date of the former job is no larger than that of the latter one.