Citation
Minimizing the maximal lateness on a single-machine: a new polynomially solvable case. In proceedings of the 5th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2011), 9-11 August 2011, Phoenix, Arizona, USA, pages 230-239, 2011.
Paper
Abstract
Scheduling jobs with release times and due-dates on a single machine with the objective to minimize the maximal job lateness is known to be strongly NP-hard. The problem can be naturally simplified by imposing some restrictions on job processing times. Two such versions are known to be polynomially solvable: When all jobs have equal length and when a job processing time can be either p or 2p, for some integer p. A straightforward generalization of the latter version with processing times p, 2p, 3p, 4p, etc., does not look too promising. On contrary, the version with mutually divisible processing times, e.g. p, 2p, 4p, 8p, etc., looks much more encouraging.We give a polynomial algorithm that solves the latter version. The algorithm is based on the general framework that reduces our problem to a version of the bin packing problem.
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Bibtex
@INPROCEEDINGS{2011-230-239-P, author = {N. Vakhania},
title = {Minimizing the maximal lateness on a single-machine: a new polynomially solvable case},
booktitle = {In proceedings of the 5th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2011), 9-11 August 2011, Phoenix, Arizona, USA},
year = {2011},
editor = {J. Fowler and G. Kendall and B. McCollum},
pages = {230--239},
note = {Paper},
abstract = {Scheduling jobs with release times and due-dates on a single machine with the objective to minimize the maximal job lateness is known to be strongly NP-hard. The problem can be naturally simplified by imposing some restrictions on job processing times. Two such versions are known to be polynomially solvable: When all jobs have equal length and when a job processing time can be either p or 2p, for some integer p. A straightforward generalization of the latter version with processing times p, 2p, 3p, 4p, etc., does not look too promising. On contrary, the version with mutually divisible processing times, e.g. p, 2p, 4p, 8p, etc., looks much more encouraging.We give a polynomial algorithm that solves the latter version. The algorithm is based on the general framework that reduces our problem to a version of the bin packing problem.},
owner = {gxk},
timestamp = {2011.08.15},
webpdf = {2011-230-239-P.pdf} }