Integer Programming and Combinatorial Optimization
Volume 920 of the series Lecture Notes in Computer Science pp 307320
Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds
 Maurice QueyranneAffiliated withFaculty of Commerce, University of British Columbia
 , Andreas S. SchulzAffiliated withTechnische Universität Berlin, Fachbereich Mathematik (MA 61)
Abstract
We consider the problem of nonpreemptively scheduling a set of jobs with identical processing requirements (unit jobs) on parallel machines with nonstationary speeds. In addition to the case of uniform machines, this allows for such predictable effects as operator learning and tool wear and tear, as well as such planned activities as machine upgrades, maintenance and the preassignment of other operations, all of which may affect the available processing speed of the machine at different points in time. We also allow release dates that satisfy a certain compatibility property. We show that the convex hull of feasible completion time vectors is a supermodular polyhedron. For nonidentical but compatible release dates, the supermodular function defining this polyhedron is the Dilworth truncation of a (non supermodular) function defined in a natural way from the release dates. This supermodularity result implies that the total weighted flow time can be minimized by a greedy algorithm. Supermodular polyhedra thus provide a general framework for several unit job, parallel machine scheduling problems and for their solution methods.
 Title
 Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds
 Book Title
 Integer Programming and Combinatorial Optimization
 Book Subtitle
 4th International IPCO Conference Copenhagen, Denmark, May 29–31, 1995 Proceedings
 Pages
 pp 307320
 Copyright
 1995
 DOI
 10.1007/3540594086_60
 Print ISBN
 9783540594086
 Online ISBN
 9783540492450
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 920
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Maurice Queyranne ^{(1)}
 Andreas S. Schulz ^{(2)}
 Author Affiliations

 1. Faculty of Commerce, University of British Columbia, Main Mall, 2053, Vancouver, B. C., Canada
 2. Technische Universität Berlin, Fachbereich Mathematik (MA 61), Straße des 17. Juni 136, D10623, Berlin, Germany
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