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- W1500197053 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.KeywordsCompletion TimeConvex HullGreedy AlgorithmRelease DateParallel MachineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W1500197053 date "1995-01-01" @default.
- W1500197053 modified "2023-10-01" @default.
- W1500197053 title "Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds" @default.
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- W1500197053 doi "https://doi.org/10.1007/3-540-59408-6_60" @default.
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