Fachbereich 3 Mathematik Scheduling Unit Jobs with Compatible Release Dates on Parallel Machines with Nonstationary Speeds Scheduling Unit Jobs with Compatible Release Dates on Parallel Machines with Nonstationary Speeds *

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 eeects 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 aaect the available processing speed of the machine at diierent 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 deening this polyhedron is the Dilworth truncation of a (non supermodular) function deened in a natural way from the release dates. This supermodularity result implies that the total weighted ow time can be minimized by a greedy algorithm. Supermodular polyhe-dra thus provide a general framework for several unit job, parallel machine scheduling problems and for their solution methods.