Integer Programming and Combinatorial Optimization

Volume 1412 of the series Lecture Notes in Computer Science pp 367-382


Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems

  • Alix MunierAffiliated withLaboratoire LIP6, Université Pierre et Marie Curie
  • , Maurice QueyranneAffiliated withFaculty of Commerce and Business Administration, University of British ColumbiaUniversità di Bologna — Sede di Rimini
  • , Andreas S. SchulzAffiliated withFachbereich Mathematik, MA 6-1, Technische Universität Berlin

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A well studied and difficult class of scheduling problems con- cerns parallel machines and precedence constraints. In order to model more realistic situations, we consider precedence delays, associating with each precedence constraint a certain amount of time which must elapse between the completion and start times of the corresponding jobs. Re- lease dates, among others, may be modeled in this fashion. We provide the first constant-factor approximation algorithms for the makespan and the total weighted completion time objectives in this general class of problems. These algorithms are rather simple and practical forms of list scheduling. Our analysis also unifies and simplifies that of a number of special cases heretofore separately studied, while actually improving some of the former approximation results.