Scheduling with processing set restrictions: PTAS results for several variants

Leah Epstein, Asaf Levin

Research output: Contribution to journalArticlepeer-review


We consider multiprocessor scheduling to minimize makespan. Each job has a given processing time and in addition, a subset of machines associated with it, also called its processing set. Each job has to be assigned to one machine in its set, thus contributing to the load of this machine. We study two variants of this problem on identical machines, the case of nested processing sets, and the case of tree-hierarchical processing sets. In addition, we consider uniformly related machines with a special case of inclusive processing sets, which has a clear motivation. We design polynomial time approximation schemes for these three variants. The first case resolves one of the open problems stated in the survey by Leung and Li (2008).

Original languageEnglish
Pages (from-to)586-595
Number of pages10
JournalInternational Journal of Production Economics
Issue number2
StatePublished - 10 Oct 2011


  • Approximation scheme
  • Scheduling

ASJC Scopus subject areas

  • General Business, Management and Accounting
  • Economics and Econometrics
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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