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Improved approximation schemes for scheduling unrelated parallel machines

Jansen, Klaus and Porkolab, Lorant

November 1998, 14 pages.

Status: available - back from printing

We consider the problem of scheduling $n$ independent jobs on $m$ unrelated parallel machines. Each job has to be processed by exactly one machine, processing job $j$ on machine $i$ requires $p_{ij}$ time units, and the objective is to minimize the makespan, i.e. the maximum job completion time. We focus on the case when $m$ is fixed and develop a fully polynomial approximation scheme whose running time depends only linearly on $n$. In the second half of the paper we extend this result to a variant of the problem, where processing job $j$ on machine $i$ also incurs a cost of $c_{ij}$, and thus there are two optimization criteria: makespan and cost. We show that for any fixed $m$, there is a fully polynomial approximation scheme that, given values $T$ and $C$, computes for any fixed $\epsilon > 0$ a schedule in $O(n)$ time with makespan at most $(1+\epsilon)T$ and cost at most $(1 + \epsilon)C$, if there exists a schedule of makespan $T$ and cost $C$.

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  AUTHOR = {Jansen, Klaus and Porkolab, Lorant},
  TITLE = {Improved approximation schemes for scheduling unrelated parallel machines},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-98-1-026},
  MONTH = {November},
  YEAR = {1998},
  ISSN = {0946-011X},