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Computing

, Volume 49, Issue 2, pp 151–158 | Cite as

A heuristic for preemptive scheduling with set-up times

  • G. J. Wöginger
  • Z. Yu
Article
  • 36 Downloads

Abstract

We investigate the problem of preemptively schedulingn jobs onm parallel machines. Whenever there is a switch from processing a job to processing another job on some machine, a set-up time is necessary. The objective is to find a schedule which minimizes the maximum completion time. Form≥2 machines, this problem obviously is NP-complete.

For the case of job-dependent set-up times, Monma and Potts derived a polynomial time heuristic whose worst case ratio tends to 5/3 as the number of machines tends to infinity. In this paper, we examine the case of constant (job- and machine-independent) set-up times. We present a polynomial time approximation algorithm with worst case ratio 7/6 form=2 machines and worst case ratio at most 3/2–1/2m form≥3 machines. Moreover, for the casem=2 we construct a fully polynomial time approximation scheme.

AMS Subject Classifications

90B35 90C27 

Key words

Scheduling identical parallel machines set-up time heuristics worst-case analysis 

Preemptives Scheduling mit Set-up-Zeiten

Zusammenfassung

Wir untersuchen ein preemptives Scheduling Problem mitm Maschinen undn Prozessen. Jedesmal wenn eine Maschine mit dem Abarbeiten eines neuen Prozesses beginnt, ist eine zusätzliche Set-up Zeit notwendig. Das Ziel ist es, ein Schedul zu finden, das alle Prozesse möglichst früh vollendet. Fürm≥2 Maschinen ist dieses Problem NP-vollständig.

Für den Fall von prozeßabhängigen Set-up Zeiten haben Monma und Potts eine polynomiale Heuristik entwickelt, deren Worst Case Ratio gegen 5/3 geht, wenn die Anzahl der Maschinen gegen unendlich strebt. Wir untersuchen den Fall mit konstanten Set-up Zeiten. Wir konstruieren einen polynomialen Approximations Algorithmus mit Worst Case Ratio 7/6 fürm=2 und Worst Case Ratio 3/2–1/2m fürm≥3. Außerdem geben wir ein fully polynomial time approximation scheme für zwei Maschinen an.

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References

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • G. J. Wöginger
    • 1
  • Z. Yu
    • 2
  1. 1.Institut für Grundlagen der InformationsverarbeitungTU GrazGrazAustria
  2. 2.Institut für Mathematik BTU GrazGrazAustria

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