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.
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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Wöginger, G.J., Yu, Z. A heuristic for preemptive scheduling with set-up times. Computing 49, 151–158 (1992). https://doi.org/10.1007/BF02238747
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DOI: https://doi.org/10.1007/BF02238747