Abstract
For the nonpreemptive two machine job-shop scheduling problem with a fixed number of jobs and objective functions Σf i and maxf i , wheref i are nondecreasing functions of the finish times of jobsi, polynomial algorithms are presented. This answers previous open questions about the complexity status of the corresponding problems with objective functionsL max, Σw i U i , and Σw i U. We generalize these results by showing that the problem with any regular criterion can be solved in polynomial time.
Zusammenfassung
Für das Zweimaschinen-Job-Shop-Problem ohne Arbeitsunterbrechnungen und den Zielfunktionen Σf i bzw. maxf i , wobei dief i monotone Funktionen der Fertigstellungszeiten der Jobsi sind, werden für den Fall fester Jobanzahlen polynomiale Algorithmen angegeben. Dies beantwortet insbesondere die bislang offene Frage nach dem Komplexitätsstatus des obigen Problems für die ZielfunktionenL max, Σw i U i , und Σw i U. Schließlich zeigen wir, daß das Problem mit beliebiger regulärer Zielfunktion ebenfalls polynomial lösbar ist.
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Supported by the International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union, Project INTAS-93-257.
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Brucker, P., Kravchenko, S.A. & Sotskov, Y.N. On the complexity of two machine job-shop scheduling with regular objective functions. OR Spektrum 19, 5–10 (1997). https://doi.org/10.1007/BF01539799
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DOI: https://doi.org/10.1007/BF01539799