Abstract
The shop-scheduling problem with two jobs andm machines is considered under the condition that the machine order is fixed in advance for the first job and nonfixed for the second job. The problems of makespan and mean flow time minimization are proved to be NP-hard if operation preemption is forbidden. In the case of preemption allowance for any given regular criterion theO(n *) algorithm is proposed. Here,n * is the maximum number of operations per job.
Zusammenfassung
Es werden Reihenfolge-probleme mit zwei Aufträgen undm Maschinen untersucht, wobei die technologische Reihenfolge der Maschinen für den ersten Auftrag gegeben und für den zweiten Auftrag variabel ist. Es wird bewiesen, daß die Probleme “Minimierung der Gesamtbearbeitungszeit” und “Minimierung der mittleren Durchlaufzeit” NP-hard sind, wenn eine Unterbrechung der Operationen verboten ist. Für ein beliebiges reguläres Kriterium wird bei Zulassung von Unterbrechungen einO(n *) Algorithmus entwickelt, wobei mitn * die maximale Anzahl der Operationen für den ersten Auftrag bezeichnet wird.
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Shakhlevich, N.V., Sotskov, Y.N. Scheduling two jobs with fixed and nonfixed routes. Computing 52, 17–30 (1994). https://doi.org/10.1007/BF02243393
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DOI: https://doi.org/10.1007/BF02243393