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Single machine parallel batch scheduling subject to precedence constraints
Author(s) -
Cheng T.C.E.,
Ng C.T.,
Yuan J.J.,
Liu Z.H.
Publication year - 2004
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20035
Subject(s) - job shop scheduling , computer science , scheduling (production processes) , subject (documents) , mathematical optimization , open shop , operations research , parallel computing , mathematics , flow shop scheduling , schedule , operating system , library science
We consider the single machine parallel batch scheduling problems to minimize makespan and total completion time, respectively, under precedence relations. The complexities of these two problems are reported as open in the literature. In this paper, we settle these open questions by showing that both problems are strongly NP‐hard, even when the precedence relations are chains. When the processing times of jobs are directly agreeable or inversely agreeable with the precedence relations, there is an O ( n 2 ) time algorithm to minimize the makespan. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004