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Title: Johnson's rule, composite jobs and the relocation problem
Authors: Cheng, T. C. Edwin
Lin, B. M. T.
Subjects: Flowshop
Johnson's rule
Composite job
Relocation problem
Issue Date: 1-Feb-2009
Publisher: Elsevier B.V.
Source: European journal of operational research, 1 Feb. 2009, v. 192, no. 3, p. 1008-1013.
Abstract: Two-machine flowshop scheduling to minimize makespan is one of the most well-known classical scheduling problems. Johnson's rule for solving this problem has been widely cited in the literature. We introduce in this paper the concept of composite job, which is an artificially constructed job with processing times such that it will incur the same amount of idle time on the second machine as that incurred by a chain of jobs in a given processing sequence. This concept due to Kurisu first appeared in 1976 to deal with the two-machine flowshop scheduling problem involving precedence constraints among the jobs. We show that this concept can be applied to reduce the computational time to solve some related scheduling problems. We also establish a link between solving the two-machine flowshop makespan minimization problem using Johnson's rule and the relocation problem introduced by Kaplan. We present an intuitive interpretation of Johnson's rule in the context of the relocation problem.
Rights: European Journal of Operational Research © 2007 Elsevier B.V. The journal web site is located at
Type: Journal/Magazine Article
DOI: 10.1016/j.ejor.2007.11.035
ISSN: 0377-2217
Appears in Collections:LMS Journal/Magazine Articles

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