A note on makespan minimization in proportionate flow shops

Byung Cheon Choi; Joseph Y.T. Leung; Michael L. Pinedo

doi:10.1016/j.ipl.2010.10.016

A note on makespan minimization in proportionate flow shops

Byung Cheon Choi, Joseph Y.T. Leung, Michael L. Pinedo

Computer Science

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A study was conducted to demonstrate the process of makespan minimization in proportionate flow shops. The objective was to find a sequence for the n jobs that minimized the makespan, denoted by C_max. It was assumed that job j had a processing requirement p_j that affected the time job j spends on each one of the m machines. It was assumed that machine i had a characteristic value q_i that affected the time each job spends on machine i. Models were considered where the time job j spends on machine i, p_ij was a given function of p_j and q_i. These models were regarded as proportionate flow shops with processing times that were machine dependent. It was demonstrated that the processing times of job j on all m machines were equal to p_j in the proportionate flow shop environment. The proportionate flow shop model was also generalized by describing the processing time on each machine as a function of a processing requirement and a machine-dependent parameter.

Original language	English (US)
Pages (from-to)	77-81
Number of pages	5
Journal	Information Processing Letters
Volume	111
Issue number	2
DOIs	https://doi.org/10.1016/j.ipl.2010.10.016
State	Published - Dec 31 2010

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

Keywords

Combinatorial problems

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10.1016/j.ipl.2010.10.016

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title = "A note on makespan minimization in proportionate flow shops",

abstract = "A study was conducted to demonstrate the process of makespan minimization in proportionate flow shops. The objective was to find a sequence for the n jobs that minimized the makespan, denoted by Cmax. It was assumed that job j had a processing requirement pj that affected the time job j spends on each one of the m machines. It was assumed that machine i had a characteristic value qi that affected the time each job spends on machine i. Models were considered where the time job j spends on machine i, pij was a given function of pj and qi. These models were regarded as proportionate flow shops with processing times that were machine dependent. It was demonstrated that the processing times of job j on all m machines were equal to pj in the proportionate flow shop environment. The proportionate flow shop model was also generalized by describing the processing time on each machine as a function of a processing requirement and a machine-dependent parameter.",

keywords = "Combinatorial problems",

author = "Choi, {Byung Cheon} and Leung, {Joseph Y.T.} and Pinedo, {Michael L.}",

note = "Funding Information: E-mail addresses: [email protected] (B.-C. Choi), [email protected] (J.Y.-T. Leung), [email protected] (M.L. Pinedo). 1 Work supported by the Korea Research Foundation Grant KRF-2008-357-D00289. 2 Work supported in part by the NSF Grant CMMI-0969830. 3 Work supported in part by the NSF Grant CMMI-0969755.",

year = "2010",

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doi = "10.1016/j.ipl.2010.10.016",

language = "English (US)",

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AU - Pinedo, Michael L.

N1 - Funding Information: E-mail addresses: [email protected] (B.-C. Choi), [email protected] (J.Y.-T. Leung), [email protected] (M.L. Pinedo). 1 Work supported by the Korea Research Foundation Grant KRF-2008-357-D00289. 2 Work supported in part by the NSF Grant CMMI-0969830. 3 Work supported in part by the NSF Grant CMMI-0969755.

PY - 2010/12/31

Y1 - 2010/12/31

N2 - A study was conducted to demonstrate the process of makespan minimization in proportionate flow shops. The objective was to find a sequence for the n jobs that minimized the makespan, denoted by Cmax. It was assumed that job j had a processing requirement pj that affected the time job j spends on each one of the m machines. It was assumed that machine i had a characteristic value qi that affected the time each job spends on machine i. Models were considered where the time job j spends on machine i, pij was a given function of pj and qi. These models were regarded as proportionate flow shops with processing times that were machine dependent. It was demonstrated that the processing times of job j on all m machines were equal to pj in the proportionate flow shop environment. The proportionate flow shop model was also generalized by describing the processing time on each machine as a function of a processing requirement and a machine-dependent parameter.

AB - A study was conducted to demonstrate the process of makespan minimization in proportionate flow shops. The objective was to find a sequence for the n jobs that minimized the makespan, denoted by Cmax. It was assumed that job j had a processing requirement pj that affected the time job j spends on each one of the m machines. It was assumed that machine i had a characteristic value qi that affected the time each job spends on machine i. Models were considered where the time job j spends on machine i, pij was a given function of pj and qi. These models were regarded as proportionate flow shops with processing times that were machine dependent. It was demonstrated that the processing times of job j on all m machines were equal to pj in the proportionate flow shop environment. The proportionate flow shop model was also generalized by describing the processing time on each machine as a function of a processing requirement and a machine-dependent parameter.

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A note on makespan minimization in proportionate flow shops

Abstract

All Science Journal Classification (ASJC) codes

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