Analysis of Antithetic Sequences in Flowshop Scheduling to Minimize Makespan

Milton Smith; R. Moras; K. S. Kumar; M. A. Azim

doi:10.1080/095372897234678

Analysis of Antithetic Sequences in Flowshop Scheduling to Minimize Makespan

Milton Smith, R. Moras, K. S. Kumar, M. A. Azim

Industrial Engineering

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3 Scopus citations

Abstract

The antithetic properties of flow shop sequences are investigated to improve the classical Monte Carlo method for solving the n-job, m-machine problem with minimization of make span. The major issues considered are (1) establishing a negative correlation of the make span values of forward and reverse sequences; (2) developing the Antithetical Monte Carlo (AM C) method, which can be used to quickly estimate the mean of the make span distribution by exploiting the antithetic property of sequences; (3) using AMC to find low make-span values; (4) determining a threshold value of make span beyond which it would be likely to find an optimal or near optimal make span when reversing a sequence. Statistical tests indicate that the performance of AM C is superior to that of the classical Monte Carlo method. Possible applications of this concept are discussed including extensions to other mathematical problems with antithetic properties.

Original language	English
Pages (from-to)	780-787
Number of pages	8
Journal	Production Planning and Control
Volume	8
Issue number	8
DOIs	https://doi.org/10.1080/095372897234678
State	Published - Jan 1 1997

Keywords

Heuristics
Scheduling
Sequencing

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10.1080/095372897234678

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abstract = "The antithetic properties of flow shop sequences are investigated to improve the classical Monte Carlo method for solving the n-job, m-machine problem with minimization of make span. The major issues considered are (1) establishing a negative correlation of the make span values of forward and reverse sequences; (2) developing the Antithetical Monte Carlo (AM C) method, which can be used to quickly estimate the mean of the make span distribution by exploiting the antithetic property of sequences; (3) using AMC to find low make-span values; (4) determining a threshold value of make span beyond which it would be likely to find an optimal or near optimal make span when reversing a sequence. Statistical tests indicate that the performance of AM C is superior to that of the classical Monte Carlo method. Possible applications of this concept are discussed including extensions to other mathematical problems with antithetic properties.",

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Analysis of Antithetic Sequences in Flowshop Scheduling to Minimize Makespan

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Keywords

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