Analysis of antithetic sequences in flowshop scheduling to minimize makespan

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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish
Pages (from-to)780-787
Number of pages8
JournalProduction Planning and Control
Issue number8
StatePublished - Jan 1 1997


  • Heuristics
  • Scheduling
  • Sequencing


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