Semi-V-shape property for two-machine no-wait proportionate flow shop problem with TADC criterion

Sergey Kovalev*, Mikhail Y. Kovalyov, Gur Mosheiov, Enrique Gerstl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

The problem of minimising total absolute deviation of job completion times in a two-machine no-wait proportionate flow shop has been recently studied. It was shown that the LPT (largest processing time first) job sequence is optimal if the number of jobs n does not exceed 7, and that the LPT sequence is not optimal for instances with n ≥ 8. We prove that there exists an optimal semi-V-shaped job sequence, in which the first job has the largest processing time, a certain number, greater than n / 2, of the following jobs appear in the LPT order, and jobs following job with the minimum processing time are sequenced in the SPT (shortest processing time first) order. We also present an O(n3) time dynamic programming algorithm to find the best V-shaped job sequence, in which the jobs on the left of the job with the minimum processing time are sequenced in the LPT order and those on the right of this job are sequenced in the SPT order.

Original languageAmerican English
Pages (from-to)560-566
Number of pages7
JournalInternational Journal of Production Research
Volume57
Issue number2
DOIs
StatePublished - 17 Jan 2019

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • dynamic programming
  • scheduling
  • two-machine no-wait flow shop
  • v-shape property

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