A note on minimising total absolute deviation of job completion times on a two-machine no-wait proportionate flowshop

Yoav Ben-Yehoshua, Eyal Hariri, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

A popular measure used in service systems is that of total absolute deviation of job completion times (TADC). It is relevant to settings where the objective is to balance the level of service provided to different customers. During the last decade, TADC has been studied in various machine settings, and under various assumptions on the job processing times. In this note, we study TADC on a two-machine no-wait proportionate flow shop, i.e. a flow shop with machine-independent processing times, and with no buffer between the machines. A very surprising and unique result is introduced: a simple index policy (the well-known largest processing time (LPT) first sequence) is shown to be optimal for instances of no more than seven jobs. This property does not hold for larger instances. We show that for instances of eight and nine jobs, there are exactly two schedules which are candidates for optimality. For the 10-job instance, the number of candidates increases. This uncommon behaviour of the optimal solution and, consequently, the complexity of the problem studied here, remain open questions, and are challenging topics for future research.

Original languageAmerican English
Pages (from-to)5717-5724
Number of pages8
JournalInternational Journal of Production Research
Volume53
Issue number19
DOIs
StatePublished - 2 Oct 2015

Bibliographical note

Publisher Copyright:
© 2014 Taylor & Francis.

Keywords

  • no-wait
  • proportionate flow shop
  • scheduling
  • total absolute deviations of job completion times

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