Annals of Operations Research

, Volume 129, Issue 1–4, pp 171–185 | Cite as

Scheduling Three-Operation Jobs in a Two-Machine Flow Shop to Minimize Makespan

  • Jatinder N.D. Gupta
  • Christos P. Koulamas
  • George J. Kyparisis
  • Chris N. Potts
  • Vitaly A. Strusevich

Abstract

This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented.

scheduling flow shop makespan approximation algorithm polynomial time approximation scheme 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Jatinder N.D. Gupta
    • 1
  • Christos P. Koulamas
    • 2
  • George J. Kyparisis
    • 2
  • Chris N. Potts
    • 3
  • Vitaly A. Strusevich
    • 4
  1. 1.Department of Accounting and Information Systems, College of Administrative ScienceUniversity of Alabama in HuntsvilleHuntsvilleUSA
  2. 2.Department of Decision Sciences and Information SystemsFlorida International UniversityMiamiUSA
  3. 3.Faculty of Mathematical StudiesUniversity of SouthamptonSouthamptonUK
  4. 4.School of Computing and Mathematical SciencesUniversity of GreenwichLondonUK

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