Gupta, Jatinder N.D., Koulamas, Christos P., Kyparisis, George J., Potts, Chris N. and Strusevich, Vitaly A. (2004) Scheduling three-operation jobs in a two-machine flow shop to minimize makespan. Annals of Operations Research, 129 (1-4). pp. 171-185. ISSN 0254-5330 (Print), 1572-9338 (Online) (doi:https://doi.org/10.1023/B:ANOR.0000030687.72169.c7)

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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.

Item Type:	Article
Additional Information:	[1] In: Annals of Operations Research, Volume 129, Issue 1-4, July 2004. Models and Algorithms for Planning and Scheduling Problems.
Uncontrolled Keywords:	scheduling, flow shop, makespan, approximation algorithm, polynomial time approximation scheme
Subjects:	Q Science > QA Mathematics
Pre-2014 Departments:	School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Mathematical Sciences School of Computing & Mathematical Sciences > Statistics & Operational Research Group
Related URLs:	Publisher
Last Modified:	14 Oct 2016 09:01
URI:	http://gala.gre.ac.uk/id/eprint/723

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