Scheduling three-operation jobs in a two-machine flow shop to minimize makespan: Models and algorithms for planning and scheduling problems
Gupta, Jatinder N.D., Koulamas, Christos P., Kyparisis, George J., Potts, Chris N. and Strusevich, Vitality A. (2004) Scheduling three-operation jobs in a two-machine flow shop to minimize makespan: Models and algorithms for planning and scheduling problems. Annals of Operations Research, 129, (1-4), 171-185. (doi:10.1023/B:ANOR.0000030687.72169.c7).
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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.
|Keywords:||scheduling, flow shop, makespan, approximation algorithm, polynomial time approximation scheme|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Operational Research
|Date Deposited:||12 May 2006|
|Last Modified:||06 Aug 2015 02:30|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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