A polynomial-time approximation scheme for parallel two-stage flowshops under makespan constraint

As a hybrid of the Parallel Two-stage Flowshop problem and the Multiple Knapsack problem, we investigate the scheduling of parallel two-stage flowshops under makespan constraint, which was motivated by applications in cloud computing and introduced by Chen et al. [3] recently. A set of two-stage job...

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Veröffentlicht in:Theoretical computer science Jg. 922; S. 438 - 446
Hauptverfasser: Tong, Weitian, Xu, Yao, Zhang, Huili
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 24.06.2022
Schlagworte:
Makespan constraint
Multiple knapsacks
Parallel two-stage flowshops
Polynomial-time approximation scheme
Rounding
Multiple knapsacks
Rounding
Polynomial-time approximation scheme
Makespan constraint
Parallel two-stage flowshops
ISSN:0304-3975, 1879-2294
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Zusammenfassung:As a hybrid of the Parallel Two-stage Flowshop problem and the Multiple Knapsack problem, we investigate the scheduling of parallel two-stage flowshops under makespan constraint, which was motivated by applications in cloud computing and introduced by Chen et al. [3] recently. A set of two-stage jobs are selected and scheduled on parallel two-stage flowshops to achieve the maximum total profit while maintaining the given makespan constraint. We give a positive answer to an open question about its approximability proposed by Chen et al. [3]. More specifically, based on guessing strategies and rounding techniques for linear programs, we present a polynomial time approximation scheme (PTAS) for the case when the number of flowshops is a fixed constant. As the case with two flowshops is already strongly NP-hard, our PTAS achieves the best possible approximation ratio.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2022.04.044