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arXiv · 2201.04196

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

Weitian Tong·Yao Xu·Huili Zhang
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Abstract

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.

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Weitian Tong, Yao Xu, Huili Zhang. 2022-01-11. A polynomial-time approximation scheme for parallel two-stage flowshops under makespan constraint. https://doi.org/10.1016/j.tcs.2022.04.044

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