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

• Published in: Theoretical computer science Vol. 922; pp. 438 - 446
• Main Authors: Tong, Weitian, Xu, Yao, Zhang, Huili
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 24.06.2022
• Subjects: 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
• DOI: 10.1016/j.tcs.2022.04.044

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.